[5563] | 1 | """Class Domain - |
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| 2 | 1D interval domains for finite-volume computations of |
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| 3 | the shallow water wave equation. |
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| 4 | |
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| 5 | This module contains a specialisation of class Domain from module domain.py |
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| 6 | consisting of methods specific to the Shallow Water Wave Equation |
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| 7 | |
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| 8 | |
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| 9 | U_t + E_x = S |
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| 10 | |
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| 11 | where |
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| 12 | |
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| 13 | U = [w, uh] |
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| 14 | E = [uh, u^2h + gh^2/2] |
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| 15 | S represents source terms forcing the system |
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| 16 | (e.g. gravity, friction, wind stress, ...) |
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| 17 | |
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| 18 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
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| 19 | |
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| 20 | The quantities are |
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| 21 | |
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| 22 | symbol variable name explanation |
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| 23 | x x horizontal distance from origin [m] |
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| 24 | z elevation elevation of bed on which flow is modelled [m] |
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| 25 | h height water height above z [m] |
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| 26 | w stage absolute water level, w = z+h [m] |
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| 27 | u speed in the x direction [m/s] |
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| 28 | uh xmomentum momentum in the x direction [m^2/s] |
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| 29 | |
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| 30 | eta mannings friction coefficient [to appear] |
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| 31 | nu wind stress coefficient [to appear] |
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| 32 | |
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| 33 | The conserved quantities are w, uh |
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| 34 | |
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| 35 | For details see e.g. |
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| 36 | Christopher Zoppou and Stephen Roberts, |
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| 37 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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| 38 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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| 39 | |
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| 40 | |
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| 41 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 42 | Geoscience Australia, 2006 |
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| 43 | """ |
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| 44 | |
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| 45 | #from domain import * |
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| 46 | #from domain_order2 import * |
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| 47 | from domain_t2 import * |
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| 48 | from comp_flux_ext import * |
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| 49 | Generic_Domain = Domain #Rename |
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| 50 | |
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| 51 | #Shallow water domain |
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| 52 | class Domain(Generic_Domain): |
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| 53 | |
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| 54 | def __init__(self, coordinates, boundary = None, tagged_elements = None, |
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| 55 | geo_reference = None): |
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| 56 | |
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| 57 | conserved_quantities = ['stage', 'xmomentum'] |
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| 58 | other_quantities = ['elevation', 'friction'] |
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| 59 | Generic_Domain.__init__(self, coordinates, boundary, |
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| 60 | conserved_quantities, other_quantities, |
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| 61 | tagged_elements, geo_reference) |
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| 62 | |
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| 63 | from config import minimum_allowed_height, g |
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| 64 | self.minimum_allowed_height = minimum_allowed_height |
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| 65 | self.g = g |
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| 66 | |
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| 67 | #forcing terms not included in 1d domain ?WHy? |
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| 68 | self.forcing_terms.append(gravity) |
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| 69 | #self.forcing_terms.append(manning_friction) |
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| 70 | #print "\nI have Removed forcing terms line 64 1dsw" |
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| 71 | |
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| 72 | #Realtime visualisation |
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| 73 | self.visualiser = None |
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| 74 | self.visualise = False |
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| 75 | self.visualise_color_stage = False |
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| 76 | self.visualise_stage_range = 1.0 |
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| 77 | self.visualise_timer = True |
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| 78 | self.visualise_range_z = None |
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| 79 | |
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| 80 | #Stored output |
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| 81 | self.store = True |
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| 82 | self.format = 'sww' |
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| 83 | self.smooth = True |
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| 84 | |
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| 85 | #Evolve parametrs |
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| 86 | self.cfl = 1.0 |
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| 87 | |
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| 88 | #Reduction operation for get_vertex_values |
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| 89 | from util import mean |
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| 90 | self.reduction = mean |
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| 91 | #self.reduction = min #Looks better near steep slopes |
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| 92 | |
