| 1 | """Finite-volume computations of the shallow water wave equation. |
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| 2 | |
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| 3 | Title: ANGUA shallow_water_domain - 2D triangular domains for finite-volume |
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| 4 | computations of the shallow water wave equation. |
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| 5 | |
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| 6 | |
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| 7 | Author: Ole Nielsen (Ole.Nielsen@ga.gov.au), |
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| 8 | Stephen Roberts (Stephen.Roberts@anu.edu.au), |
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| 9 | Duncan Gray (Duncan.Gray@ga.gov.au), etc |
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| 10 | |
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| 11 | CreationDate: 2004 |
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| 12 | |
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| 13 | Description: |
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| 14 | This module contains a specialisation of class Domain from |
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| 15 | module domain.py consisting of methods specific to the |
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| 16 | Shallow Water Wave Equation |
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| 17 | |
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| 18 | U_t + E_x + G_y = S |
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| 19 | |
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| 20 | where |
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| 21 | |
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| 22 | U = [w, uh, vh] |
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| 23 | E = [uh, u^2h + gh^2/2, uvh] |
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| 24 | G = [vh, uvh, v^2h + gh^2/2] |
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| 25 | S represents source terms forcing the system |
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| 26 | (e.g. gravity, friction, wind stress, ...) |
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| 27 | |
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| 28 | and _t, _x, _y denote the derivative with respect to t, x and y |
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| 29 | respectively. |
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| 30 | |
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| 31 | |
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| 32 | The quantities are |
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| 33 | |
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| 34 | symbol variable name explanation |
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| 35 | x x horizontal distance from origin [m] |
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| 36 | y y vertical distance from origin [m] |
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| 37 | z elevation elevation of bed on which flow is modelled [m] |
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| 38 | h height water height above z [m] |
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| 39 | w stage absolute water level, w = z+h [m] |
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| 40 | u speed in the x direction [m/s] |
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| 41 | v speed in the y direction [m/s] |
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| 42 | uh xmomentum momentum in the x direction [m^2/s] |
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| 43 | vh ymomentum momentum in the y direction [m^2/s] |
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| 44 | |
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| 45 | eta mannings friction coefficient [to appear] |
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| 46 | nu wind stress coefficient [to appear] |
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| 47 | |
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| 48 | The conserved quantities are w, uh, vh |
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| 49 | |
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| 50 | Reference: |
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| 51 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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| 52 | Christopher Zoppou and Stephen Roberts, |
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| 53 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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| 54 | |
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| 55 | Hydrodynamic modelling of coastal inundation. |
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| 56 | Nielsen, O., S. Roberts, D. Gray, A. McPherson and A. Hitchman |
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| 57 | In Zerger, A. and Argent, R.M. (eds) MODSIM 2005 International Congress on |
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| 58 | Modelling and Simulation. Modelling and Simulation Society of Australia and |
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| 59 | New Zealand, December 2005, pp. 518-523. ISBN: 0-9758400-2-9. |
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| 60 | http://www.mssanz.org.au/modsim05/papers/nielsen.pdf |
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| 61 | |
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| 62 | |
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| 63 | SeeAlso: |
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| 64 | TRAC administration of ANUGA (User Manuals etc) at |
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| 65 | https://datamining.anu.edu.au/anuga and Subversion repository at |
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| 66 | $HeadURL: anuga_core/source/anuga/shallow_water/shallow_water_domain.py $ |
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| 67 | |
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| 68 | Constraints: See GPL license in the user guide |
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| 69 | Version: 1.0 ($Revision: 4254 $) |
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| 70 | ModifiedBy: |
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| 71 | $Author: duncan $ |
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| 72 | $Date: 2007-02-12 06:18:20 +0000 (Mon, 12 Feb 2007) $ |
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| 73 | |
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| 74 | """ |
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| 75 | |
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| 76 | #Subversion keywords: |
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| 77 | # |
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| 78 | #$LastChangedDate: 2007-02-12 06:18:20 +0000 (Mon, 12 Feb 2007) $ |
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| 79 | #$LastChangedRevision: 4254 $ |
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| 80 | #$LastChangedBy: duncan $ |
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| 81 | |
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| 82 | from Numeric import zeros, ones, Float, array, sum, size |
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| 83 | from Numeric import compress, arange |
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| 84 | |
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| 85 | |
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| 86 | from anuga.abstract_2d_finite_volumes.domain import Domain as Generic_Domain |
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| 87 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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| 88 | import Boundary |
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| 89 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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| 90 | import File_boundary |
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| 91 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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| 92 | import Dirichlet_boundary |
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| 93 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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| 94 | import Time_boundary |
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| 95 | from anuga.abstract_2d_finite_volumes.generic_boundary_conditions\ |
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| 96 | import Transmissive_boundary |
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| 97 | |
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| 98 | from anuga.utilities.numerical_tools import gradient, mean |
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| 99 | from anuga.config import minimum_storable_height |
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| 100 | from anuga.config import minimum_allowed_height, maximum_allowed_speed |
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| 101 | from anuga.config import g, beta_h, beta_w, beta_w_dry,\ |
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| 102 | beta_uh, beta_uh_dry, beta_vh, beta_vh_dry, limit2007 |
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| 103 | from anuga.config import alpha_balance |
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| 104 | |
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| 105 | |
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| 106 | #Shallow water domain |
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| 107 | class Domain(Generic_Domain): |
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| 108 | |
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| 109 | def __init__(self, |
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| 110 | coordinates=None, |
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| 111 | vertices=None, |
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| 112 | boundary=None, |
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| 113 | tagged_elements=None, |
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| 114 | geo_reference=None, |
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| 115 | use_inscribed_circle=False, |
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| 116 | mesh_filename=None, |
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| 117 | use_cache=False, |
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| 118 | verbose=False, |
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| 119 | full_send_dict=None, |
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| 120 | ghost_recv_dict=None, |
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| 121 | processor=0, |
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| 122 | numproc=1, |
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| 123 | number_of_full_nodes=None, |
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| 124 | number_of_full_triangles=None): |
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| 125 | |
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| 126 | |
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| 127 | conserved_quantities = ['stage', 'xmomentum', 'ymomentum'] |
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| 128 | other_quantities = ['elevation', 'friction'] |
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| 129 | Generic_Domain.__init__(self, |
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| 130 | coordinates, |
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| 131 | vertices, |
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| 132 | boundary, |
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| 133 | conserved_quantities, |
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| 134 | other_quantities, |
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| 135 | tagged_elements, |
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| 136 | geo_reference, |
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| 137 | use_inscribed_circle, |
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| 138 | mesh_filename, |
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| 139 | use_cache, |
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| 140 | verbose, |
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| 141 | full_send_dict, |
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| 142 | ghost_recv_dict, |
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| 143 | processor, |
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| 144 | numproc, |
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| 145 | number_of_full_nodes=number_of_full_nodes, |
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| 146 | number_of_full_triangles=number_of_full_triangles) |
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| 147 | |
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| 148 | self.minimum_allowed_height = minimum_allowed_height |
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| 149 | self.H0 = minimum_allowed_height # Minimal height for flux computation |
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| 150 | self.maximum_allowed_speed = maximum_allowed_speed |