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| 93 | self.quantities_to_be_stored = ['stage','xmomentum'] |
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| 94 | |
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| 95 | |
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| 96 | def set_quantities_to_be_stored(self, q): |
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| 97 | """Specify which quantities will be stored in the sww file. |
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| 98 | |
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| 99 | q must be either: |
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| 100 | - the name of a quantity |
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| 101 | - a list of quantity names |
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| 102 | - None |
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| 103 | |
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| 104 | In the two first cases, the named quantities will be stored at each |
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| 105 | yieldstep |
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| 106 | (This is in addition to the quantities elevation and friction) |
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| 107 | If q is None, storage will be switched off altogether. |
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| 108 | """ |
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| 109 | |
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| 110 | |
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| 111 | if q is None: |
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| 112 | self.quantities_to_be_stored = [] |
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| 113 | self.store = False |
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| 114 | return |
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| 115 | |
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| 116 | if isinstance(q, basestring): |
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| 117 | q = [q] # Turn argument into a list |
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| 118 | |
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| 119 | #Check correcness |
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| 120 | for quantity_name in q: |
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| 121 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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| 122 | assert quantity_name in self.conserved_quantities, msg |
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| 123 | |
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| 124 | self.quantities_to_be_stored = q |
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| 125 | |
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| 126 | |
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| 127 | def initialise_visualiser(self,scale_z=1.0,rect=None): |
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| 128 | #Realtime visualisation |
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| 129 | if self.visualiser is None: |
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| 130 | from realtime_visualisation_new import Visualiser |
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| 131 | self.visualiser = Visualiser(self,scale_z,rect) |
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| 132 | self.visualiser.setup['elevation']=True |
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| 133 | self.visualiser.updating['stage']=True |
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| 134 | self.visualise = True |
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| 135 | if self.visualise_color_stage == True: |
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| 136 | self.visualiser.coloring['stage'] = True |
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| 137 | self.visualiser.qcolor['stage'] = (0.0, 0.0, 0.8) |
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| 138 | print 'initialise visualiser' |
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| 139 | print self.visualiser.setup |
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| 140 | print self.visualiser.updating |
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| 141 | |
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| 142 | def check_integrity(self): |
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| 143 | Generic_Domain.check_integrity(self) |
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| 144 | #Check that we are solving the shallow water wave equation |
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| 145 | |
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| 146 | msg = 'First conserved quantity must be "stage"' |
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| 147 | assert self.conserved_quantities[0] == 'stage', msg |
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| 148 | msg = 'Second conserved quantity must be "xmomentum"' |
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| 149 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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| 150 | |
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| 151 | def extrapolate_second_order_sw(self): |
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| 152 | #Call correct module function |
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| 153 | #(either from this module or C-extension) |
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| 154 | extrapolate_second_order_sw(self) |
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| 155 | |
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| 156 | def compute_fluxes(self): |
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| 157 | #Call correct module function |
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| 158 | #(either from this module or C-extension) |
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| 159 | compute_fluxes(self) |
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| 160 | |
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| 161 | def compute_timestep(self): |
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| 162 | #Call correct module function |
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| 163 | compute_timestep(self) |
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| 164 | |
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| 165 | def distribute_to_vertices_and_edges(self): |
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| 166 | #Call correct module function |
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| 167 | #(either from this module or C-extension) |
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| 168 | distribute_to_vertices_and_edges(self) |
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| 169 | |
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| 170 | def evolve(self, yieldstep = None, finaltime = None, |
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| 171 | skip_initial_step = False): |
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| 172 | """Specialisation of basic evolve method from parent class |
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| 173 | """ |
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| 174 | |
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| 175 | #Call check integrity here rather than from user scripts |
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| 176 | #self.check_integrity() |
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| 177 | |
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| 178 | #msg = 'Parameter beta_h must be in the interval [0, 1)' |
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| 179 | #assert 0 <= self.beta_h < 1.0, msg |
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| 180 | #msg = 'Parameter beta_w must be in the interval [0, 1)' |
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| 181 | #assert 0 <= self.beta_w < 1.0, msg |
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| 182 | |
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| 183 | |
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| 184 | #Initial update of vertex and edge values before any storage |
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| 185 | #and or visualisation |
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| 186 | |
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| 187 | self.distribute_to_vertices_and_edges() |
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| 188 | |
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| 189 | #Call basic machinery from parent class |
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| 190 | for t in Generic_Domain.evolve(self, yieldstep, finaltime, |
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| 191 | skip_initial_step): |
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| 192 | yield(t) |
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| 193 | |
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| 194 | def initialise_storage(self): |
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| 195 | """Create and initialise self.writer object for storing data. |
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| 196 | Also, save x and bed elevation |
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| 197 | """ |
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| 198 | |
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| 199 | import data_manager |
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| 200 | |
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| 201 | #Initialise writer |
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| 202 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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| 203 | |
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| 204 | #Store vertices and connectivity |
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| 205 | self.writer.store_connectivity() |
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| 206 | |
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| 207 | |
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| 208 | def store_timestep(self, name): |
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| 209 | """Store named quantity and time. |
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| 210 | |
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| 211 | Precondition: |
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| 212 | self.write has been initialised |
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| 213 | """ |
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| 214 | self.writer.store_timestep(name) |
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| 215 | |
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| 216 | |
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| 217 | #=============== End of Shallow Water Domain =============================== |
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| 218 | |
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| 219 | #Rotation of momentum vector |
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| 220 | def rotate(q, normal, direction = 1): |
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| 221 | """Rotate the momentum component q (q[1], q[2]) |
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| 222 | from x,y coordinates to coordinates based on normal vector. |
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| 223 | |
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| 224 | If direction is negative the rotation is inverted. |
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| 225 | |
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| 226 | Input vector is preserved |
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| 227 | |
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| 228 | This function is specific to the shallow water wave equation |
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| 229 | """ |
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| 230 | |
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| 231 | from Numeric import zeros, Float |
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| 232 | |
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| 233 | assert len(q) == 3,\ |
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| 234 | 'Vector of conserved quantities must have length 3'\ |
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| 235 | 'for 2D shallow water equation' |
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| 236 | |
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| 237 | try: |
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| 238 | l = len(normal) |
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| 239 | except: |
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| 240 | raise 'Normal vector must be an Numeric array' |
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| 241 | |
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| 242 | assert l == 2, 'Normal vector must have 2 components' |
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| 243 | |
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| 244 | |
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| 245 | n1 = normal[0] |
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| 246 | n2 = normal[1] |
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| 247 | |
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| 248 | r = zeros(len(q), Float) #Rotated quantities |
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| 249 | r[0] = q[0] #First quantity, height, is not rotated |
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| 250 | |
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| 251 | if direction == -1: |
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| 252 | n2 = -n2 |
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| 253 | |
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| 254 | |
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| 255 | r[1] = n1*q[1] + n2*q[2] |
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| 256 | r[2] = -n2*q[1] + n1*q[2] |
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| 257 | |
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| 258 | return r |
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| 259 | """++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++""" |
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| 260 | # Compute flux definition |
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| 261 | def compute_fluxes(domain): |
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| 262 | from Numeric import zeros, Float |
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| 263 | import sys |
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| 264 | |
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| 265 | timestep = float(sys.maxint) |
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| 266 | print 'timestep=',timestep |
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| 267 | print 'The type of timestep is',type(timestep) |
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| 268 | |
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| 269 | epsilon = domain.epsilon |
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| 270 | print 'epsilon=',epsilon |
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| 271 | print 'The type of epsilon is',type(epsilon) |
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| 272 | |
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| 273 | g = domain.g |
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| 274 | print 'g=',g |