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| 151 | self.g = g |
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| 152 | self.beta_w = beta_w |
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| 153 | self.beta_w_dry = beta_w_dry |
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| 154 | self.beta_uh = beta_uh |
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| 155 | self.beta_uh_dry = beta_uh_dry |
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| 156 | self.beta_vh = beta_vh |
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| 157 | self.beta_vh_dry = beta_vh_dry |
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| 158 | self.beta_h = beta_h |
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| 159 | self.alpha_balance = alpha_balance |
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| 160 | |
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| 161 | self.limit2007 = limit2007 |
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| 162 | |
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| 163 | self.flux_function = flux_function_central |
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| 164 | #self.flux_function = flux_function_kinetic |
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| 165 | |
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| 166 | self.forcing_terms.append(manning_friction) |
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| 167 | self.forcing_terms.append(gravity) |
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| 168 | |
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| 169 | #Stored output |
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| 170 | self.store = True |
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| 171 | self.format = 'sww' |
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| 172 | self.set_store_vertices_uniquely(False) |
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| 173 | self.minimum_storable_height = minimum_storable_height |
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| 174 | self.quantities_to_be_stored = ['stage','xmomentum','ymomentum'] |
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| 175 | |
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| 176 | |
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| 177 | def set_all_limiters(self, beta): |
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| 178 | """Shorthand to assign one constant value [0,1[ to all limiters. |
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| 179 | 0 Corresponds to first order, where as larger values make use of |
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| 180 | the second order scheme. |
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| 181 | """ |
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| 182 | |
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| 183 | self.beta_w = beta |
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| 184 | self.beta_w_dry = beta |
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| 185 | self.beta_uh = beta |
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| 186 | self.beta_uh_dry = beta |
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| 187 | self.beta_vh = beta |
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| 188 | self.beta_vh_dry = beta |
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| 189 | self.beta_h = beta |
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| 190 | |
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| 191 | |
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| 192 | def set_store_vertices_uniquely(self, flag, reduction=None): |
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| 193 | """Decide whether vertex values should be stored uniquely as |
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| 194 | computed in the model or whether they should be reduced to one |
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| 195 | value per vertex using self.reduction. |
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| 196 | """ |
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| 197 | |
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| 198 | # FIXME (Ole): how about using the word continuous vertex values? |
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| 199 | self.smooth = not flag |
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| 200 | |
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| 201 | #Reduction operation for get_vertex_values |
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| 202 | if reduction is None: |
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| 203 | self.reduction = mean |
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| 204 | #self.reduction = min #Looks better near steep slopes |
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| 205 | |
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| 206 | |
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| 207 | def set_minimum_storable_height(self, minimum_storable_height): |
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| 208 | """ |
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| 209 | Set the minimum depth that will be recognised when writing |
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| 210 | to an sww file. This is useful for removing thin water layers |
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| 211 | that seems to be caused by friction creep. |
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| 212 | |
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| 213 | The minimum allowed sww depth is in meters. |
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| 214 | """ |
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| 215 | self.minimum_storable_height = minimum_storable_height |
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| 216 | |
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| 217 | |
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| 218 | def set_maximum_allowed_speed(self, maximum_allowed_speed): |
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| 219 | """ |
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| 220 | Set the maximum particle speed that is allowed in water |
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| 221 | shallower than minimum_allowed_height. This is useful for |
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| 222 | controlling speeds in very thin layers of water and at the same time |
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| 223 | allow some movement avoiding pooling of water. |
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| 224 | |
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| 225 | """ |
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| 226 | self.maximum_allowed_speed = maximum_allowed_speed |
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| 227 | |
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| 228 | |
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| 229 | def set_points_file_block_line_size(self,points_file_block_line_size): |
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| 230 | """ |
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| 231 | Set the minimum depth that will be recognised when writing |
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| 232 | to an sww file. This is useful for removing thin water layers |
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| 233 | that seems to be caused by friction creep. |
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| 234 | |
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| 235 | The minimum allowed sww depth is in meters. |
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| 236 | """ |
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| 237 | self.points_file_block_line_size = points_file_block_line_size |
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| 238 | |
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| 239 | def set_quantities_to_be_stored(self, q): |
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| 240 | """Specify which quantities will be stored in the sww file. |
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| 241 | |
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| 242 | q must be either: |
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| 243 | - the name of a quantity |
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| 244 | - a list of quantity names |
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| 245 | - None |
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| 246 | |
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| 247 | In the two first cases, the named quantities will be stored at |
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| 248 | each yieldstep (This is in addition to the quantities elevation |
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| 249 | and friction) |
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| 250 | |
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| 251 | If q is None, storage will be switched off altogether. |
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| 252 | """ |
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| 253 | |
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| 254 | |
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| 255 | if q is None: |
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| 256 | self.quantities_to_be_stored = [] |
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| 257 | self.store = False |
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| 258 | return |
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| 259 | |
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| 260 | if isinstance(q, basestring): |
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| 261 | q = [q] # Turn argument into a list |
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| 262 | |
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| 263 | #Check correcness |
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| 264 | for quantity_name in q: |
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| 265 | msg = 'Quantity %s is not a valid conserved quantity'\ |
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| 266 | %quantity_name |
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| 267 | |
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| 268 | assert quantity_name in self.conserved_quantities, msg |
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| 269 | |
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| 270 | self.quantities_to_be_stored = q |
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| 271 | |
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| 272 | |
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| 273 | |
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| 274 | def get_wet_elements(self, indices=None): |
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| 275 | """Return indices for elements where h > minimum_allowed_height |
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| 276 | |
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| 277 | Optional argument: |
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| 278 | indices is the set of element ids that the operation applies to. |
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| 279 | |
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| 280 | Usage: |
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| 281 | indices = get_wet_elements() |
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| 282 | |
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| 283 | Note, centroid values are used for this operation |
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| 284 | """ |
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| 285 | |
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| 286 | # Water depth below which it is considered to be 0 in the model |
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| 287 | # FIXME (Ole): Allow this to be specified as a keyword argument as well |
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| 288 | from anuga.config import minimum_allowed_height |
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| 289 | |
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| 290 | |
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| 291 | elevation = self.get_quantity('elevation').\ |
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| 292 | get_values(location='centroids', indices=indices) |
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| 293 | stage = self.get_quantity('stage').\ |
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| 294 | get_values(location='centroids', indices=indices) |
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| 295 | depth = stage - elevation |
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| 296 | |
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| 297 | # Select indices for which depth > 0 |
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| 298 | wet_indices = compress(depth > minimum_allowed_height, |
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| 299 | arange(len(depth))) |
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| 300 | return wet_indices |
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| 301 | |
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| 302 | |