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| 275 | print 'The type of g is',type(g) |
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| 276 | |
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| 277 | neighbours = domain.neighbours |
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| 278 | print 'neighbours=',neighbours |
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| 279 | print 'The type of neighbours is',type(neighbours) |
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| 280 | |
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| 281 | neighbour_vertices = domain.neighbour_vertices |
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| 282 | print 'neighbour_vertices=',neighbour_vertices |
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| 283 | print 'The type of neighbour_vertices is',type(neighbour_vertices) |
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| 284 | |
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| 285 | normals = domain.normals |
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| 286 | print 'normals=',normals |
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| 287 | print 'The type of normals is',type(normals) |
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| 288 | |
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| 289 | areas = domain.areas |
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| 290 | print 'areas=',areas |
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| 291 | print 'The type of areas is',type(areas) |
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| 292 | |
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| 293 | stage_edge_values = domain.quantities['stage'].vertex_values |
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| 294 | print 'stage_edge_values=',stage_edge_values |
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| 295 | print 'The type of stage_edge_values is',type(stage_edge_values) |
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| 296 | |
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| 297 | xmom_edge_values = domain.quantities['xmomentum'].vertex_values |
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| 298 | print 'xmom_edge_values=',xmom_edge_values |
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| 299 | print 'The type of xmom_edge_values is',type(xmom_edge_values) |
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| 300 | |
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| 301 | bed_edge_values = domain.quantities['elevation'].vertex_values |
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| 302 | print 'bed_edge_values=',bed_edge_values |
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| 303 | print 'The type of bed_edge_values is',type(bed_edge_values) |
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| 304 | |
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| 305 | stage_boundary_values = domain.quantities['stage'].boundary_values |
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| 306 | print 'stage_boundary_values=',stage_boundary_values |
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| 307 | print 'The type of stage_boundary_values is',type(stage_boundary_values) |
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| 308 | |
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| 309 | xmom_boundary_values = domain.quantities['xmomentum'].boundary_values |
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| 310 | print 'xmom_boundary_values=',xmom_boundary_values |
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| 311 | print 'The type of xmom_boundary_values is',type(xmom_boundary_values) |
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| 312 | |
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| 313 | stage_explicit_update = domain.quantities['stage'].explicit_update |
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| 314 | print 'stage_explicit_update=',stage_explicit_update |
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| 315 | print 'The type of stage_explicit_update is',type(stage_explicit_update) |
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| 316 | |
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| 317 | xmom_explicit_update = domain.quantities['xmomentum'].explicit_update |
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| 318 | print 'xmom_explicit_update=',xmom_explicit_update |
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| 319 | print 'The type of xmom_explicit_update is',type(xmom_explicit_update) |
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| 320 | |
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| 321 | number_of_elements = len(stage_edge_values) |
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| 322 | print 'number_of_elements=',number_of_elements |
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| 323 | print 'The type of number_of_elements is',type(number_of_elements) |
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| 324 | |
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| 325 | max_speed_array = zeros(number_of_elements, Float) |
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| 326 | print 'max_speed_array=',max_speed_array |
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| 327 | print 'The type of max_speed_array is',type(max_speed_array) |
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| 328 | |
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| 329 | return compute_fluxes_ext(timestep, epsilon, g, neighbours, neighbour_vertices, normals, areas, |
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| 330 | stage_edge_values, xmom_edge_values, bed_edge_values, stage_boundary_values, xmom_boundary_values, |
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| 331 | number_of_elements, max_speed_array) |
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| 332 | #################################### |
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| 333 | |
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| 334 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
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| 335 | |
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| 336 | def distribute_to_vertices_and_edges(domain): |
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| 337 | """Distribution from centroids to vertices specific to the |
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| 338 | shallow water wave |
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| 339 | equation. |
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| 340 | |
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| 341 | It will ensure that h (w-z) is always non-negative even in the |
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| 342 | presence of steep bed-slopes by taking a weighted average between shallow |
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| 343 | and deep cases. |
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| 344 | |
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| 345 | In addition, all conserved quantities get distributed as per either a |
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| 346 | constant (order==1) or a piecewise linear function (order==2). |
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| 347 | |
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| 348 | FIXME: more explanation about removal of artificial variability etc |
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| 349 | |
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| 350 | Precondition: |
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| 351 | All quantities defined at centroids and bed elevation defined at |
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| 352 | vertices. |
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| 353 | |
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| 354 | Postcondition |
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| 355 | Conserved quantities defined at vertices |
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| 356 | |
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| 357 | """ |
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| 358 | |
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| 359 | #from config import optimised_gradient_limiter |
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| 360 | |
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| 361 | #Remove very thin layers of water |
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| 362 | protect_against_infinitesimal_and_negative_heights(domain) |
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| 363 | |
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| 364 | |
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| 365 | #Extrapolate all conserved quantities |
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| 366 | #if optimised_gradient_limiter: |
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| 367 | # #MH090605 if second order, |
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| 368 | # #perform the extrapolation and limiting on |
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| 369 | # #all of the conserved quantities |
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| 370 | |
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| 371 | # if (domain.order == 1): |
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| 372 | # for name in domain.conserved_quantities: |
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| 373 | # Q = domain.quantities[name] |
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| 374 | # Q.extrapolate_first_order() |
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| 375 | # elif domain.order == 2: |
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| 376 | # domain.extrapolate_second_order_sw() |
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| 377 | # else: |
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| 378 | # raise 'Unknown order' |
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| 379 | #else: |
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| 380 | #old code: |
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| 381 | |
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| 382 | for name in domain.conserved_quantities: |
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| 383 | Q = domain.quantities[name] |
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| 384 | if domain.order == 1: |
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| 385 | Q.extrapolate_first_order() |
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| 386 | elif domain.order == 2: |
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| 387 | #print "add extrapolate second order to shallow water" |
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| 388 | #if name != 'height': |
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| 389 | Q.extrapolate_second_order() |
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| 390 | #Q.limit() |
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| 391 | else: |
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| 392 | raise 'Unknown order' |
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| 393 | |
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| 394 | #Take bed elevation into account when water heights are small |
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| 395 | #balance_deep_and_shallow(domain) |
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| 396 | #protect_against_infinitesimal_and_negative_heights(domain) |
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| 397 | |
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| 398 | #Compute edge values by interpolation |
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| 399 | #for name in domain.conserved_quantities: |
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| 400 | # Q = domain.quantities[name] |
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| 401 | # Q.interpolate_from_vertices_to_edges() |
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| 402 | |
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| 403 | def protect_against_infinitesimal_and_negative_heights(domain): |
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| 404 | """Protect against infinitesimal heights and associated high velocities |
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| 405 | """ |
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| 406 | |
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| 407 | #Shortcuts |
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| 408 | wc = domain.quantities['stage'].centroid_values |
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| 409 | zc = domain.quantities['elevation'].centroid_values |
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| 410 | xmomc = domain.quantities['xmomentum'].centroid_values |
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| 411 | # ymomc = domain.quantities['ymomentum'].centroid_values |
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| 412 | hc = wc - zc #Water depths at centroids |
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| 413 | |
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| 414 | zv = domain.quantities['elevation'].vertex_values |
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| 415 | wv = domain.quantities['stage'].vertex_values |
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| 416 | hv = wv-zv |
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| 417 | xmomv = domain.quantities['xmomentum'].vertex_values |
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| 418 | #remove the above two lines and corresponding code below |
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| 419 | |
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| 420 | #Update |
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| 421 | for k in range(domain.number_of_elements): |
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| 422 | |
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| 423 | if hc[k] < domain.minimum_allowed_height: |
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| 424 | #Control stage |
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| 425 | if hc[k] < domain.epsilon: |
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| 426 | wc[k] = zc[k] # Contain 'lost mass' error |
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| 427 | wv[k,0] = zv[k,0] |
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| 428 | wv[k,1] = zv[k,1] |
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| 429 | |
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| 430 | xmomc[k] = 0.0 |
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| 431 | |
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| 432 | #N = domain.number_of_elements |
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| 433 | #if (k == 0) | (k==N-1): |
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| 434 | # wc[k] = zc[k] # Contain 'lost mass' error |
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| 435 | # wv[k,0] = zv[k,0] |
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| 436 | # wv[k,1] = zv[k,1] |
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| 437 | |
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| 438 | def h_limiter(domain): |
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| 439 | """Limit slopes for each volume to eliminate artificial variance |
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| 440 | introduced by e.g. second order extrapolator |
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| 441 | |
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| 442 | limit on h = w-z |