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| 303 | def get_maximum_inundation_elevation(self, indices=None): |
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| 304 | """Return highest elevation where h > 0 |
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| 305 | |
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| 306 | Optional argument: |
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| 307 | indices is the set of element ids that the operation applies to. |
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| 308 | |
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| 309 | Usage: |
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| 310 | q = get_maximum_inundation_elevation() |
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| 311 | |
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| 312 | Note, centroid values are used for this operation |
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| 313 | """ |
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| 314 | |
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| 315 | wet_elements = self.get_wet_elements(indices) |
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| 316 | return self.get_quantity('elevation').\ |
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| 317 | get_maximum_value(indices=wet_elements) |
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| 318 | |
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| 319 | |
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| 320 | def get_maximum_inundation_location(self, indices=None): |
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| 321 | """Return highest elevation where h > 0 |
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| 322 | |
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| 323 | Optional argument: |
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| 324 | indices is the set of element ids that the operation applies to. |
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| 325 | |
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| 326 | Usage: |
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| 327 | q = get_maximum_inundation_elevation() |
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| 328 | |
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| 329 | Note, centroid values are used for this operation |
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| 330 | """ |
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| 331 | |
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| 332 | wet_elements = self.get_wet_elements(indices) |
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| 333 | return self.get_quantity('elevation').\ |
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| 334 | get_maximum_location(indices=wet_elements) |
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| 335 | |
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| 336 | def check_integrity(self): |
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| 337 | Generic_Domain.check_integrity(self) |
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| 338 | |
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| 339 | #Check that we are solving the shallow water wave equation |
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| 340 | |
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| 341 | msg = 'First conserved quantity must be "stage"' |
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| 342 | assert self.conserved_quantities[0] == 'stage', msg |
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| 343 | msg = 'Second conserved quantity must be "xmomentum"' |
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| 344 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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| 345 | msg = 'Third conserved quantity must be "ymomentum"' |
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| 346 | assert self.conserved_quantities[2] == 'ymomentum', msg |
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| 347 | |
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| 348 | def extrapolate_second_order_sw(self): |
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| 349 | #Call correct module function |
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| 350 | #(either from this module or C-extension) |
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| 351 | extrapolate_second_order_sw(self) |
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| 352 | |
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| 353 | def compute_fluxes(self): |
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| 354 | #Call correct module function |
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| 355 | #(either from this module or C-extension) |
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| 356 | compute_fluxes(self) |
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| 357 | |
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| 358 | def distribute_to_vertices_and_edges(self): |
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| 359 | #Call correct module function |
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| 360 | #(either from this module or C-extension) |
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| 361 | distribute_to_vertices_and_edges(self) |
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| 362 | |
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| 363 | |
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| 364 | #FIXME: Under construction |
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| 365 | # def set_defaults(self): |
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| 366 | # """Set default values for uninitialised quantities. |
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| 367 | # This is specific to the shallow water wave equation |
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| 368 | # Defaults for 'elevation', 'friction', 'xmomentum' and 'ymomentum' |
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| 369 | # are 0.0. Default for 'stage' is whatever the value of 'elevation'. |
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| 370 | # """ |
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| 371 | |
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| 372 | # for name in self.other_quantities + self.conserved_quantities: |
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| 373 | # print name |
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| 374 | # print self.quantities.keys() |
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| 375 | # if not self.quantities.has_key(name): |
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| 376 | # if name == 'stage': |
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| 377 | |
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| 378 | # if self.quantities.has_key('elevation'): |
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| 379 | # z = self.quantities['elevation'].vertex_values |
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| 380 | # self.set_quantity(name, z) |
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| 381 | # else: |
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| 382 | # self.set_quantity(name, 0.0) |
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| 383 | # else: |
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| 384 | # self.set_quantity(name, 0.0) |
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| 385 | |
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| 386 | |
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| 387 | |
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| 388 | # #Lift negative heights up |
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| 389 | # #z = self.quantities['elevation'].vertex_values |
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| 390 | # #w = self.quantities['stage'].vertex_values |
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| 391 | |
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| 392 | # #h = w-z |
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| 393 | |
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| 394 | # #for k in range(h.shape[0]): |
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| 395 | # # for i in range(3): |
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| 396 | # # if h[k, i] < 0.0: |
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| 397 | # # w[k, i] = z[k, i] |
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| 398 | |
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| 399 | |
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| 400 | # #self.quantities['stage'].interpolate() |
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| 401 | |
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| 402 | |
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| 403 | def evolve(self, |
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| 404 | yieldstep = None, |
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| 405 | finaltime = None, |
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| 406 | duration = None, |
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| 407 | skip_initial_step = False): |
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| 408 | """Specialisation of basic evolve method from parent class |
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| 409 | """ |
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| 410 | |
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| 411 | #Call check integrity here rather than from user scripts |
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| 412 | #self.check_integrity() |
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| 413 | |
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| 414 | msg = 'Parameter beta_h must be in the interval [0, 1[' |
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| 415 | assert 0 <= self.beta_h <= 1.0, msg |
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| 416 | msg = 'Parameter beta_w must be in the interval [0, 1[' |
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| 417 | assert 0 <= self.beta_w <= 1.0, msg |
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| 418 | |
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| 419 | |
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| 420 | #Initial update of vertex and edge values before any storage |
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| 421 | #and or visualisation |
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| 422 | self.distribute_to_vertices_and_edges() |
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| 423 | |
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| 424 | if self.store is True and self.time == 0.0: |
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| 425 | self.initialise_storage() |
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| 426 | #print 'Storing results in ' + self.writer.filename |
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| 427 | else: |
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| 428 | pass |
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| 429 | #print 'Results will not be stored.' |
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| 430 | #print 'To store results set domain.store = True' |
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| 431 | #FIXME: Diagnostic output should be controlled by |
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| 432 | # a 'verbose' flag living in domain (or in a parent class) |
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| 433 | |
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| 434 | #Call basic machinery from parent class |
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| 435 | for t in Generic_Domain.evolve(self, |
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| 436 | yieldstep=yieldstep, |
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| 437 | finaltime=finaltime, |
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| 438 | duration=duration, |
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| 439 | skip_initial_step=skip_initial_step): |
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| 440 | |
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| 441 | #Store model data, e.g. for subsequent visualisation |
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| 442 | if self.store is True: |
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| 443 | self.store_timestep(self.quantities_to_be_stored) |
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| 444 | |
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| 445 | #FIXME: Could maybe be taken from specified list |
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| 446 | #of 'store every step' quantities |
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| 447 | |
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| 448 | #Pass control on to outer loop for more specific actions |
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| 449 | yield(t) |
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| 450 | |
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| 451 | def initialise_storage(self): |
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| 452 | """Create and initialise self.writer object for storing data. |