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| 443 | |
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| 444 | This limiter depends on two quantities (w,z) so it resides within |
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| 445 | this module rather than within quantity.py |
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| 446 | """ |
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| 447 | |
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| 448 | from Numeric import zeros, Float |
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| 449 | |
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| 450 | N = domain.number_of_elements |
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| 451 | beta_h = domain.beta_h |
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| 452 | |
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| 453 | #Shortcuts |
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| 454 | wc = domain.quantities['stage'].centroid_values |
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| 455 | zc = domain.quantities['elevation'].centroid_values |
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| 456 | hc = wc - zc |
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| 457 | |
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| 458 | wv = domain.quantities['stage'].vertex_values |
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| 459 | zv = domain.quantities['elevation'].vertex_values |
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| 460 | hv = wv-zv |
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| 461 | |
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| 462 | hvbar = zeros(hv.shape, Float) #h-limited values |
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| 463 | |
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| 464 | #Find min and max of this and neighbour's centroid values |
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| 465 | hmax = zeros(hc.shape, Float) |
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| 466 | hmin = zeros(hc.shape, Float) |
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| 467 | |
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| 468 | for k in range(N): |
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| 469 | hmax[k] = hmin[k] = hc[k] |
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| 470 | #for i in range(3): |
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| 471 | for i in range(2): |
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| 472 | n = domain.neighbours[k,i] |
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| 473 | if n >= 0: |
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| 474 | hn = hc[n] #Neighbour's centroid value |
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| 475 | |
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| 476 | hmin[k] = min(hmin[k], hn) |
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| 477 | hmax[k] = max(hmax[k], hn) |
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| 478 | |
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| 479 | |
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| 480 | #Diffences between centroids and maxima/minima |
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| 481 | dhmax = hmax - hc |
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| 482 | dhmin = hmin - hc |
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| 483 | |
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| 484 | #Deltas between vertex and centroid values |
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| 485 | dh = zeros(hv.shape, Float) |
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| 486 | #for i in range(3): |
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| 487 | for i in range(2): |
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| 488 | dh[:,i] = hv[:,i] - hc |
---|
| 489 | |
---|
| 490 | #Phi limiter |
---|
| 491 | for k in range(N): |
---|
| 492 | |
---|
| 493 | #Find the gradient limiter (phi) across vertices |
---|
| 494 | phi = 1.0 |
---|
| 495 | #for i in range(3): |
---|
| 496 | for i in range(2): |
---|
| 497 | r = 1.0 |
---|
| 498 | if (dh[k,i] > 0): r = dhmax[k]/dh[k,i] |
---|
| 499 | if (dh[k,i] < 0): r = dhmin[k]/dh[k,i] |
---|
| 500 | |
---|
| 501 | phi = min( min(r*beta_h, 1), phi ) |
---|
| 502 | |
---|
| 503 | #Then update using phi limiter |
---|
| 504 | #for i in range(3): |
---|
| 505 | for i in range(2): |
---|
| 506 | hvbar[k,i] = hc[k] + phi*dh[k,i] |
---|
| 507 | |
---|
| 508 | return hvbar |
---|
| 509 | |
---|
| 510 | def balance_deep_and_shallow(domain): |
---|
| 511 | """Compute linear combination between stage as computed by |
---|
| 512 | gradient-limiters limiting using w, and stage computed by |
---|
| 513 | gradient-limiters limiting using h (h-limiter). |
---|
| 514 | The former takes precedence when heights are large compared to the |
---|
| 515 | bed slope while the latter takes precedence when heights are |
---|
| 516 | relatively small. Anything in between is computed as a balanced |
---|
| 517 | linear combination in order to avoid numerical disturbances which |
---|
| 518 | would otherwise appear as a result of hard switching between |
---|
| 519 | modes. |
---|
| 520 | |
---|
| 521 | The h-limiter is always applied irrespective of the order. |
---|
| 522 | """ |
---|
| 523 | |
---|
| 524 | #Shortcuts |
---|
| 525 | wc = domain.quantities['stage'].centroid_values |
---|
| 526 | zc = domain.quantities['elevation'].centroid_values |
---|
| 527 | hc = wc - zc |
---|
| 528 | |
---|
| 529 | wv = domain.quantities['stage'].vertex_values |
---|
| 530 | zv = domain.quantities['elevation'].vertex_values |
---|
| 531 | hv = wv-zv |
---|
| 532 | |
---|
| 533 | #Limit h |
---|
| 534 | hvbar = h_limiter(domain) |
---|
| 535 | |
---|
| 536 | for k in range(domain.number_of_elements): |
---|
| 537 | #Compute maximal variation in bed elevation |
---|
| 538 | # This quantitiy is |
---|
| 539 | # dz = max_i abs(z_i - z_c) |
---|
| 540 | # and it is independent of dimension |
---|
| 541 | # In the 1d case zc = (z0+z1)/2 |
---|
| 542 | # In the 2d case zc = (z0+z1+z2)/3 |
---|
| 543 | |
---|
| 544 | dz = max(abs(zv[k,0]-zc[k]), |
---|
| 545 | abs(zv[k,1]-zc[k]))#, |
---|
| 546 | # abs(zv[k,2]-zc[k])) |
---|
| 547 | |
---|
| 548 | |
---|
| 549 | hmin = min( hv[k,:] ) |
---|
| 550 | |
---|
| 551 | #Create alpha in [0,1], where alpha==0 means using the h-limited |
---|
| 552 | #stage and alpha==1 means using the w-limited stage as |
---|
| 553 | #computed by the gradient limiter (both 1st or 2nd order) |
---|
| 554 | |
---|
| 555 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
---|
| 556 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
---|
| 557 | |
---|
| 558 | if dz > 0.0: |
---|
| 559 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
---|
| 560 | else: |
---|
| 561 | #Flat bed |
---|
| 562 | alpha = 1.0 |
---|
| 563 | |
---|
| 564 | alpha = 0.0 |
---|
| 565 | #Let |
---|
| 566 | # |
---|
| 567 | # wvi be the w-limited stage (wvi = zvi + hvi) |
---|
| 568 | # wvi- be the h-limited state (wvi- = zvi + hvi-) |
---|
| 569 | # |
---|
| 570 | # |
---|
| 571 | #where i=0,1,2 denotes the vertex ids |
---|
| 572 | # |
---|
| 573 | #Weighted balance between w-limited and h-limited stage is |
---|
| 574 | # |
---|
| 575 | # wvi := (1-alpha)*(zvi+hvi-) + alpha*(zvi+hvi) |
---|
| 576 | # |
---|
| 577 | #It follows that the updated wvi is |
---|
| 578 | # wvi := zvi + (1-alpha)*hvi- + alpha*hvi |
---|
| 579 | # |
---|
| 580 | # Momentum is balanced between constant and limited |
---|
| 581 | |
---|
| 582 | |
---|
| 583 | #for i in range(3): |
---|
| 584 | # wv[k,i] = zv[k,i] + hvbar[k,i] |
---|
| 585 | |
---|
| 586 | #return |
---|
| 587 | |
---|
| 588 | if alpha < 1: |
---|
| 589 | |
---|
| 590 | #for i in range(3): |
---|
| 591 | for i in range(2): |
---|
| 592 | wv[k,i] = zv[k,i] + (1.0-alpha)*hvbar[k,i] + alpha*hv[k,i] |