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| 453 | Also, save x,y and bed elevation |
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| 454 | """ |
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| 455 | |
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| 456 | from anuga.shallow_water.data_manager import get_dataobject |
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| 457 | |
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| 458 | #Initialise writer |
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| 459 | self.writer = get_dataobject(self, mode = 'w') |
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| 460 | |
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| 461 | #Store vertices and connectivity |
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| 462 | self.writer.store_connectivity() |
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| 463 | |
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| 464 | |
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| 465 | def store_timestep(self, name): |
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| 466 | """Store named quantity and time. |
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| 467 | |
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| 468 | Precondition: |
|---|
| 469 | self.write has been initialised |
|---|
| 470 | """ |
|---|
| 471 | self.writer.store_timestep(name) |
|---|
| 472 | |
|---|
| 473 | |
|---|
| 474 | #=============== End of Shallow Water Domain =============================== |
|---|
| 475 | |
|---|
| 476 | |
|---|
| 477 | |
|---|
| 478 | #Rotation of momentum vector |
|---|
| 479 | def rotate(q, normal, direction = 1): |
|---|
| 480 | """Rotate the momentum component q (q[1], q[2]) |
|---|
| 481 | from x,y coordinates to coordinates based on normal vector. |
|---|
| 482 | |
|---|
| 483 | If direction is negative the rotation is inverted. |
|---|
| 484 | |
|---|
| 485 | Input vector is preserved |
|---|
| 486 | |
|---|
| 487 | This function is specific to the shallow water wave equation |
|---|
| 488 | """ |
|---|
| 489 | |
|---|
| 490 | assert len(q) == 3,\ |
|---|
| 491 | 'Vector of conserved quantities must have length 3'\ |
|---|
| 492 | 'for 2D shallow water equation' |
|---|
| 493 | |
|---|
| 494 | try: |
|---|
| 495 | l = len(normal) |
|---|
| 496 | except: |
|---|
| 497 | raise 'Normal vector must be an Numeric array' |
|---|
| 498 | |
|---|
| 499 | assert l == 2, 'Normal vector must have 2 components' |
|---|
| 500 | |
|---|
| 501 | |
|---|
| 502 | n1 = normal[0] |
|---|
| 503 | n2 = normal[1] |
|---|
| 504 | |
|---|
| 505 | r = zeros(len(q), Float) #Rotated quantities |
|---|
| 506 | r[0] = q[0] #First quantity, height, is not rotated |
|---|
| 507 | |
|---|
| 508 | if direction == -1: |
|---|
| 509 | n2 = -n2 |
|---|
| 510 | |
|---|
| 511 | |
|---|
| 512 | r[1] = n1*q[1] + n2*q[2] |
|---|
| 513 | r[2] = -n2*q[1] + n1*q[2] |
|---|
| 514 | |
|---|
| 515 | return r |
|---|
| 516 | |
|---|
| 517 | |
|---|
| 518 | |
|---|
| 519 | #################################### |
|---|
| 520 | # Flux computation |
|---|
| 521 | def flux_function_central(normal, ql, qr, zl, zr): |
|---|
| 522 | """Compute fluxes between volumes for the shallow water wave equation |
|---|
| 523 | cast in terms of w = h+z using the 'central scheme' as described in |
|---|
| 524 | |
|---|
| 525 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
|---|
| 526 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
|---|
| 527 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
|---|
| 528 | |
|---|
| 529 | The implemented formula is given in equation (3.15) on page 714 |
|---|
| 530 | |
|---|
| 531 | Conserved quantities w, uh, vh are stored as elements 0, 1 and 2 |
|---|
| 532 | in the numerical vectors ql and qr. |
|---|
| 533 | |
|---|
| 534 | Bed elevations zl and zr. |
|---|
| 535 | """ |
|---|
| 536 | |
|---|
| 537 | from anuga.config import g, epsilon |
|---|
| 538 | from math import sqrt |
|---|
| 539 | |
|---|
| 540 | #Align momentums with x-axis |
|---|
| 541 | q_left = rotate(ql, normal, direction = 1) |
|---|
| 542 | q_right = rotate(qr, normal, direction = 1) |
|---|
| 543 | |
|---|
| 544 | z = (zl+zr)/2 #Take average of field values |
|---|
| 545 | |
|---|
| 546 | w_left = q_left[0] #w=h+z |
|---|
| 547 | h_left = w_left-z |
|---|
| 548 | uh_left = q_left[1] |
|---|
| 549 | |
|---|
| 550 | if h_left < epsilon: |
|---|
| 551 | u_left = 0.0 #Could have been negative |
|---|
| 552 | h_left = 0.0 |
|---|
| 553 | else: |
|---|
| 554 | u_left = uh_left/h_left |
|---|
| 555 | |
|---|
| 556 | |
|---|
| 557 | w_right = q_right[0] #w=h+z |
|---|
| 558 | h_right = w_right-z |
|---|
| 559 | uh_right = q_right[1] |
|---|
| 560 | |
|---|
| 561 | |
|---|
| 562 | if h_right < epsilon: |
|---|
| 563 | u_right = 0.0 #Could have been negative |
|---|
| 564 | h_right = 0.0 |
|---|
| 565 | else: |
|---|
| 566 | u_right = uh_right/h_right |
|---|
| 567 | |
|---|
| 568 | vh_left = q_left[2] |
|---|
| 569 | vh_right = q_right[2] |
|---|
| 570 | |
|---|
| 571 | soundspeed_left = sqrt(g*h_left) |
|---|
| 572 | soundspeed_right = sqrt(g*h_right) |
|---|
| 573 | |
|---|
| 574 | #Maximal wave speed |
|---|
| 575 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
|---|
| 576 | |
|---|
| 577 | #Minimal wave speed |
|---|
| 578 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
|---|
| 579 | |
|---|
| 580 | #Flux computation |
|---|
| 581 | |
|---|
| 582 | #FIXME(Ole): Why is it again that we don't |
|---|
| 583 | #use uh_left and uh_right directly in the first entries? |
|---|
| 584 | flux_left = array([u_left*h_left, |
|---|
| 585 | u_left*uh_left + 0.5*g*h_left**2, |
|---|
| 586 | u_left*vh_left]) |
|---|
| 587 | flux_right = array([u_right*h_right, |
|---|
| 588 | u_right*uh_right + 0.5*g*h_right**2, |
|---|
| 589 | u_right*vh_right]) |
|---|
| 590 | |
|---|
| 591 | denom = s_max-s_min |
|---|
| 592 | if denom == 0.0: |
|---|
| 593 | edgeflux = array([0.0, 0.0, 0.0]) |
|---|
| 594 | max_speed = 0.0 |
|---|
| 595 | else: |
|---|
| 596 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
|---|
| 597 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
|---|
| 598 | |
|---|
| 599 | edgeflux = rotate(edgeflux, normal, direction=-1) |
|---|
| 600 | max_speed = max(abs(s_max), abs(s_min)) |
|---|
| 601 | |
|---|
| 602 | return edgeflux, max_speed |
|---|
| 603 | |
|---|
| 604 | def erfcc(x): |
|---|
| 605 | |
|---|
| 606 | from math import fabs, exp |
|---|
| 607 | |
|---|
| 608 | z=fabs(x) |
|---|
| 609 | t=1.0/(1.0+0.5*z) |
|---|
| 610 | result=t*exp(-z*z-1.26551223+t*(1.00002368+t*(.37409196+ |
|---|
| 611 | t*(.09678418+t*(-.18628806+t*(.27886807+t*(-1.13520398+ |
|---|
| 612 | t*(1.48851587+t*(-.82215223+t*.17087277))))))))) |
|---|
| 613 | if x < 0.0: |
|---|
| 614 | result = 2.0-result |
|---|
| 615 | |
|---|
| 616 | return result |
|---|
| 617 | |
|---|
| 618 | def flux_function_kinetic(normal, ql, qr, zl, zr): |
|---|
| 619 | """Compute fluxes between volumes for the shallow water wave equation |
|---|
| 620 | cast in terms of w = h+z using the 'central scheme' as described in |
|---|
| 621 | |
|---|
| 622 | Zhang et. al., Advances in Water Resources, 26(6), 2003, 635-647. |
|---|
| 623 | |
|---|
| 624 | |
|---|
| 625 | Conserved quantities w, uh, vh are stored as elements 0, 1 and 2 |
|---|
| 626 | in the numerical vectors ql an qr. |
|---|
| 627 | |
|---|
| 628 | Bed elevations zl and zr. |
|---|
| 629 | """ |
|---|
| 630 | |
|---|
| 631 | from anuga.config import g, epsilon |
|---|
| 632 | from math import sqrt |
|---|
| 633 | from Numeric import array |
|---|
| 634 | |
|---|
| 635 | #Align momentums with x-axis |
|---|
| 636 | q_left = rotate(ql, normal, direction = 1) |
|---|
| 637 | q_right = rotate(qr, normal, direction = 1) |
|---|
| 638 | |
|---|
| 639 | z = (zl+zr)/2 #Take average of field values |
|---|
| 640 | |
|---|
| 641 | w_left = q_left[0] #w=h+z |
|---|
| 642 | h_left = w_left-z |
|---|
| 643 | uh_left = q_left[1] |
|---|
| 644 | |
|---|
| 645 | if h_left < epsilon: |
|---|
| 646 | u_left = 0.0 #Could have been negative |
|---|
| 647 | h_left = 0.0 |
|---|
| 648 | else: |
|---|
| 649 | u_left = uh_left/h_left |
|---|
| 650 | |
|---|
| 651 | |
|---|
| 652 | w_right = q_right[0] #w=h+z |
|---|
| 653 | h_right = w_right-z |
|---|
| 654 | uh_right = q_right[1] |
|---|
| 655 | |
|---|
| 656 | |
|---|
| 657 | if h_right < epsilon: |
|---|
| 658 | u_right = 0.0 #Could have been negative |
|---|
| 659 | h_right = 0.0 |
|---|
| 660 | else: |
|---|
| 661 | u_right = uh_right/h_right |
|---|
| 662 | |
|---|
| 663 | vh_left = q_left[2] |
|---|
| 664 | vh_right = q_right[2] |
|---|
| 665 | |
|---|
| 666 | soundspeed_left = sqrt(g*h_left) |
|---|
| 667 | soundspeed_right = sqrt(g*h_right) |
|---|
| 668 | |
|---|
| 669 | #Maximal wave speed |
|---|
| 670 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
|---|
| 671 | |
|---|
| 672 | #Minimal wave speed |
|---|
| 673 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
|---|
| 674 | |
|---|
| 675 | #Flux computation |
|---|
| 676 | |
|---|
| 677 | F_left = 0.0 |
|---|
| 678 | F_right = 0.0 |
|---|
| 679 | from math import sqrt, pi, exp |
|---|
| 680 | if h_left > 0.0: |
|---|
| 681 | F_left = u_left/sqrt(g*h_left) |
|---|
| 682 | if h_right > 0.0: |
|---|
| 683 | F_right = u_right/sqrt(g*h_right) |
|---|
| 684 | |
|---|
| 685 | edgeflux = array([0.0, 0.0, 0.0]) |
|---|
| 686 | |
|---|
| 687 | edgeflux[0] = h_left*u_left/2.0*erfcc(-F_left) + \ |
|---|
| 688 | h_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left**2)) + \ |
|---|
| 689 | h_right*u_right/2.0*erfcc(F_right) - \ |
|---|
| 690 | h_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right**2)) |
|---|
| 691 | |
|---|
| 692 | edgeflux[1] = (h_left*u_left**2 + g/2.0*h_left**2)/2.0*erfcc(-F_left) + \ |
|---|
| 693 | u_left*h_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left**2)) + \ |
|---|
| 694 | (h_right*u_right**2 + g/2.0*h_right**2)/2.0*erfcc(F_right) - \ |
|---|
| 695 | u_right*h_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right**2)) |
|---|
| 696 | |
|---|
| 697 | edgeflux[2] = vh_left*u_left/2.0*erfcc(-F_left) + \ |
|---|
| 698 | vh_left*sqrt(g*h_left)/2.0/sqrt(pi)*exp(-(F_left**2)) + \ |
|---|
| 699 | vh_right*u_right/2.0*erfcc(F_right) - \ |
|---|
| 700 | vh_right*sqrt(g*h_right)/2.0/sqrt(pi)*exp(-(F_right**2)) |
|---|
| 701 | |
|---|
| 702 | |
|---|
| 703 | edgeflux = rotate(edgeflux, normal, direction=-1) |
|---|
| 704 | max_speed = max(abs(s_max), abs(s_min)) |
|---|
| 705 | |
|---|
| 706 | return edgeflux, max_speed |
|---|
| 707 | |
|---|
| 708 | |
|---|
| 709 | |
|---|
| 710 | def compute_fluxes(domain): |
|---|
| 711 | """Compute all fluxes and the timestep suitable for all volumes |
|---|
| 712 | in domain. |
|---|
| 713 | |
|---|
| 714 | Compute total flux for each conserved quantity using "flux_function" |
|---|
| 715 | |
|---|
| 716 | Fluxes across each edge are scaled by edgelengths and summed up |
|---|
| 717 | Resulting flux is then scaled by area and stored in |
|---|
| 718 | explicit_update for each of the three conserved quantities |
|---|
| 719 | stage, xmomentum and ymomentum |
|---|
| 720 | |
|---|
| 721 | The maximal allowable speed computed by the flux_function for each volume |
|---|
| 722 | is converted to a timestep that must not be exceeded. The minimum of |
|---|
| 723 | those is computed as the next overall timestep. |
|---|
| 724 | |
|---|
| 725 | Post conditions: |
|---|
| 726 | domain.explicit_update is reset to computed flux values |
|---|
| 727 | domain.timestep is set to the largest step satisfying all volumes. |
|---|
| 728 | """ |
|---|
| 729 | |
|---|
| 730 | import sys |
|---|
| 731 | |
|---|
| 732 | N = len(domain) # number_of_triangles |
|---|
| 733 | |
|---|
| 734 | #Shortcuts |
|---|
| 735 | Stage = domain.quantities['stage'] |
|---|
| 736 | Xmom = domain.quantities['xmomentum'] |
|---|
| 737 | Ymom = domain.quantities['ymomentum'] |
|---|
| 738 | Bed = domain.quantities['elevation'] |
|---|
| 739 | |
|---|
| 740 | #Arrays |
|---|
| 741 | stage = Stage.edge_values |
|---|
| 742 | xmom = Xmom.edge_values |
|---|
| 743 | ymom = Ymom.edge_values |
|---|
| 744 | bed = Bed.edge_values |
|---|
| 745 | |
|---|
| 746 | stage_bdry = Stage.boundary_values |
|---|
| 747 | xmom_bdry = Xmom.boundary_values |
|---|
| 748 | ymom_bdry = Ymom.boundary_values |
|---|
| 749 | |
|---|
| 750 | flux = zeros(3, Float) #Work array for summing up fluxes |
|---|
| 751 | |
|---|
| 752 | |
|---|
| 753 | #Loop |
|---|
| 754 | timestep = float(sys.maxint) |
|---|
| 755 | for k in range(N): |
|---|
| 756 | |
|---|
| 757 | flux[:] = 0. #Reset work array |
|---|
| 758 | for i in range(3): |
|---|
| 759 | #Quantities inside volume facing neighbour i |
|---|
| 760 | ql = [stage[k, i], xmom[k, i], ymom[k, i]] |
|---|
| 761 | zl = bed[k, i] |
|---|
| 762 | |
|---|
| 763 | #Quantities at neighbour on nearest face |
|---|
| 764 | n = domain.neighbours[k,i] |
|---|
| 765 | if n < 0: |
|---|
| 766 | m = -n-1 #Convert negative flag to index |
|---|
| 767 | qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] |
|---|
| 768 | zr = zl #Extend bed elevation to boundary |
|---|
| 769 | else: |
|---|
| 770 | m = domain.neighbour_edges[k,i] |
|---|
| 771 | qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
|---|
| 772 | zr = bed[n, m] |
|---|
| 773 | |
|---|
| 774 | |
|---|
| 775 | #Outward pointing normal vector |
|---|
| 776 | normal = domain.normals[k, 2*i:2*i+2] |
|---|
| 777 | |
|---|
| 778 | #Flux computation using provided function |