---|
| 593 | |
---|
| 594 | #Momentums at centroids |
---|
| 595 | xmomc = domain.quantities['xmomentum'].centroid_values |
---|
| 596 | # ymomc = domain.quantities['ymomentum'].centroid_values |
---|
| 597 | |
---|
| 598 | #Momentums at vertices |
---|
| 599 | xmomv = domain.quantities['xmomentum'].vertex_values |
---|
| 600 | # ymomv = domain.quantities['ymomentum'].vertex_values |
---|
| 601 | |
---|
| 602 | # Update momentum as a linear combination of |
---|
| 603 | # xmomc and ymomc (shallow) and momentum |
---|
| 604 | # from extrapolator xmomv and ymomv (deep). |
---|
| 605 | xmomv[k,:] = (1.0-alpha)*xmomc[k] + alpha*xmomv[k,:] |
---|
| 606 | # ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
---|
| 607 | |
---|
| 608 | |
---|
| 609 | ############################################### |
---|
| 610 | #Boundaries - specific to the shallow water wave equation |
---|
| 611 | class Reflective_boundary(Boundary): |
---|
| 612 | """Reflective boundary returns same conserved quantities as |
---|
| 613 | those present in its neighbour volume but reflected. |
---|
| 614 | |
---|
| 615 | This class is specific to the shallow water equation as it |
---|
| 616 | works with the momentum quantities assumed to be the second |
---|
| 617 | and third conserved quantities. |
---|
| 618 | """ |
---|
| 619 | |
---|
| 620 | def __init__(self, domain = None): |
---|
| 621 | Boundary.__init__(self) |
---|
| 622 | |
---|
| 623 | if domain is None: |
---|
| 624 | msg = 'Domain must be specified for reflective boundary' |
---|
| 625 | raise msg |
---|
| 626 | |
---|
| 627 | #Handy shorthands |
---|
| 628 | #self.stage = domain.quantities['stage'].edge_values |
---|
| 629 | #self.xmom = domain.quantities['xmomentum'].edge_values |
---|
| 630 | #self.ymom = domain.quantities['ymomentum'].edge_values |
---|
| 631 | self.normals = domain.normals |
---|
| 632 | self.stage = domain.quantities['stage'].vertex_values |
---|
| 633 | self.xmom = domain.quantities['xmomentum'].vertex_values |
---|
| 634 | |
---|
| 635 | from Numeric import zeros, Float |
---|
| 636 | #self.conserved_quantities = zeros(3, Float) |
---|
| 637 | self.conserved_quantities = zeros(2, Float) |
---|
| 638 | |
---|
| 639 | def __repr__(self): |
---|
| 640 | return 'Reflective_boundary' |
---|
| 641 | |
---|
| 642 | |
---|
| 643 | def evaluate(self, vol_id, edge_id): |
---|
| 644 | """Reflective boundaries reverses the outward momentum |
---|
| 645 | of the volume they serve. |
---|
| 646 | """ |
---|
| 647 | |
---|
| 648 | q = self.conserved_quantities |
---|
| 649 | q[0] = self.stage[vol_id, edge_id] |
---|
| 650 | q[1] = self.xmom[vol_id, edge_id] |
---|
| 651 | #q[2] = self.ymom[vol_id, edge_id] |
---|
| 652 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
---|
| 653 | #normal = self.normals[vol_id, 2*edge_id:2*edge_id+1] |
---|
| 654 | normal = self.normals[vol_id,edge_id] |
---|
| 655 | |
---|
| 656 | #r = rotate(q, normal, direction = 1) |
---|
| 657 | #r[1] = -r[1] |
---|
| 658 | #q = rotate(r, normal, direction = -1) |
---|
| 659 | r = q |
---|
| 660 | r[1] = normal*r[1] |
---|
| 661 | r[1] = -r[1] |
---|
| 662 | r[1] = normal*r[1] |
---|
| 663 | q = r |
---|
| 664 | #For start interval there is no outward momentum so do not need to |
---|
| 665 | #reverse direction in this case |
---|
| 666 | |
---|
| 667 | return q |
---|
| 668 | |
---|
| 669 | class Dirichlet_boundary(Boundary): |
---|
| 670 | """Dirichlet boundary returns constant values for the |
---|
| 671 | conserved quantities |
---|
| 672 | """ |
---|
| 673 | |
---|
| 674 | |
---|
| 675 | def __init__(self, conserved_quantities=None): |
---|
| 676 | Boundary.__init__(self) |
---|
| 677 | |
---|
| 678 | if conserved_quantities is None: |
---|
| 679 | msg = 'Must specify one value for each conserved quantity' |
---|
| 680 | raise msg |
---|
| 681 | |
---|
| 682 | from Numeric import array, Float |
---|
| 683 | self.conserved_quantities=array(conserved_quantities).astype(Float) |
---|
| 684 | |
---|
| 685 | def __repr__(self): |
---|
| 686 | return 'Dirichlet boundary (%s)' %self.conserved_quantities |
---|
| 687 | |
---|
| 688 | def evaluate(self, vol_id=None, edge_id=None): |
---|
| 689 | return self.conserved_quantities |
---|
| 690 | |
---|
| 691 | |
---|
| 692 | ######################### |
---|
| 693 | #Standard forcing terms: |
---|
| 694 | # |
---|
| 695 | def gravity(domain): |
---|
| 696 | """Apply gravitational pull in the presence of bed slope |
---|
| 697 | """ |
---|
| 698 | |
---|
| 699 | from util import gradient |
---|
| 700 | from Numeric import zeros, Float, array, sum |
---|
| 701 | |
---|
| 702 | xmom = domain.quantities['xmomentum'].explicit_update |
---|
| 703 | stage = domain.quantities['stage'].explicit_update |
---|
| 704 | # ymom = domain.quantities['ymomentum'].explicit_update |
---|
| 705 | |
---|
| 706 | Stage = domain.quantities['stage'] |
---|
| 707 | Elevation = domain.quantities['elevation'] |
---|
| 708 | #h = Stage.edge_values - Elevation.edge_values |
---|
| 709 | h = Stage.vertex_values - Elevation.vertex_values |
---|
| 710 | b = Elevation.vertex_values |
---|
| 711 | w = Stage.vertex_values |
---|
| 712 | |
---|
| 713 | x = domain.get_vertex_coordinates() |
---|
| 714 | g = domain.g |
---|
| 715 | |
---|
| 716 | for k in range(domain.number_of_elements): |
---|
| 717 | # avg_h = sum( h[k,:] )/3 |
---|
| 718 | avg_h = sum( h[k,:] )/2 |
---|
| 719 | |
---|
| 720 | #Compute bed slope |
---|
| 721 | #x0, y0, x1, y1, x2, y2 = x[k,:] |
---|
| 722 | x0, x1 = x[k,:] |
---|
| 723 | #z0, z1, z2 = v[k,:] |
---|
| 724 | b0, b1 = b[k,:] |
---|
| 725 | |
---|
| 726 | w0, w1 = w[k,:] |
---|
| 727 | wx = gradient(x0, x1, w0, w1) |
---|
| 728 | |
---|
| 729 | #zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
---|
| 730 | bx = gradient(x0, x1, b0, b1) |
---|
| 731 | |
---|
| 732 | #Update momentum (explicit update is reset to source values) |
---|
| 733 | if domain.split == False: |
---|
| 734 | xmom[k] += -g*bx*avg_h |
---|
| 735 | #xmom[k] = -g*bx*avg_h |
---|
| 736 | #stage[k] = 0.0 |
---|
| 737 | elif domain.split == True: |
---|
| 738 | xmom[k] += -g*wx*avg_h |
---|
| 739 | #xmom[k] = -g*wx*avg_h |
---|
| 740 | #ymom[k] += -g*zy*avg_h |
---|
| 741 | |
---|
| 742 | def manning_friction(domain): |
---|
| 743 | """Apply (Manning) friction to water momentum |
---|
| 744 | """ |
---|
| 745 | |
---|
| 746 | from math import sqrt |
---|
| 747 | |
---|
| 748 | w = domain.quantities['stage'].centroid_values |
---|
| 749 | z = domain.quantities['elevation'].centroid_values |
---|
| 750 | h = w-z |
---|
| 751 | |
---|
| 752 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 753 | #vh = domain.quantities['ymomentum'].centroid_values |
---|
| 754 | eta = domain.quantities['friction'].centroid_values |
---|
| 755 | |
---|
| 756 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 757 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
| 758 | |
---|
| 759 | N = domain.number_of_elements |
---|
| 760 | eps = domain.minimum_allowed_height |
---|
| 761 | g = domain.g |
---|
| 762 | |
---|
| 763 | for k in range(N): |
---|
| 764 | if eta[k] >= eps: |
---|
| 765 | if h[k] >= eps: |
---|
| 766 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
---|
| 767 | S = -g * eta[k]**2 * uh[k] |
---|
| 768 | S /= h[k]**(7.0/3) |
---|
| 769 | |
---|
| 770 | #Update momentum |
---|
| 771 | xmom_update[k] += S*uh[k] |
---|
| 772 | #ymom_update[k] += S*vh[k] |
---|
| 773 | |
---|
| 774 | def linear_friction(domain): |
---|
| 775 | """Apply linear friction to water momentum |
---|
| 776 | |
---|
| 777 | Assumes quantity: 'linear_friction' to be present |
---|
| 778 | """ |
---|
| 779 | |
---|
| 780 | from math import sqrt |
---|
| 781 | |
---|
| 782 | w = domain.quantities['stage'].centroid_values |
---|
| 783 | z = domain.quantities['elevation'].centroid_values |
---|
| 784 | h = w-z |
---|
| 785 | |
---|
| 786 | uh = domain.quantities['xmomentum'].centroid_values |
---|
| 787 | # vh = domain.quantities['ymomentum'].centroid_values |
---|
| 788 | tau = domain.quantities['linear_friction'].centroid_values |
---|
| 789 | |
---|
| 790 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
---|
| 791 | # ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
---|
| 792 | |
---|
| 793 | N = domain.number_of_elements |
---|
| 794 | eps = domain.minimum_allowed_height |
---|
| 795 | g = domain.g #Not necessary? Why was this added? |
---|
| 796 | |
---|
| 797 | for k in range(N): |
---|
| 798 | if tau[k] >= eps: |
---|
| 799 | if h[k] >= eps: |
---|
| 800 | S = -tau[k]/h[k] |
---|
| 801 | |
---|
| 802 | #Update momentum |
---|
| 803 | xmom_update[k] += S*uh[k] |
---|
| 804 | # ymom_update[k] += S*vh[k] |
---|
| 805 | |
---|
| 806 | |
---|
| 807 | |
---|
| 808 | def check_forcefield(f): |
---|
| 809 | """Check that f is either |
---|
| 810 | 1: a callable object f(t,x,y), where x and y are vectors |
---|
| 811 | and that it returns an array or a list of same length |
---|
| 812 | as x and y |
---|
| 813 | 2: a scalar |
---|
| 814 | """ |
---|
| 815 | |
---|
| 816 | from Numeric import ones, Float, array |
---|
| 817 | |
---|
| 818 | |
---|
| 819 | if callable(f): |
---|
| 820 | #N = 3 |
---|
| 821 | N = 2 |
---|
| 822 | #x = ones(3, Float) |
---|
| 823 | #y = ones(3, Float) |
---|
| 824 | x = ones(2, Float) |
---|
| 825 | #y = ones(2, Float) |
---|
| 826 | |
---|
| 827 | try: |
---|
| 828 | #q = f(1.0, x=x, y=y) |
---|
| 829 | q = f(1.0, x=x) |
---|
| 830 | except Exception, e: |
---|
| 831 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
---|
| 832 | #FIXME: Reconsider this semantics |
---|
| 833 | raise msg |
---|
| 834 | |
---|
| 835 | try: |
---|
| 836 | q = array(q).astype(Float) |
---|
| 837 | except: |
---|
| 838 | msg = 'Return value from vector function %s could ' %f |
---|
| 839 | msg += 'not be converted into a Numeric array of floats.\n' |
---|
| 840 | msg += 'Specified function should return either list or array.' |
---|
| 841 | raise msg |
---|
| 842 | |
---|
| 843 | #Is this really what we want? |
---|
| 844 | msg = 'Return vector from function %s ' %f |
---|
| 845 | msg += 'must have same lenght as input vectors' |
---|
| 846 | assert len(q) == N, msg |
---|
| 847 | |
---|
| 848 | else: |
---|
| 849 | try: |
---|
| 850 | f = float(f) |
---|
| 851 | except: |
---|
| 852 | msg = 'Force field %s must be either a scalar' %f |
---|
| 853 | msg += ' or a vector function' |
---|
| 854 | raise msg |
---|
| 855 | return f |
---|
| 856 | |
---|
| 857 | class Wind_stress: |
---|
| 858 | """Apply wind stress to water momentum in terms of |
---|
| 859 | wind speed [m/s] and wind direction [degrees] |
---|
| 860 | """ |
---|
| 861 | |
---|
| 862 | def __init__(self, *args, **kwargs): |
---|
| 863 | """Initialise windfield from wind speed s [m/s] |
---|
| 864 | and wind direction phi [degrees] |
---|
| 865 | |
---|
| 866 | Inputs v and phi can be either scalars or Python functions, e.g. |
---|
| 867 | |
---|
| 868 | W = Wind_stress(10, 178) |
---|
| 869 | |
---|
| 870 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
---|
| 871 | vector (1,0) has zero degrees. |
---|
| 872 | We may need to convert from 'compass' degrees later on and also |
---|
| 873 | map from True north to grid north. |
---|
| 874 | |
---|
| 875 | Arguments can also be Python functions of t,x,y as in |
---|
| 876 | |
---|
| 877 | def speed(t,x,y): |
---|
| 878 | ... |
---|
| 879 | return s |
---|
| 880 | |
---|
| 881 | def angle(t,x,y): |
---|
| 882 | ... |
---|
| 883 | return phi |
---|
| 884 | |
---|
| 885 | where x and y are vectors. |
---|
| 886 | |
---|
| 887 | and then pass the functions in |
---|
| 888 | |
---|
| 889 | W = Wind_stress(speed, angle) |
---|
| 890 | |
---|
| 891 | The instantiated object W can be appended to the list of |
---|
| 892 | forcing_terms as in |
---|
| 893 | |
---|
| 894 | Alternatively, one vector valued function for (speed, angle) |
---|
| 895 | can be applied, providing both quantities simultaneously. |
---|
| 896 | As in |
---|
| 897 | W = Wind_stress(F), where returns (speed, angle) for each t. |
---|
| 898 | |
---|
| 899 | domain.forcing_terms.append(W) |
---|
| 900 | """ |
---|
| 901 | |
---|
| 902 | from config import rho_a, rho_w, eta_w |
---|
| 903 | from Numeric import array, Float |
---|
| 904 | |
---|
| 905 | if len(args) == 2: |
---|
| 906 | s = args[0] |
---|
| 907 | phi = args[1] |
---|
| 908 | elif len(args) == 1: |
---|
| 909 | #Assume vector function returning (s, phi)(t,x,y) |
---|
| 910 | vector_function = args[0] |
---|
| 911 | #s = lambda t,x,y: vector_function(t,x=x,y=y)[0] |
---|
| 912 | #phi = lambda t,x,y: vector_function(t,x=x,y=y)[1] |
---|
| 913 | s = lambda t,x: vector_function(t,x=x)[0] |
---|
| 914 | phi = lambda t,x: vector_function(t,x=x)[1] |
---|
| 915 | else: |
---|
| 916 | #Assume info is in 2 keyword arguments |
---|
| 917 | |
---|
| 918 | if len(kwargs) == 2: |
---|
| 919 | s = kwargs['s'] |
---|
| 920 | phi = kwargs['phi'] |
---|
| 921 | else: |
---|
| 922 | raise 'Assumes two keyword arguments: s=..., phi=....' |
---|
| 923 | |
---|
| 924 | print 'phi', phi |
---|
| 925 | self.speed = check_forcefield(s) |
---|
| 926 | self.phi = check_forcefield(phi) |
---|
| 927 | |
---|
| 928 | self.const = eta_w*rho_a/rho_w |
---|
| 929 | |
---|
| 930 | |
---|
| 931 | def __call__(self, domain): |
---|
| 932 | """Evaluate windfield based on values found in domain |
---|
| 933 | """ |
---|
| 934 | |
---|
| 935 | from math import pi, cos, sin, sqrt |
---|
| 936 | from Numeric import Float, ones, ArrayType |
---|
| 937 | |
---|
| 938 | xmom_update = domain.quantities['xmomentum'].explicit_update |
---|
| 939 | #ymom_update = domain.quantities['ymomentum'].explicit_update |
---|
| 940 | |
---|
| 941 | N = domain.number_of_elements |
---|
| 942 | t = domain.time |
---|
| 943 | |
---|
| 944 | if callable(self.speed): |
---|
| 945 | xc = domain.get_centroid_coordinates() |
---|
| 946 | #s_vec = self.speed(t, xc[:,0], xc[:,1]) |
---|
| 947 | s_vec = self.speed(t, xc) |
---|
| 948 | else: |
---|
| 949 | #Assume s is a scalar |
---|
| 950 | |
---|
| 951 | try: |
---|
| 952 | s_vec = self.speed * ones(N, Float) |
---|
| 953 | except: |
---|
| 954 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
---|
| 955 | raise msg |
---|
| 956 | |
---|
| 957 | |
---|
| 958 | if callable(self.phi): |
---|
| 959 | xc = domain.get_centroid_coordinates() |
---|
| 960 | #phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
---|
| 961 | phi_vec = self.phi(t, xc) |
---|
| 962 | else: |
---|
| 963 | #Assume phi is a scalar |
---|
| 964 | |
---|
| 965 | try: |
---|
| 966 | phi_vec = self.phi * ones(N, Float) |
---|
| 967 | except: |
---|
| 968 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
---|
| 969 | raise msg |
---|
| 970 | |
---|
| 971 | #assign_windfield_values(xmom_update, ymom_update, |
---|
| 972 | # s_vec, phi_vec, self.const) |
---|
| 973 | assign_windfield_values(xmom_update, s_vec, phi_vec, self.const) |
---|
| 974 | |
---|
| 975 | |
---|
| 976 | #def assign_windfield_values(xmom_update, ymom_update, |
---|
| 977 | # s_vec, phi_vec, const): |
---|
| 978 | def assign_windfield_values(xmom_update, s_vec, phi_vec, const): |
---|
| 979 | """Python version of assigning wind field to update vectors. |
---|
| 980 | A c version also exists (for speed) |
---|
| 981 | """ |
---|
| 982 | from math import pi, cos, sin, sqrt |
---|
| 983 | |
---|
| 984 | N = len(s_vec) |
---|
| 985 | for k in range(N): |
---|
| 986 | s = s_vec[k] |
---|
| 987 | phi = phi_vec[k] |
---|
| 988 | |
---|
| 989 | #Convert to radians |
---|
| 990 | phi = phi*pi/180 |
---|
| 991 | |
---|
| 992 | #Compute velocity vector (u, v) |
---|
| 993 | u = s*cos(phi) |
---|
| 994 | v = s*sin(phi) |
---|
| 995 | |
---|
| 996 | #Compute wind stress |
---|
| 997 | #S = const * sqrt(u**2 + v**2) |
---|
| 998 | S = const * u |
---|
| 999 | xmom_update[k] += S*u |
---|
| 1000 | #ymom_update[k] += S*v |
---|