|---|
| 779 | edgeflux, max_speed = domain.flux_function(normal, ql, qr, zl, zr) |
|---|
| 780 | flux -= edgeflux * domain.edgelengths[k,i] |
|---|
| 781 | |
|---|
| 782 | #Update optimal_timestep on full cells |
|---|
| 783 | if domain.tri_full_flag[k] == 1: |
|---|
| 784 | try: |
|---|
| 785 | timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
|---|
| 786 | except ZeroDivisionError: |
|---|
| 787 | pass |
|---|
| 788 | |
|---|
| 789 | #Normalise by area and store for when all conserved |
|---|
| 790 | #quantities get updated |
|---|
| 791 | flux /= domain.areas[k] |
|---|
| 792 | Stage.explicit_update[k] = flux[0] |
|---|
| 793 | Xmom.explicit_update[k] = flux[1] |
|---|
| 794 | Ymom.explicit_update[k] = flux[2] |
|---|
| 795 | domain.max_speed[k] = max_speed |
|---|
| 796 | |
|---|
| 797 | |
|---|
| 798 | domain.timestep = timestep |
|---|
| 799 | |
|---|
| 800 | #MH090605 The following method belongs to the shallow_water domain class |
|---|
| 801 | #see comments in the corresponding method in shallow_water_ext.c |
|---|
| 802 | def extrapolate_second_order_sw_c(domain): |
|---|
| 803 | """Wrapper calling C version of extrapolate_second_order_sw |
|---|
| 804 | """ |
|---|
| 805 | import sys |
|---|
| 806 | |
|---|
| 807 | N = len(domain) # number_of_triangles |
|---|
| 808 | |
|---|
| 809 | #Shortcuts |
|---|
| 810 | Stage = domain.quantities['stage'] |
|---|
| 811 | Xmom = domain.quantities['xmomentum'] |
|---|
| 812 | Ymom = domain.quantities['ymomentum'] |
|---|
| 813 | Elevation = domain.quantities['elevation'] |
|---|
| 814 | from shallow_water_ext import extrapolate_second_order_sw |
|---|
| 815 | extrapolate_second_order_sw(domain, |
|---|
| 816 | domain.surrogate_neighbours, |
|---|
| 817 | domain.number_of_boundaries, |
|---|
| 818 | domain.centroid_coordinates, |
|---|
| 819 | Stage.centroid_values, |
|---|
| 820 | Xmom.centroid_values, |
|---|
| 821 | Ymom.centroid_values, |
|---|
| 822 | Elevation.centroid_values, |
|---|
| 823 | domain.vertex_coordinates, |
|---|
| 824 | Stage.vertex_values, |
|---|
| 825 | Xmom.vertex_values, |
|---|
| 826 | Ymom.vertex_values, |
|---|
| 827 | Elevation.vertex_values) |
|---|
| 828 | |
|---|
| 829 | def compute_fluxes_c(domain): |
|---|
| 830 | """Wrapper calling C version of compute fluxes |
|---|
| 831 | """ |
|---|
| 832 | |
|---|
| 833 | import sys |
|---|
| 834 | |
|---|
| 835 | N = len(domain) # number_of_triangles |
|---|
| 836 | |
|---|
| 837 | #Shortcuts |
|---|
| 838 | Stage = domain.quantities['stage'] |
|---|
| 839 | Xmom = domain.quantities['xmomentum'] |
|---|
| 840 | Ymom = domain.quantities['ymomentum'] |
|---|
| 841 | Bed = domain.quantities['elevation'] |
|---|
| 842 | |
|---|
| 843 | timestep = float(sys.maxint) |
|---|
| 844 | from shallow_water_ext import\ |
|---|
| 845 | compute_fluxes_ext_central as compute_fluxes_ext |
|---|
| 846 | |
|---|
| 847 | |
|---|
| 848 | domain.timestep = compute_fluxes_ext(timestep, domain.epsilon, |
|---|
| 849 | domain.H0, |
|---|
| 850 | domain.g, |
|---|
| 851 | domain.neighbours, |
|---|
| 852 | domain.neighbour_edges, |
|---|
| 853 | domain.normals, |
|---|
| 854 | domain.edgelengths, |
|---|
| 855 | domain.radii, |
|---|
| 856 | domain.areas, |
|---|
| 857 | domain.tri_full_flag, |
|---|
| 858 | Stage.edge_values, |
|---|
| 859 | Xmom.edge_values, |
|---|
| 860 | Ymom.edge_values, |
|---|
| 861 | Bed.edge_values, |
|---|
| 862 | Stage.boundary_values, |
|---|
| 863 | Xmom.boundary_values, |
|---|
| 864 | Ymom.boundary_values, |
|---|
| 865 | Stage.explicit_update, |
|---|
| 866 | Xmom.explicit_update, |
|---|
| 867 | Ymom.explicit_update, |
|---|
| 868 | domain.already_computed_flux, |
|---|
| 869 | domain.max_speed) |
|---|
| 870 | |
|---|
| 871 | |
|---|
| 872 | #################################### |
|---|
| 873 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
|---|
| 874 | |
|---|
| 875 | def distribute_to_vertices_and_edges(domain): |
|---|
| 876 | """Distribution from centroids to vertices specific to the |
|---|
| 877 | shallow water wave |
|---|
| 878 | equation. |
|---|
| 879 | |
|---|
| 880 | It will ensure that h (w-z) is always non-negative even in the |
|---|
| 881 | presence of steep bed-slopes by taking a weighted average between shallow |
|---|
| 882 | and deep cases. |
|---|
| 883 | |
|---|
| 884 | In addition, all conserved quantities get distributed as per either a |
|---|
| 885 | constant (order==1) or a piecewise linear function (order==2). |
|---|
| 886 | |
|---|
| 887 | FIXME: more explanation about removal of artificial variability etc |
|---|
| 888 | |
|---|
| 889 | Precondition: |
|---|
| 890 | All quantities defined at centroids and bed elevation defined at |
|---|
| 891 | vertices. |
|---|
| 892 | |
|---|
| 893 | Postcondition |
|---|
| 894 | Conserved quantities defined at vertices |
|---|
| 895 | |
|---|
| 896 | """ |
|---|
| 897 | |
|---|
| 898 | from anuga.config import optimised_gradient_limiter |
|---|
| 899 | |
|---|
| 900 | #Remove very thin layers of water |
|---|
| 901 | protect_against_infinitesimal_and_negative_heights(domain) |
|---|
| 902 | |
|---|
| 903 | #Extrapolate all conserved quantities |
|---|
| 904 | if optimised_gradient_limiter: |
|---|
| 905 | #MH090605 if second order, |
|---|
| 906 | #perform the extrapolation and limiting on |
|---|
| 907 | #all of the conserved quantitie |
|---|
| 908 | |
|---|
| 909 | if (domain._order_ == 1): |
|---|
| 910 | for name in domain.conserved_quantities: |
|---|
| 911 | Q = domain.quantities[name] |
|---|
| 912 | Q.extrapolate_first_order() |
|---|
| 913 | elif domain._order_ == 2: |
|---|
| 914 | domain.extrapolate_second_order_sw() |
|---|
| 915 | else: |
|---|
| 916 | raise 'Unknown order' |
|---|
| 917 | else: |
|---|
| 918 | #old code: |
|---|
| 919 | for name in domain.conserved_quantities: |
|---|
| 920 | Q = domain.quantities[name] |
|---|
| 921 | if domain._order_ == 1: |
|---|
| 922 | Q.extrapolate_first_order() |
|---|
| 923 | elif domain._order_ == 2: |
|---|
| 924 | Q.extrapolate_second_order() |
|---|
| 925 | Q.limit() |
|---|
| 926 | else: |
|---|
| 927 | raise 'Unknown order' |
|---|
| 928 | |
|---|
| 929 | |
|---|
| 930 | #Take bed elevation into account when water heights are small |
|---|
| 931 | balance_deep_and_shallow(domain) |
|---|
| 932 | |
|---|
| 933 | #Compute edge values by interpolation |
|---|
| 934 | for name in domain.conserved_quantities: |
|---|
| 935 | Q = domain.quantities[name] |
|---|
| 936 | Q.interpolate_from_vertices_to_edges() |
|---|
| 937 | |
|---|
| 938 | |
|---|
| 939 | def protect_against_infinitesimal_and_negative_heights(domain): |
|---|
| 940 | """Protect against infinitesimal heights and associated high velocities |
|---|
| 941 | """ |
|---|
| 942 | |
|---|
| 943 | #Shortcuts |
|---|
| 944 | wc = domain.quantities['stage'].centroid_values |
|---|
| 945 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 946 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 947 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 948 | hc = wc - zc #Water depths at centroids |
|---|
| 949 | |
|---|
| 950 | #Update |
|---|
| 951 | #FIXME: Modify according to c-version - or discard altogether. |
|---|
| 952 | for k in range(len(domain)): |
|---|
| 953 | |
|---|
| 954 | if hc[k] < domain.minimum_allowed_height: |
|---|
| 955 | #Control stage |
|---|
| 956 | if hc[k] < domain.epsilon: |
|---|
| 957 | wc[k] = zc[k] # Contain 'lost mass' error |
|---|
| 958 | |
|---|
| 959 | #Control momentum |
|---|
| 960 | xmomc[k] = ymomc[k] = 0.0 |
|---|
| 961 | |
|---|
| 962 | |
|---|
| 963 | def protect_against_infinitesimal_and_negative_heights_c(domain): |
|---|
| 964 | """Protect against infinitesimal heights and associated high velocities |
|---|
| 965 | """ |
|---|
| 966 | |
|---|
| 967 | #Shortcuts |
|---|
| 968 | wc = domain.quantities['stage'].centroid_values |
|---|
| 969 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 970 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 971 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 972 | |
|---|
| 973 | from shallow_water_ext import protect |
|---|
| 974 | |
|---|
| 975 | protect(domain.minimum_allowed_height, domain.maximum_allowed_speed, |
|---|
| 976 | domain.epsilon, wc, zc, xmomc, ymomc) |
|---|
| 977 | |
|---|
| 978 | |
|---|
| 979 | |
|---|
| 980 | def h_limiter(domain): |
|---|
| 981 | """Limit slopes for each volume to eliminate artificial variance |
|---|
| 982 | introduced by e.g. second order extrapolator |
|---|
| 983 | |
|---|
| 984 | limit on h = w-z |
|---|
| 985 | |
|---|
| 986 | This limiter depends on two quantities (w,z) so it resides within |
|---|
| 987 | this module rather than within quantity.py |
|---|
| 988 | """ |
|---|
| 989 | |
|---|
| 990 | N = len(domain) |
|---|
| 991 | beta_h = domain.beta_h |
|---|
| 992 | |
|---|
| 993 | #Shortcuts |
|---|
| 994 | wc = domain.quantities['stage'].centroid_values |
|---|
| 995 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 996 | hc = wc - zc |
|---|
| 997 | |
|---|
| 998 | wv = domain.quantities['stage'].vertex_values |
|---|
| 999 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 1000 | hv = wv-zv |
|---|
| 1001 | |
|---|
| 1002 | hvbar = zeros(hv.shape, Float) #h-limited values |
|---|
| 1003 | |
|---|
| 1004 | #Find min and max of this and neighbour's centroid values |
|---|
| 1005 | hmax = zeros(hc.shape, Float) |
|---|
| 1006 | hmin = zeros(hc.shape, Float) |
|---|
| 1007 | |
|---|
| 1008 | for k in range(N): |
|---|
| 1009 | hmax[k] = hmin[k] = hc[k] |
|---|
| 1010 | for i in range(3): |
|---|
| 1011 | n = domain.neighbours[k,i] |
|---|
| 1012 | if n >= 0: |
|---|
| 1013 | hn = hc[n] #Neighbour's centroid value |
|---|
| 1014 | |
|---|
| 1015 | hmin[k] = min(hmin[k], hn) |
|---|
| 1016 | hmax[k] = max(hmax[k], hn) |
|---|
| 1017 | |
|---|
| 1018 | |
|---|
| 1019 | #Diffences between centroids and maxima/minima |
|---|
| 1020 | dhmax = hmax - hc |
|---|
| 1021 | dhmin = hmin - hc |
|---|
| 1022 | |
|---|
| 1023 | #Deltas between vertex and centroid values |
|---|
| 1024 | dh = zeros(hv.shape, Float) |
|---|
| 1025 | for i in range(3): |
|---|
| 1026 | dh[:,i] = hv[:,i] - hc |
|---|
| 1027 | |
|---|
| 1028 | #Phi limiter |
|---|
| 1029 | for k in range(N): |
|---|
| 1030 | |
|---|
| 1031 | #Find the gradient limiter (phi) across vertices |
|---|
| 1032 | phi = 1.0 |
|---|
| 1033 | for i in range(3): |
|---|
| 1034 | r = 1.0 |
|---|
| 1035 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
|---|
| 1036 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
|---|
| 1037 | |
|---|
| 1038 | phi = min( min(r*beta_h, 1), phi ) |
|---|
| 1039 | |
|---|
| 1040 | #Then update using phi limiter |
|---|
| 1041 | for i in range(3): |
|---|
| 1042 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
|---|
| 1043 | |
|---|
| 1044 | return hvbar |
|---|
| 1045 | |
|---|
| 1046 | |
|---|
| 1047 | |
|---|
| 1048 | def h_limiter_c(domain): |
|---|
| 1049 | """Limit slopes for each volume to eliminate artificial variance |
|---|
| 1050 | introduced by e.g. second order extrapolator |
|---|
| 1051 | |
|---|
| 1052 | limit on h = w-z |
|---|
| 1053 | |
|---|
| 1054 | This limiter depends on two quantities (w,z) so it resides within |
|---|
| 1055 | this module rather than within quantity.py |
|---|
| 1056 | |
|---|
| 1057 | Wrapper for c-extension |
|---|
| 1058 | """ |
|---|
| 1059 | |
|---|
| 1060 | N = len(domain) # number_of_triangles |
|---|
| 1061 | beta_h = domain.beta_h |
|---|
| 1062 | |
|---|
| 1063 | #Shortcuts |
|---|
| 1064 | wc = domain.quantities['stage'].centroid_values |
|---|
| 1065 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 1066 | hc = wc - zc |
|---|
| 1067 | |
|---|
| 1068 | wv = domain.quantities['stage'].vertex_values |
|---|
| 1069 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 1070 | hv = wv - zv |
|---|
| 1071 | |
|---|
| 1072 | #Call C-extension |
|---|
| 1073 | from shallow_water_ext import h_limiter_sw as h_limiter |
|---|
| 1074 | hvbar = h_limiter(domain, hc, hv) |
|---|
| 1075 | |
|---|
| 1076 | return hvbar |
|---|
| 1077 | |
|---|
| 1078 | |
|---|
| 1079 | def balance_deep_and_shallow(domain): |
|---|
| 1080 | """Compute linear combination between stage as computed by |
|---|
| 1081 | gradient-limiters limiting using w, and stage computed by |
|---|
| 1082 | gradient-limiters limiting using h (h-limiter). |
|---|
| 1083 | The former takes precedence when heights are large compared to the |
|---|
| 1084 | bed slope while the latter takes precedence when heights are |
|---|
| 1085 | relatively small. Anything in between is computed as a balanced |
|---|
| 1086 | linear combination in order to avoid numerical disturbances which |
|---|
| 1087 | would otherwise appear as a result of hard switching between |
|---|
| 1088 | modes. |
|---|
| 1089 | |
|---|
| 1090 | The h-limiter is always applied irrespective of the order. |
|---|
| 1091 | """ |
|---|
| 1092 | |
|---|
| 1093 | #Shortcuts |
|---|
| 1094 | wc = domain.quantities['stage'].centroid_values |
|---|
| 1095 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 1096 | hc = wc - zc |
|---|
| 1097 | |
|---|
| 1098 | wv = domain.quantities['stage'].vertex_values |
|---|
| 1099 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 1100 | hv = wv-zv |
|---|
| 1101 | |
|---|
| 1102 | #Limit h |
|---|
| 1103 | hvbar = h_limiter(domain) |
|---|
| 1104 | |
|---|
| 1105 | for k in range(len(domain)): |
|---|
| 1106 | #Compute maximal variation in bed elevation |
|---|
| 1107 | # This quantitiy is |
|---|
| 1108 | # dz = max_i abs(z_i - z_c) |
|---|
| 1109 | # and it is independent of dimension |
|---|
| 1110 | # In the 1d case zc = (z0+z1)/2 |
|---|
| 1111 | # In the 2d case zc = (z0+z1+z2)/3 |
|---|
| 1112 | |
|---|
| 1113 | dz = max(abs(zv[k,0]-zc[k]), |
|---|
| 1114 | abs(zv[k,1]-zc[k]), |
|---|
| 1115 | abs(zv[k,2]-zc[k])) |
|---|
| 1116 | |
|---|
| 1117 | |
|---|
| 1118 | hmin = min( hv[k,:] ) |
|---|
| 1119 | |
|---|
| 1120 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
|---|
| 1121 | #stage and alpha==1 means using the w-limited stage as |
|---|
| 1122 | #computed by the gradient limiter (both 1st or 2nd order) |
|---|
| 1123 | |
|---|
| 1124 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
|---|
| 1125 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
|---|
| 1126 | |
|---|
| 1127 | if dz > 0.0: |
|---|
| 1128 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
|---|
| 1129 | else: |
|---|
| 1130 | #Flat bed |
|---|
| 1131 | alpha = 1.0 |
|---|
| 1132 | |
|---|
| 1133 | #Let |
|---|
| 1134 | # |
|---|
| 1135 | # wvi be the w-limited stage (wvi = zvi + hvi) |
|---|
| 1136 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
|---|
| 1137 | # |
|---|
| 1138 | # |
|---|
| 1139 | #where i=0,1,2 denotes the vertex ids |
|---|
| 1140 | # |
|---|
| 1141 | #Weighted balance between w-limited and h-limited stage is |
|---|
| 1142 | # |
|---|
| 1143 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
|---|
| 1144 | # |
|---|
| 1145 | #It follows that the updated wvi is |
|---|
| 1146 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
|---|
| 1147 | # |
|---|
| 1148 | # Momentum is balanced between constant and limited |
|---|
| 1149 | |
|---|
| 1150 | |
|---|
| 1151 | #for i in range(3): |
|---|
| 1152 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
|---|
| 1153 | |
|---|
| 1154 | #return |
|---|
| 1155 | |
|---|
| 1156 | if alpha < 1: |
|---|
| 1157 | |
|---|
| 1158 | for i in range(3): |
|---|
| 1159 | wv[k,i] = zv[k,i] + (1-alpha)*hvbar[k,i] + alpha*hv[k,i] |
|---|
| 1160 | |
|---|
| 1161 | #Momentums at centroids |
|---|
| 1162 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 1163 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 1164 | |
|---|
| 1165 | #Momentums at vertices |
|---|
| 1166 | xmomv = domain.quantities['xmomentum'].vertex_values |
|---|
| 1167 | ymomv = domain.quantities['ymomentum'].vertex_values |
|---|
| 1168 | |
|---|
| 1169 | # Update momentum as a linear combination of |
|---|
| 1170 | # xmomc and ymomc (shallow) and momentum |
|---|
| 1171 | # from extrapolator xmomv and ymomv (deep). |
|---|
| 1172 | xmomv[k,:] = (1-alpha)*xmomc[k] + alpha*xmomv[k,:] |
|---|
| 1173 | ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
|---|
| 1174 | |
|---|
| 1175 | |
|---|
| 1176 | def balance_deep_and_shallow_c(domain): |
|---|
| 1177 | """Wrapper for C implementation |
|---|
| 1178 | """ |
|---|
| 1179 | |
|---|
| 1180 | #Shortcuts |
|---|
| 1181 | wc = domain.quantities['stage'].centroid_values |
|---|
| 1182 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 1183 | hc = wc - zc |
|---|
| 1184 | |
|---|
| 1185 | wv = domain.quantities['stage'].vertex_values |
|---|
| 1186 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 1187 | hv = wv - zv |
|---|
| 1188 | |
|---|
| 1189 | #Momentums at centroids |
|---|
| 1190 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 1191 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 1192 | |
|---|
| 1193 | #Momentums at vertices |
|---|
| 1194 | xmomv = domain.quantities['xmomentum'].vertex_values |
|---|
| 1195 | ymomv = domain.quantities['ymomentum'].vertex_values |
|---|
| 1196 | |
|---|
| 1197 | #Limit h |
|---|
| 1198 | if domain.beta_h > 0: |
|---|
| 1199 | hvbar = h_limiter(domain) |
|---|
| 1200 | else: |
|---|
| 1201 | # print 'Using first order h-limiter' |
|---|
| 1202 | |
|---|
| 1203 | |
|---|
| 1204 | #This is how one would make a first order h_limited value |
|---|
| 1205 | #as in the old balancer (pre 17 Feb 2005): |
|---|
| 1206 | # If we wish to hard wire this, one should modify the C-code |
|---|
| 1207 | from Numeric import zeros, Float |
|---|
| 1208 | hvbar = zeros( (len(hc), 3), Float) |
|---|
| 1209 | for i in range(3): |
|---|
| 1210 | hvbar[:,i] = hc[:] |
|---|
| 1211 | |
|---|
| 1212 | from shallow_water_ext import balance_deep_and_shallow |
|---|
| 1213 | balance_deep_and_shallow(domain, wc, zc, hc, wv, zv, hv, hvbar, |
|---|
| 1214 | xmomc, ymomc, xmomv, ymomv) |
|---|
| 1215 | |
|---|
| 1216 | |
|---|
| 1217 | |
|---|
| 1218 | |
|---|
| 1219 | ############################################### |
|---|
| 1220 | #Boundaries - specific to the shallow water wave equation |
|---|
| 1221 | class Reflective_boundary(Boundary): |
|---|
| 1222 | """Reflective boundary returns same conserved quantities as |
|---|
| 1223 | those present in its neighbour volume but reflected. |
|---|
| 1224 | |
|---|
| 1225 | This class is specific to the shallow water equation as it |
|---|
| 1226 | works with the momentum quantities assumed to be the second |
|---|
| 1227 | and third conserved quantities. |
|---|
| 1228 | """ |
|---|
| 1229 | |
|---|
| 1230 | def __init__(self, domain = None): |
|---|
| 1231 | Boundary.__init__(self) |
|---|
| 1232 | |
|---|
| 1233 | if domain is None: |
|---|
| 1234 | msg = 'Domain must be specified for reflective boundary' |
|---|
| 1235 | raise msg |
|---|
| 1236 | |
|---|
| 1237 | #Handy shorthands |
|---|
| 1238 | self.stage = domain.quantities['stage'].edge_values |
|---|
| 1239 | self.xmom = domain.quantities['xmomentum'].edge_values |
|---|
| 1240 | self.ymom = domain.quantities['ymomentum'].edge_values |
|---|
| 1241 | self.normals = domain.normals |
|---|
| 1242 | |
|---|
| 1243 | self.conserved_quantities = zeros(3, Float) |
|---|
| 1244 | |
|---|
| 1245 | def __repr__(self): |
|---|
| 1246 | return 'Reflective_boundary' |
|---|
| 1247 | |
|---|
| 1248 | |
|---|
| 1249 | def evaluate(self, vol_id, edge_id): |
|---|
| 1250 | """Reflective boundaries reverses the outward momentum |
|---|
| 1251 | of the volume they serve. |
|---|
| 1252 | """ |
|---|
| 1253 | |
|---|
| 1254 | q = self.conserved_quantities |
|---|
| 1255 | q[0] = self.stage[vol_id, edge_id] |
|---|
| 1256 | q[1] = self.xmom[vol_id, edge_id] |
|---|
| 1257 | q[2] = self.ymom[vol_id, edge_id] |
|---|
| 1258 | |
|---|
| 1259 | normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
|---|
| 1260 | |
|---|
| 1261 | |
|---|
| 1262 | r = rotate(q, normal, direction = 1) |
|---|
| 1263 | r[1] = -r[1] |
|---|
| 1264 | q = rotate(r, normal, direction = -1) |
|---|
| 1265 | |
|---|
| 1266 | return q |
|---|
| 1267 | |
|---|
| 1268 | |
|---|
| 1269 | |
|---|
| 1270 | class Transmissive_Momentum_Set_Stage_boundary(Boundary): |
|---|
| 1271 | """Returns same momentum conserved quantities as |
|---|
| 1272 | those present in its neighbour volume. |
|---|
| 1273 | Sets stage by specifying a function f of time which may either be a |
|---|
| 1274 | vector function or a scalar function |
|---|
| 1275 | |
|---|
| 1276 | Example: |
|---|
| 1277 | |
|---|
| 1278 | def waveform(t): |
|---|
| 1279 | return sea_level + normalized_amplitude/cosh(t-25)**2 |
|---|
| 1280 | |
|---|
| 1281 | Bts = Transmissive_Momentum_Set_Stage_boundary(domain, waveform) |
|---|
| 1282 | |
|---|
| 1283 | |
|---|
| 1284 | Underlying domain must be specified when boundary is instantiated |
|---|
| 1285 | """ |
|---|
| 1286 | |
|---|
| 1287 | def __init__(self, domain = None, function=None): |
|---|
| 1288 | Boundary.__init__(self) |
|---|
| 1289 | |
|---|
| 1290 | if domain is None: |
|---|
| 1291 | msg = 'Domain must be specified for this type boundary' |
|---|
| 1292 | raise msg |
|---|
| 1293 | |
|---|
| 1294 | if function is None: |
|---|
| 1295 | msg = 'Function must be specified for this type boundary' |
|---|
| 1296 | raise msg |
|---|
| 1297 | |
|---|
| 1298 | self.domain = domain |
|---|
| 1299 | self.function = function |
|---|
| 1300 | |
|---|
| 1301 | def __repr__(self): |
|---|
| 1302 | return 'Transmissive_Momentum_Set_Stage_boundary(%s)' %self.domain |
|---|
| 1303 | |
|---|
| 1304 | def evaluate(self, vol_id, edge_id): |
|---|
| 1305 | """Transmissive Momentum Set Stage boundaries return the edge momentum |
|---|
| 1306 | values of the volume they serve. |
|---|
| 1307 | """ |
|---|
| 1308 | |
|---|
| 1309 | q = self.domain.get_conserved_quantities(vol_id, edge = edge_id) |
|---|
| 1310 | value = self.function(self.domain.time) |
|---|
| 1311 | |
|---|
| 1312 | try: |
|---|
| 1313 | x = float(value) |
|---|
| 1314 | except: |
|---|
| 1315 | x = float(value[0]) |
|---|
| 1316 | |
|---|
| 1317 | q[0] = x |
|---|
| 1318 | return q |
|---|
| 1319 | |
|---|
| 1320 | |
|---|
| 1321 | #FIXME: Consider this (taken from File_boundary) to allow |
|---|
| 1322 | #spatial variation |
|---|
| 1323 | #if vol_id is not None and edge_id is not None: |
|---|
| 1324 | # i = self.boundary_indices[ vol_id, edge_id ] |
|---|
| 1325 | # return self.F(t, point_id = i) |
|---|
| 1326 | #else: |
|---|
| 1327 | # return self.F(t) |
|---|
| 1328 | |
|---|
| 1329 | |
|---|
| 1330 | |
|---|
| 1331 | class Dirichlet_Discharge_boundary(Boundary): |
|---|
| 1332 | """ |
|---|
| 1333 | Sets stage (stage0) |
|---|
| 1334 | Sets momentum (wh0) in the inward normal direction. |
|---|
| 1335 | |
|---|
| 1336 | Underlying domain must be specified when boundary is instantiated |
|---|
| 1337 | """ |
|---|
| 1338 | |
|---|
| 1339 | def __init__(self, domain = None, stage0=None, wh0=None): |
|---|
| 1340 | Boundary.__init__(self) |
|---|
| 1341 | |
|---|
| 1342 | if domain is None: |
|---|
| 1343 | msg = 'Domain must be specified for this type boundary' |
|---|
| 1344 | raise msg |
|---|
| 1345 | |
|---|
| 1346 | if stage0 is None: |
|---|
| 1347 | raise 'set stage' |
|---|
| 1348 | |
|---|
| 1349 | if wh0 is None: |
|---|
| 1350 | wh0 = 0.0 |
|---|
| 1351 | |
|---|
| 1352 | self.domain = domain |
|---|
| 1353 | self.stage0 = stage0 |
|---|
| 1354 | self.wh0 = wh0 |
|---|
| 1355 | |
|---|
| 1356 | def __repr__(self): |
|---|
| 1357 | return 'Dirichlet_Discharge_boundary(%s)' %self.domain |
|---|
| 1358 | |
|---|
| 1359 | def evaluate(self, vol_id, edge_id): |
|---|
| 1360 | """Set discharge in the (inward) normal direction |
|---|
| 1361 | """ |
|---|
| 1362 | |
|---|
| 1363 | normal = self.domain.get_normal(vol_id,edge_id) |
|---|
| 1364 | q = [self.stage0, -self.wh0*normal[0], -self.wh0*normal[1]] |
|---|
| 1365 | return q |
|---|
| 1366 | |
|---|
| 1367 | |
|---|
| 1368 | #FIXME: Consider this (taken from File_boundary) to allow |
|---|
| 1369 | #spatial variation |
|---|
| 1370 | #if vol_id is not None and edge_id is not None: |
|---|
| 1371 | # i = self.boundary_indices[ vol_id, edge_id ] |
|---|
| 1372 | # return self.F(t, point_id = i) |
|---|
| 1373 | #else: |
|---|
| 1374 | # return self.F(t) |
|---|
| 1375 | |
|---|
| 1376 | |
|---|
| 1377 | |
|---|
| 1378 | |
|---|
| 1379 | |
|---|
| 1380 | ######################### |
|---|
| 1381 | #Standard forcing terms: |
|---|
| 1382 | # |
|---|
| 1383 | def gravity(domain): |
|---|
| 1384 | """Apply gravitational pull in the presence of bed slope |
|---|
| 1385 | """ |
|---|
| 1386 | |
|---|
| 1387 | xmom = domain.quantities['xmomentum'].explicit_update |
|---|
| 1388 | ymom = domain.quantities['ymomentum'].explicit_update |
|---|
| 1389 | |
|---|
| 1390 | Stage = domain.quantities['stage'] |
|---|
| 1391 | Elevation = domain.quantities['elevation'] |
|---|
| 1392 | h = Stage.edge_values - Elevation.edge_values |
|---|
| 1393 | v = Elevation.vertex_values |
|---|
| 1394 | |
|---|
| 1395 | x = domain.get_vertex_coordinates() |
|---|
| 1396 | g = domain.g |
|---|
| 1397 | |
|---|
| 1398 | for k in range(len(domain)): |
|---|
| 1399 | avg_h = sum( h[k,:] )/3 |
|---|
| 1400 | |
|---|
| 1401 | #Compute bed slope |
|---|
| 1402 | x0, y0, x1, y1, x2, y2 = x[k,:] |
|---|
| 1403 | z0, z1, z2 = v[k,:] |
|---|
| 1404 | |
|---|
| 1405 | zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
|---|
| 1406 | |
|---|
| 1407 | #Update momentum |
|---|
| 1408 | xmom[k] += -g*zx*avg_h |
|---|
| 1409 | ymom[k] += -g*zy*avg_h |
|---|
| 1410 | |
|---|
| 1411 | |
|---|
| 1412 | def gravity_c(domain): |
|---|
| 1413 | """Wrapper calling C version |
|---|
| 1414 | """ |
|---|
| 1415 | |
|---|
| 1416 | xmom = domain.quantities['xmomentum'].explicit_update |
|---|
| 1417 | ymom = domain.quantities['ymomentum'].explicit_update |
|---|
| 1418 | |
|---|
| 1419 | Stage = domain.quantities['stage'] |
|---|
| 1420 | Elevation = domain.quantities['elevation'] |
|---|
| 1421 | h = Stage.edge_values - Elevation.edge_values |
|---|
| 1422 | v = Elevation.vertex_values |
|---|
| 1423 | |
|---|
| 1424 | x = domain.get_vertex_coordinates() |
|---|
| 1425 | g = domain.g |
|---|
| 1426 | |
|---|
| 1427 | |
|---|
| 1428 | from shallow_water_ext import gravity |
|---|
| 1429 | gravity(g, h, v, x, xmom, ymom) |
|---|
| 1430 | |
|---|
| 1431 | |
|---|
| 1432 | def manning_friction(domain): |
|---|
| 1433 | """Apply (Manning) friction to water momentum |
|---|
| 1434 | (Python version) |
|---|
| 1435 | """ |
|---|
| 1436 | |
|---|
| 1437 | from math import sqrt |
|---|
| 1438 | |
|---|
| 1439 | w = domain.quantities['stage'].centroid_values |
|---|
| 1440 | z = domain.quantities['elevation'].centroid_values |
|---|
| 1441 | h = w-z |
|---|
| 1442 | |
|---|
| 1443 | uh = domain.quantities['xmomentum'].centroid_values |
|---|
| 1444 | vh = domain.quantities['ymomentum'].centroid_values |
|---|
| 1445 | eta = domain.quantities['friction'].centroid_values |
|---|
| 1446 | |
|---|
| 1447 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
|---|
| 1448 | ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
|---|
| 1449 | |
|---|
| 1450 | N = len(domain) |
|---|
| 1451 | eps = domain.minimum_allowed_height |
|---|
| 1452 | g = domain.g |
|---|
| 1453 | |
|---|
| 1454 | for k in range(N): |
|---|
| 1455 | if eta[k] >= eps: |
|---|
| 1456 | if h[k] >= eps: |
|---|
| 1457 | S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
|---|
| 1458 | S /= h[k]**(7.0/3) |
|---|
| 1459 | |
|---|
| 1460 | #Update momentum |
|---|
| 1461 | xmom_update[k] += S*uh[k] |
|---|
| 1462 | ymom_update[k] += S*vh[k] |
|---|
| 1463 | |
|---|
| 1464 | |
|---|
| 1465 | def manning_friction_implicit_c(domain): |
|---|
| 1466 | """Wrapper for c version |
|---|
| 1467 | """ |
|---|
| 1468 | |
|---|
| 1469 | |
|---|
| 1470 | #print 'Implicit friction' |
|---|
| 1471 | |
|---|
| 1472 | xmom = domain.quantities['xmomentum'] |
|---|
| 1473 | ymom = domain.quantities['ymomentum'] |
|---|
| 1474 | |
|---|
| 1475 | w = domain.quantities['stage'].centroid_values |
|---|
| 1476 | z = domain.quantities['elevation'].centroid_values |
|---|
| 1477 | |
|---|
| 1478 | uh = xmom.centroid_values |
|---|
| 1479 | vh = ymom.centroid_values |
|---|
| 1480 | eta = domain.quantities['friction'].centroid_values |
|---|
| 1481 | |
|---|
| 1482 | xmom_update = xmom.semi_implicit_update |
|---|
| 1483 | ymom_update = ymom.semi_implicit_update |
|---|
| 1484 | |
|---|
| 1485 | N = len(domain) |
|---|
| 1486 | eps = domain.minimum_allowed_height |
|---|
| 1487 | g = domain.g |
|---|
| 1488 | |
|---|
| 1489 | from shallow_water_ext import manning_friction |
|---|
| 1490 | manning_friction(g, eps, w, z, uh, vh, eta, xmom_update, ymom_update) |
|---|
| 1491 | |
|---|
| 1492 | |
|---|
| 1493 | def manning_friction_explicit_c(domain): |
|---|
| 1494 | """Wrapper for c version |
|---|
| 1495 | """ |
|---|
| 1496 | |
|---|
| 1497 | #print 'Explicit friction' |
|---|
| 1498 | |
|---|
| 1499 | xmom = domain.quantities['xmomentum'] |
|---|
| 1500 | ymom = domain.quantities['ymomentum'] |
|---|
| 1501 | |
|---|
| 1502 | w = domain.quantities['stage'].centroid_values |
|---|
| 1503 | z = domain.quantities['elevation'].centroid_values |
|---|
| 1504 | |
|---|
| 1505 | uh = xmom.centroid_values |
|---|
| 1506 | vh = ymom.centroid_values |
|---|
| 1507 | eta = domain.quantities['friction'].centroid_values |
|---|
| 1508 | |
|---|
| 1509 | xmom_update = xmom.explicit_update |
|---|
| 1510 | ymom_update = ymom.explicit_update |
|---|
| 1511 | |
|---|
| 1512 | N = len(domain) |
|---|
| 1513 | eps = domain.minimum_allowed_height |
|---|
| 1514 | g = domain.g |
|---|
| 1515 | |
|---|
| 1516 | from shallow_water_ext import manning_friction |
|---|
| 1517 | manning_friction(g, eps, w, z, uh, vh, eta, xmom_update, ymom_update) |
|---|
| 1518 | |
|---|
| 1519 | |
|---|
| 1520 | def linear_friction(domain): |
|---|
| 1521 | """Apply linear friction to water momentum |
|---|
| 1522 | |
|---|
| 1523 | Assumes quantity: 'linear_friction' to be present |
|---|
| 1524 | """ |
|---|
| 1525 | |
|---|
| 1526 | from math import sqrt |
|---|
| 1527 | |
|---|
| 1528 | w = domain.quantities['stage'].centroid_values |
|---|
| 1529 | z = domain.quantities['elevation'].centroid_values |
|---|
| 1530 | h = w-z |
|---|
| 1531 | |
|---|
| 1532 | uh = domain.quantities['xmomentum'].centroid_values |
|---|
| 1533 | vh = domain.quantities['ymomentum'].centroid_values |
|---|
| 1534 | tau = domain.quantities['linear_friction'].centroid_values |
|---|
| 1535 | |
|---|
| 1536 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
|---|
| 1537 | ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
|---|
| 1538 | |
|---|
| 1539 | N = len(domain) # number_of_triangles |
|---|
| 1540 | eps = domain.minimum_allowed_height |
|---|
| 1541 | g = domain.g #Not necessary? Why was this added? |
|---|
| 1542 | |
|---|
| 1543 | for k in range(N): |
|---|
| 1544 | if tau[k] >= eps: |
|---|
| 1545 | if h[k] >= eps: |
|---|
| 1546 | S = -tau[k]/h[k] |
|---|
| 1547 | |
|---|
| 1548 | #Update momentum |
|---|
| 1549 | xmom_update[k] += S*uh[k] |
|---|
| 1550 | ymom_update[k] += S*vh[k] |
|---|
| 1551 | |
|---|
| 1552 | |
|---|
| 1553 | |
|---|
| 1554 | def check_forcefield(f): |
|---|
| 1555 | """Check that f is either |
|---|
| 1556 | 1: a callable object f(t,x,y), where x and y are vectors |
|---|
| 1557 | and that it returns an array or a list of same length |
|---|
| 1558 | as x and y |
|---|
| 1559 | 2: a scalar |
|---|
| 1560 | """ |
|---|
| 1561 | |
|---|
| 1562 | if callable(f): |
|---|
| 1563 | N = 3 |
|---|
| 1564 | x = ones(3, Float) |
|---|
| 1565 | y = ones(3, Float) |
|---|
| 1566 | try: |
|---|
| 1567 | q = f(1.0, x=x, y=y) |
|---|
| 1568 | except Exception, e: |
|---|
| 1569 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
|---|
| 1570 | #FIXME: Reconsider this semantics |
|---|
| 1571 | raise msg |
|---|
| 1572 | |
|---|
| 1573 | try: |
|---|
| 1574 | q = array(q).astype(Float) |
|---|
| 1575 | except: |
|---|
| 1576 | msg = 'Return value from vector function %s could ' %f |
|---|
| 1577 | msg += 'not be converted into a Numeric array of floats.\n' |
|---|
| 1578 | msg += 'Specified function should return either list or array.' |
|---|
| 1579 | raise msg |
|---|
| 1580 | |
|---|
| 1581 | #Is this really what we want? |
|---|
| 1582 | msg = 'Return vector from function %s ' %f |
|---|
| 1583 | msg += 'must have same lenght as input vectors' |
|---|
| 1584 | assert len(q) == N, msg |
|---|
| 1585 | |
|---|
| 1586 | else: |
|---|
| 1587 | try: |
|---|
| 1588 | f = float(f) |
|---|
| 1589 | except: |
|---|
| 1590 | msg = 'Force field %s must be either a scalar' %f |
|---|
| 1591 | msg += ' or a vector function' |
|---|
| 1592 | raise Exception(msg) |
|---|
| 1593 | return f |
|---|
| 1594 | |
|---|
| 1595 | |
|---|
| 1596 | class Wind_stress: |
|---|
| 1597 | """Apply wind stress to water momentum in terms of |
|---|
| 1598 | wind speed [m/s] and wind direction [degrees] |
|---|
| 1599 | """ |
|---|
| 1600 | |
|---|
| 1601 | def __init__(self, *args, **kwargs): |
|---|
| 1602 | """Initialise windfield from wind speed s [m/s] |
|---|
| 1603 | and wind direction phi [degrees] |
|---|
| 1604 | |
|---|
| 1605 | Inputs v and phi can be either scalars or Python functions, e.g. |
|---|
| 1606 | |
|---|
| 1607 | W = Wind_stress(10, 178) |
|---|
| 1608 | |
|---|
| 1609 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
|---|
| 1610 | vector (1,0) has zero degrees. |
|---|
| 1611 | We may need to convert from 'compass' degrees later on and also |
|---|
| 1612 | map from True north to grid north. |
|---|
| 1613 | |
|---|
| 1614 | Arguments can also be Python functions of t,x,y as in |
|---|
| 1615 | |
|---|
| 1616 | def speed(t,x,y): |
|---|
| 1617 | ... |
|---|
| 1618 | return s |
|---|
| 1619 | |
|---|
| 1620 | def angle(t,x,y): |
|---|
| 1621 | ... |
|---|
| 1622 | return phi |
|---|
| 1623 | |
|---|
| 1624 | where x and y are vectors. |
|---|
| 1625 | |
|---|
| 1626 | and then pass the functions in |
|---|
| 1627 | |
|---|
| 1628 | W = Wind_stress(speed, angle) |
|---|
| 1629 | |
|---|
| 1630 | The instantiated object W can be appended to the list of |
|---|
| 1631 | forcing_terms as in |
|---|
| 1632 | |
|---|
| 1633 | Alternatively, one vector valued function for (speed, angle) |
|---|
| 1634 | can be applied, providing both quantities simultaneously. |
|---|
| 1635 | As in |
|---|
| 1636 | W = Wind_stress(F), where returns (speed, angle) for each t. |
|---|
| 1637 | |
|---|
| 1638 | domain.forcing_terms.append(W) |
|---|
| 1639 | """ |
|---|
| 1640 | |
|---|
| 1641 | from anuga.config import rho_a, rho_w, eta_w |
|---|
| 1642 | from Numeric import array, Float |
|---|
| 1643 | |
|---|
| 1644 | if len(args) == 2: |
|---|
| 1645 | s = args[0] |
|---|
| 1646 | phi = args[1] |
|---|
| 1647 | elif len(args) == 1: |
|---|
| 1648 | #Assume vector function returning (s, phi)(t,x,y) |
|---|
| 1649 | vector_function = args[0] |
|---|
| 1650 | s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
|---|
| 1651 | phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
|---|
| 1652 | else: |
|---|
| 1653 | #Assume info is in 2 keyword arguments |
|---|
| 1654 | |
|---|
| 1655 | if len(kwargs) == 2: |
|---|
| 1656 | s = kwargs['s'] |
|---|
| 1657 | phi = kwargs['phi'] |
|---|
| 1658 | else: |
|---|
| 1659 | raise 'Assumes two keyword arguments: s=..., phi=....' |
|---|
| 1660 | |
|---|
| 1661 | self.speed = check_forcefield(s) |
|---|
| 1662 | self.phi = check_forcefield(phi) |
|---|
| 1663 | |
|---|
| 1664 | self.const = eta_w*rho_a/rho_w |
|---|
| 1665 | |
|---|
| 1666 | |
|---|
| 1667 | def __call__(self, domain): |
|---|
| 1668 | """Evaluate windfield based on values found in domain |
|---|
| 1669 | """ |
|---|
| 1670 | |
|---|
| 1671 | from math import pi, cos, sin, sqrt |
|---|
| 1672 | from Numeric import Float, ones, ArrayType |
|---|
| 1673 | |
|---|
| 1674 | xmom_update = domain.quantities['xmomentum'].explicit_update |
|---|
| 1675 | ymom_update = domain.quantities['ymomentum'].explicit_update |
|---|
| 1676 | |
|---|
| 1677 | N = len(domain) # number_of_triangles |
|---|
| 1678 | t = domain.time |
|---|
| 1679 | |
|---|
| 1680 | if callable(self.speed): |
|---|
| 1681 | xc = domain.get_centroid_coordinates() |
|---|
| 1682 | s_vec = self.speed(t, xc[:,0], xc[:,1]) |
|---|
| 1683 | else: |
|---|
| 1684 | #Assume s is a scalar |
|---|
| 1685 | |
|---|
| 1686 | try: |
|---|
| 1687 | s_vec = self.speed * ones(N, Float) |
|---|
| 1688 | except: |
|---|
| 1689 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
|---|
| 1690 | raise msg |
|---|
| 1691 | |
|---|
| 1692 | |
|---|
| 1693 | if callable(self.phi): |
|---|
| 1694 | xc = domain.get_centroid_coordinates() |
|---|
| 1695 | phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
|---|
| 1696 | else: |
|---|
| 1697 | #Assume phi is a scalar |
|---|
| 1698 | |
|---|
| 1699 | try: |
|---|
| 1700 | phi_vec = self.phi * ones(N, Float) |
|---|
| 1701 | except: |
|---|
| 1702 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
|---|
| 1703 | raise msg |
|---|
| 1704 | |
|---|
| 1705 | assign_windfield_values(xmom_update, ymom_update, |
|---|
| 1706 | s_vec, phi_vec, self.const) |
|---|
| 1707 | |
|---|
| 1708 | |
|---|
| 1709 | def assign_windfield_values(xmom_update, ymom_update, |
|---|
| 1710 | s_vec, phi_vec, const): |
|---|
| 1711 | """Python version of assigning wind field to update vectors. |
|---|
| 1712 | A c version also exists (for speed) |
|---|
| 1713 | """ |
|---|
| 1714 | from math import pi, cos, sin, sqrt |
|---|
| 1715 | |
|---|
| 1716 | N = len(s_vec) |
|---|
| 1717 | for k in range(N): |
|---|
| 1718 | s = s_vec[k] |
|---|
| 1719 | phi = phi_vec[k] |
|---|
| 1720 | |
|---|
| 1721 | #Convert to radians |
|---|
| 1722 | phi = phi*pi/180 |
|---|
| 1723 | |
|---|
| 1724 | #Compute velocity vector (u, v) |
|---|
| 1725 | u = s*cos(phi) |
|---|
| 1726 | v = s*sin(phi) |
|---|
| 1727 | |
|---|
| 1728 | #Compute wind stress |
|---|
| 1729 | S = const * sqrt(u**2 + v**2) |
|---|
| 1730 | xmom_update[k] += S*u |
|---|
| 1731 | ymom_update[k] += S*v |
|---|
| 1732 | |
|---|
| 1733 | |
|---|
| 1734 | |
|---|
| 1735 | ############################## |
|---|
| 1736 | #OBSOLETE STUFF |
|---|
| 1737 | |
|---|
| 1738 | def balance_deep_and_shallow_old(domain): |
|---|
| 1739 | """Compute linear combination between stage as computed by |
|---|
| 1740 | gradient-limiters and stage computed as constant height above bed. |
|---|
| 1741 | The former takes precedence when heights are large compared to the |
|---|
| 1742 | bed slope while the latter takes precedence when heights are |
|---|
| 1743 | relatively small. Anything in between is computed as a balanced |
|---|
| 1744 | linear combination in order to avoid numerical disturbances which |
|---|
| 1745 | would otherwise appear as a result of hard switching between |
|---|
| 1746 | modes. |
|---|
| 1747 | """ |
|---|
| 1748 | |
|---|
| 1749 | #OBSOLETE |
|---|
| 1750 | |
|---|
| 1751 | #Shortcuts |
|---|
| 1752 | wc = domain.quantities['stage'].centroid_values |
|---|
| 1753 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 1754 | hc = wc - zc |
|---|
| 1755 | |
|---|
| 1756 | wv = domain.quantities['stage'].vertex_values |
|---|
| 1757 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 1758 | hv = wv-zv |
|---|
| 1759 | |
|---|
| 1760 | |
|---|
| 1761 | #Computed linear combination between constant stages and and |
|---|
| 1762 | #stages parallel to the bed elevation. |
|---|
| 1763 | for k in range(len(domain)): |
|---|
| 1764 | #Compute maximal variation in bed elevation |
|---|
| 1765 | # This quantitiy is |
|---|
| 1766 | # dz = max_i abs(z_i - z_c) |
|---|
| 1767 | # and it is independent of dimension |
|---|
| 1768 | # In the 1d case zc = (z0+z1)/2 |
|---|
| 1769 | # In the 2d case zc = (z0+z1+z2)/3 |
|---|
| 1770 | |
|---|
| 1771 | dz = max(abs(zv[k,0]-zc[k]), |
|---|
| 1772 | abs(zv[k,1]-zc[k]), |
|---|
| 1773 | abs(zv[k,2]-zc[k])) |
|---|
| 1774 | |
|---|
| 1775 | |
|---|
| 1776 | hmin = min( hv[k,:] ) |
|---|
| 1777 | |
|---|
| 1778 | #Create alpha in [0,1], where alpha==0 means using shallow |
|---|
| 1779 | #first order scheme and alpha==1 means using the stage w as |
|---|
| 1780 | #computed by the gradient limiter (1st or 2nd order) |
|---|
| 1781 | # |
|---|
| 1782 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
|---|
| 1783 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
|---|
| 1784 | |
|---|
| 1785 | if dz > 0.0: |
|---|
| 1786 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
|---|
| 1787 | else: |
|---|
| 1788 | #Flat bed |
|---|
| 1789 | alpha = 1.0 |
|---|
| 1790 | |
|---|
| 1791 | #Weighted balance between stage parallel to bed elevation |
|---|
| 1792 | #(wvi = zvi + hc) and stage as computed by 1st or 2nd |
|---|
| 1793 | #order gradient limiter |
|---|
| 1794 | #(wvi = zvi + hvi) where i=0,1,2 denotes the vertex ids |
|---|
| 1795 | # |
|---|
| 1796 | #It follows that the updated wvi is |
|---|
| 1797 | # wvi := (1-alpha)*(zvi+hc) + alpha*(zvi+hvi) = |
|---|
| 1798 | # zvi + hc + alpha*(hvi - hc) |
|---|
| 1799 | # |
|---|
| 1800 | #Note that hvi = zc+hc-zvi in the first order case (constant). |
|---|
| 1801 | |
|---|
| 1802 | if alpha < 1: |
|---|
| 1803 | for i in range(3): |
|---|
| 1804 | wv[k,i] = zv[k,i] + hc[k] + alpha*(hv[k,i]-hc[k]) |
|---|
| 1805 | |
|---|
| 1806 | |
|---|
| 1807 | #Momentums at centroids |
|---|
| 1808 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 1809 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 1810 | |
|---|
| 1811 | #Momentums at vertices |
|---|
| 1812 | xmomv = domain.quantities['xmomentum'].vertex_values |
|---|
| 1813 | ymomv = domain.quantities['ymomentum'].vertex_values |
|---|
| 1814 | |
|---|
| 1815 | # Update momentum as a linear combination of |
|---|
| 1816 | # xmomc and ymomc (shallow) and momentum |
|---|
| 1817 | # from extrapolator xmomv and ymomv (deep). |
|---|
| 1818 | xmomv[k,:] = (1-alpha)*xmomc[k] + alpha*xmomv[k,:] |
|---|
| 1819 | ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
|---|
| 1820 | |
|---|
| 1821 | |
|---|
| 1822 | |
|---|
| 1823 | |
|---|
| 1824 | |
|---|
| 1825 | ########################### |
|---|
| 1826 | ########################### |
|---|
| 1827 | #Geometries |
|---|
| 1828 | |
|---|
| 1829 | |
|---|
| 1830 | #FIXME: Rethink this way of creating values. |
|---|
| 1831 | |
|---|
| 1832 | |
|---|
| 1833 | class Weir: |
|---|
| 1834 | """Set a bathymetry for weir with a hole and a downstream gutter |
|---|
| 1835 | x,y are assumed to be in the unit square |
|---|
| 1836 | """ |
|---|
| 1837 | |
|---|
| 1838 | def __init__(self, stage): |
|---|
| 1839 | self.inflow_stage = stage |
|---|
| 1840 | |
|---|
| 1841 | def __call__(self, x, y): |
|---|
| 1842 | from Numeric import zeros, Float |
|---|
| 1843 | from math import sqrt |
|---|
| 1844 | |
|---|
| 1845 | N = len(x) |
|---|
| 1846 | assert N == len(y) |
|---|
| 1847 | |
|---|
| 1848 | z = zeros(N, Float) |
|---|
| 1849 | for i in range(N): |
|---|
| 1850 | z[i] = -x[i]/2 #General slope |
|---|
| 1851 | |
|---|
| 1852 | #Flattish bit to the left |
|---|
| 1853 | if x[i] < 0.3: |
|---|
| 1854 | z[i] = -x[i]/10 |
|---|
| 1855 | |
|---|
| 1856 | #Weir |
|---|
| 1857 | if x[i] >= 0.3 and x[i] < 0.4: |
|---|
| 1858 | z[i] = -x[i]+0.9 |
|---|
| 1859 | |
|---|
| 1860 | #Dip |
|---|
| 1861 | x0 = 0.6 |
|---|
| 1862 | #depth = -1.3 |
|---|
| 1863 | depth = -1.0 |
|---|
| 1864 | #plateaux = -0.9 |
|---|
| 1865 | plateaux = -0.6 |
|---|
| 1866 | if y[i] < 0.7: |
|---|
| 1867 | if x[i] > x0 and x[i] < 0.9: |
|---|
| 1868 | z[i] = depth |
|---|
| 1869 | |
|---|
| 1870 | #RHS plateaux |
|---|
| 1871 | if x[i] >= 0.9: |
|---|
| 1872 | z[i] = plateaux |
|---|
| 1873 | |
|---|
| 1874 | |
|---|
| 1875 | elif y[i] >= 0.7 and y[i] < 1.5: |
|---|
| 1876 | #Restrict and deepen |
|---|
| 1877 | if x[i] >= x0 and x[i] < 0.8: |
|---|
| 1878 | z[i] = depth-(y[i]/3-0.3) |
|---|
| 1879 | #z[i] = depth-y[i]/5 |
|---|
| 1880 | #z[i] = depth |
|---|
| 1881 | elif x[i] >= 0.8: |
|---|
| 1882 | #RHS plateaux |
|---|
| 1883 | z[i] = plateaux |
|---|
| 1884 | |
|---|
| 1885 | elif y[i] >= 1.5: |
|---|
| 1886 | if x[i] >= x0 and x[i] < 0.8 + (y[i]-1.5)/1.2: |
|---|
| 1887 | #Widen up and stay at constant depth |
|---|
| 1888 | z[i] = depth-1.5/5 |
|---|
| 1889 | elif x[i] >= 0.8 + (y[i]-1.5)/1.2: |
|---|
| 1890 | #RHS plateaux |
|---|
| 1891 | z[i] = plateaux |
|---|
| 1892 | |
|---|
| 1893 | |
|---|
| 1894 | #Hole in weir (slightly higher than inflow condition) |
|---|
| 1895 | if x[i] >= 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1896 | z[i] = -x[i]+self.inflow_stage + 0.02 |
|---|
| 1897 | |
|---|
| 1898 | #Channel behind weir |
|---|
| 1899 | x0 = 0.5 |
|---|
| 1900 | if x[i] >= 0.4 and x[i] < x0 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1901 | z[i] = -x[i]+self.inflow_stage + 0.02 |
|---|
| 1902 | |
|---|
| 1903 | if x[i] >= x0 and x[i] < 0.6 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1904 | #Flatten it out towards the end |
|---|
| 1905 | z[i] = -x0+self.inflow_stage + 0.02 + (x0-x[i])/5 |
|---|
| 1906 | |
|---|
| 1907 | #Hole to the east |
|---|
| 1908 | x0 = 1.1; y0 = 0.35 |
|---|
| 1909 | #if x[i] < -0.2 and y < 0.5: |
|---|
| 1910 | if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: |
|---|
| 1911 | z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-1.0 |
|---|
| 1912 | |
|---|
| 1913 | #Tiny channel draining hole |
|---|
| 1914 | if x[i] >= 1.14 and x[i] < 1.2 and y[i] >= 0.4 and y[i] < 0.6: |
|---|
| 1915 | z[i] = -0.9 #North south |
|---|
| 1916 | |
|---|
| 1917 | if x[i] >= 0.9 and x[i] < 1.18 and y[i] >= 0.58 and y[i] < 0.65: |
|---|
| 1918 | z[i] = -1.0 + (x[i]-0.9)/3 #East west |
|---|
| 1919 | |
|---|
| 1920 | |
|---|
| 1921 | |
|---|
| 1922 | #Stuff not in use |
|---|
| 1923 | |
|---|
| 1924 | #Upward slope at inlet to the north west |
|---|
| 1925 | #if x[i] < 0.0: # and y[i] > 0.5: |
|---|
| 1926 | # #z[i] = -y[i]+0.5 #-x[i]/2 |
|---|
| 1927 | # z[i] = x[i]/4 - y[i]**2 + 0.5 |
|---|
| 1928 | |
|---|
| 1929 | #Hole to the west |
|---|
| 1930 | #x0 = -0.4; y0 = 0.35 # center |
|---|
| 1931 | #if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: |
|---|
| 1932 | # z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-0.2 |
|---|
| 1933 | |
|---|
| 1934 | |
|---|
| 1935 | |
|---|
| 1936 | |
|---|
| 1937 | |
|---|
| 1938 | return z/2 |
|---|
| 1939 | |
|---|
| 1940 | class Weir_simple: |
|---|
| 1941 | """Set a bathymetry for weir with a hole and a downstream gutter |
|---|
| 1942 | x,y are assumed to be in the unit square |
|---|
| 1943 | """ |
|---|
| 1944 | |
|---|
| 1945 | def __init__(self, stage): |
|---|
| 1946 | self.inflow_stage = stage |
|---|
| 1947 | |
|---|
| 1948 | def __call__(self, x, y): |
|---|
| 1949 | from Numeric import zeros, Float |
|---|
| 1950 | |
|---|
| 1951 | N = len(x) |
|---|
| 1952 | assert N == len(y) |
|---|
| 1953 | |
|---|
| 1954 | z = zeros(N, Float) |
|---|
| 1955 | for i in range(N): |
|---|
| 1956 | z[i] = -x[i] #General slope |
|---|
| 1957 | |
|---|
| 1958 | #Flat bit to the left |
|---|
| 1959 | if x[i] < 0.3: |
|---|
| 1960 | z[i] = -x[i]/10 #General slope |
|---|
| 1961 | |
|---|
| 1962 | #Weir |
|---|
| 1963 | if x[i] > 0.3 and x[i] < 0.4: |
|---|
| 1964 | z[i] = -x[i]+0.9 |
|---|
| 1965 | |
|---|
| 1966 | #Dip |
|---|
| 1967 | if x[i] > 0.6 and x[i] < 0.9: |
|---|
| 1968 | z[i] = -x[i]-0.5 #-y[i]/5 |
|---|
| 1969 | |
|---|
| 1970 | #Hole in weir (slightly higher than inflow condition) |
|---|
| 1971 | if x[i] > 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1972 | z[i] = -x[i]+self.inflow_stage + 0.05 |
|---|
| 1973 | |
|---|
| 1974 | |
|---|
| 1975 | return z/2 |
|---|
| 1976 | |
|---|
| 1977 | |
|---|
| 1978 | |
|---|
| 1979 | class Constant_stage: |
|---|
| 1980 | """Set an initial condition with constant stage |
|---|
| 1981 | """ |
|---|
| 1982 | def __init__(self, s): |
|---|
| 1983 | self.s = s |
|---|
| 1984 | |
|---|
| 1985 | def __call__(self, x, y): |
|---|
| 1986 | return self.s |
|---|
| 1987 | |
|---|
| 1988 | class Constant_height: |
|---|
| 1989 | """Set an initial condition with constant water height, e.g |
|---|
| 1990 | stage s = z+h |
|---|
| 1991 | """ |
|---|
| 1992 | |
|---|
| 1993 | def __init__(self, W, h): |
|---|
| 1994 | self.W = W |
|---|
| 1995 | self.h = h |
|---|
| 1996 | |
|---|
| 1997 | def __call__(self, x, y): |
|---|
| 1998 | if self.W is None: |
|---|
| 1999 | from Numeric import ones, Float |
|---|
| 2000 | return self.h*ones(len(x), Float) |
|---|
| 2001 | else: |
|---|
| 2002 | return self.W(x,y) + self.h |
|---|
| 2003 | |
|---|
| 2004 | |
|---|
| 2005 | |
|---|
| 2006 | |
|---|
| 2007 | def compute_fluxes_python(domain): |
|---|
| 2008 | """Compute all fluxes and the timestep suitable for all volumes |
|---|
| 2009 | in domain. |
|---|
| 2010 | |
|---|
| 2011 | Compute total flux for each conserved quantity using "flux_function" |
|---|
| 2012 | |
|---|
| 2013 | Fluxes across each edge are scaled by edgelengths and summed up |
|---|
| 2014 | Resulting flux is then scaled by area and stored in |
|---|
| 2015 | explicit_update for each of the three conserved quantities |
|---|
| 2016 | stage, xmomentum and ymomentum |
|---|
| 2017 | |
|---|
| 2018 | The maximal allowable speed computed by the flux_function for each volume |
|---|
| 2019 | is converted to a timestep that must not be exceeded. The minimum of |
|---|
| 2020 | those is computed as the next overall timestep. |
|---|
| 2021 | |
|---|
| 2022 | Post conditions: |
|---|
| 2023 | domain.explicit_update is reset to computed flux values |
|---|
| 2024 | domain.timestep is set to the largest step satisfying all volumes. |
|---|
| 2025 | """ |
|---|
| 2026 | |
|---|
| 2027 | import sys |
|---|
| 2028 | from Numeric import zeros, Float |
|---|
| 2029 | |
|---|
| 2030 | N = len(domain) # number_of_triangles |
|---|
| 2031 | |
|---|
| 2032 | #Shortcuts |
|---|
| 2033 | Stage = domain.quantities['stage'] |
|---|
| 2034 | Xmom = domain.quantities['xmomentum'] |
|---|
| 2035 | Ymom = domain.quantities['ymomentum'] |
|---|
| 2036 | Bed = domain.quantities['elevation'] |
|---|
| 2037 | |
|---|
| 2038 | #Arrays |
|---|
| 2039 | stage = Stage.edge_values |
|---|
| 2040 | xmom = Xmom.edge_values |
|---|
| 2041 | ymom = Ymom.edge_values |
|---|
| 2042 | bed = Bed.edge_values |
|---|
| 2043 | |
|---|
| 2044 | stage_bdry = Stage.boundary_values |
|---|
| 2045 | xmom_bdry = Xmom.boundary_values |
|---|
| 2046 | ymom_bdry = Ymom.boundary_values |
|---|
| 2047 | |
|---|
| 2048 | flux = zeros((N,3), Float) #Work array for summing up fluxes |
|---|
| 2049 | |
|---|
| 2050 | #Loop |
|---|
| 2051 | timestep = float(sys.maxint) |
|---|
| 2052 | for k in range(N): |
|---|
| 2053 | |
|---|
| 2054 | for i in range(3): |
|---|
| 2055 | #Quantities inside volume facing neighbour i |
|---|
| 2056 | ql = [stage[k, i], xmom[k, i], ymom[k, i]] |
|---|
| 2057 | zl = bed[k, i] |
|---|
| 2058 | |
|---|
| 2059 | #Quantities at neighbour on nearest face |
|---|
| 2060 | n = domain.neighbours[k,i] |
|---|
| 2061 | if n < 0: |
|---|
| 2062 | m = -n-1 #Convert negative flag to index |
|---|
| 2063 | qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] |
|---|
| 2064 | zr = zl #Extend bed elevation to boundary |
|---|
| 2065 | else: |
|---|
| 2066 | m = domain.neighbour_edges[k,i] |
|---|
| 2067 | qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
|---|
| 2068 | zr = bed[n, m] |
|---|
| 2069 | |
|---|
| 2070 | |
|---|
| 2071 | #Outward pointing normal vector |
|---|
| 2072 | normal = domain.normals[k, 2*i:2*i+2] |
|---|
| 2073 | |
|---|
| 2074 | #Flux computation using provided function |
|---|
| 2075 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
|---|
| 2076 | |
|---|
| 2077 | flux[k,:] = edgeflux |
|---|
| 2078 | |
|---|
| 2079 | return flux |
|---|
| 2080 | |
|---|
| 2081 | |
|---|
| 2082 | |
|---|
| 2083 | |
|---|
| 2084 | |
|---|
| 2085 | |
|---|
| 2086 | |
|---|
| 2087 | ############################################## |
|---|
| 2088 | #Initialise module |
|---|
| 2089 | |
|---|
| 2090 | |
|---|
| 2091 | from anuga.utilities import compile |
|---|
| 2092 | if compile.can_use_C_extension('shallow_water_ext.c'): |
|---|
| 2093 | #Replace python version with c implementations |
|---|
| 2094 | |
|---|
| 2095 | from shallow_water_ext import rotate, assign_windfield_values |
|---|
| 2096 | compute_fluxes = compute_fluxes_c |
|---|
| 2097 | extrapolate_second_order_sw=extrapolate_second_order_sw_c |
|---|
| 2098 | gravity = gravity_c |
|---|
| 2099 | manning_friction = manning_friction_implicit_c |
|---|
| 2100 | h_limiter = h_limiter_c |
|---|
| 2101 | balance_deep_and_shallow = balance_deep_and_shallow_c |
|---|
| 2102 | protect_against_infinitesimal_and_negative_heights =\ |
|---|
| 2103 | protect_against_infinitesimal_and_negative_heights_c |
|---|
| 2104 | |
|---|
| 2105 | #distribute_to_vertices_and_edges =\ |
|---|
| 2106 | # distribute_to_vertices_and_edges_c #(like MH's) |
|---|
| 2107 | |
|---|
| 2108 | |
|---|
| 2109 | |
|---|
| 2110 | #Optimisation with psyco |
|---|
| 2111 | from anuga.config import use_psyco |
|---|
| 2112 | if use_psyco: |
|---|
| 2113 | try: |
|---|
| 2114 | import psyco |
|---|
| 2115 | except: |
|---|
| 2116 | import os |
|---|
| 2117 | if os.name == 'posix' and os.uname()[4] == 'x86_64': |
|---|
| 2118 | pass |
|---|
| 2119 | #Psyco isn't supported on 64 bit systems, but it doesn't matter |
|---|
| 2120 | else: |
|---|
| 2121 | msg = 'WARNING: psyco (speedup) could not import'+\ |
|---|
| 2122 | ', you may want to consider installing it' |
|---|
| 2123 | print msg |
|---|
| 2124 | else: |
|---|
| 2125 | psyco.bind(Domain.distribute_to_vertices_and_edges) |
|---|
| 2126 | psyco.bind(Domain.compute_fluxes) |
|---|
| 2127 | |
|---|
| 2128 | if __name__ == "__main__": |
|---|
| 2129 | pass |
|---|
| 2130 | |
|---|
| 2131 | # Profiling stuff |
|---|
| 2132 | #import profile |
|---|
| 2133 | #profiler = profile.Profile() |
|---|
