[7827] | 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 | This particular modification of the Domain class implements the ability to |
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| 9 | vary the width of the 1D channel that the water flows in. As a result the |
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| 10 | conserved variables are different than previous implementations and so are the |
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| 11 | equations. |
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| 12 | |
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| 13 | U_t + E_x = S |
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| 14 | |
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| 15 | where |
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| 16 | ------------!!!! NOTE THIS NEEDS UPDATING !!!!------------------ |
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| 17 | U = [A, Q] |
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| 18 | E = [Q, Q^2/A + gh^2/2] |
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| 19 | S represents source terms forcing the system |
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| 20 | (e.g. gravity, friction, wind stress, ...) |
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| 21 | |
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| 22 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
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| 23 | |
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| 24 | The quantities are |
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| 25 | |
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| 26 | symbol variable name explanation |
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| 27 | x x horizontal distance from origin [m] |
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| 28 | z elevation elevation of bed on which flow is modelled [m] |
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| 29 | h height water height above z [m] |
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| 30 | w stage absolute water level, w = z+h [m] |
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| 31 | u speed in the x direction [m/s] |
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| 32 | uh xmomentum momentum in the x direction [m^2/s] |
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| 33 | |
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| 34 | eta mannings friction coefficient [to appear] |
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| 35 | nu wind stress coefficient [to appear] |
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| 36 | |
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| 37 | The conserved quantities are w, uh |
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| 38 | -------------------------------------------------------------------------- |
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| 39 | For details see e.g. |
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| 40 | Christopher Zoppou and Stephen Roberts, |
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| 41 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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| 42 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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| 43 | |
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| 44 | |
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| 45 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou, |
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| 46 | Padarn Wilson, Geoscience Australia, 2008 |
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| 47 | """ |
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| 48 | |
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| 49 | |
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| 50 | from domain import * |
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| 51 | Generic_Domain = Domain #Rename |
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| 52 | |
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| 53 | #Shallow water domain |
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| 54 | class Domain(Generic_Domain): |
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| 55 | |
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| 56 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
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| 57 | |
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| 58 | conserved_quantities = ['area', 'discharge'] |
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| 59 | evolved_quantities = ['area', 'discharge', 'elevation', 'height', 'velocity','width','stage'] |
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| 60 | other_quantities = ['friction'] |
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| 61 | Generic_Domain.__init__(self, |
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| 62 | coordinates = coordinates, |
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| 63 | boundary = boundary, |
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| 64 | conserved_quantities = conserved_quantities, |
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| 65 | evolved_quantities = evolved_quantities, |
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| 66 | other_quantities = other_quantities, |
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| 67 | tagged_elements = tagged_elements) |
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| 68 | |
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| 69 | from config import minimum_allowed_height, g, h0 |
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| 70 | self.minimum_allowed_height = minimum_allowed_height |
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| 71 | self.g = g |
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| 72 | self.h0 = h0 |
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| 73 | self.setstageflag = False |
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| 74 | self.discontinousb = False |
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| 75 | |
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| 76 | |
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| 77 | #self.forcing_terms.append(gravity) |
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| 78 | #self.forcing_terms.append(boundary_stress) |
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| 79 | #self.forcing_terms.append(manning_friction) |
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| 80 | |
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| 81 | |
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| 82 | |
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| 83 | #Stored output |
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| 84 | self.store = True |
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| 85 | self.format = 'sww' |
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| 86 | self.smooth = True |
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| 87 | |
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| 88 | |
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| 89 | #Reduction operation for get_vertex_values |
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| 90 | from util import mean |
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| 91 | self.reduction = mean |
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| 92 | #self.reduction = min #Looks better near steep slopes |
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| 93 | |
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| 94 | self.set_quantities_to_be_stored(['area','discharge']) |
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| 95 | |
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| 96 | self.__doc__ = 'channel_domain_Ab' |
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| 97 | |
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| 98 | self.check_integrity() |
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| 99 | |
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| 100 | |
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| 101 | def check_integrity(self): |
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| 102 | |
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| 103 | #Check that we are solving the shallow water wave equation |
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| 104 | |
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| 105 | msg = 'First conserved quantity must be "area"' |
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| 106 | assert self.conserved_quantities[0] == 'area', msg |
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| 107 | msg = 'Second conserved quantity must be "discharge"' |
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| 108 | assert self.conserved_quantities[1] == 'discharge', msg |
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| 109 | |
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| 110 | msg = 'First evolved quantity must be "area"' |
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| 111 | assert self.evolved_quantities[0] == 'area', msg |
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| 112 | msg = 'Second evolved quantity must be "discharge"' |
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| 113 | assert self.evolved_quantities[1] == 'discharge', msg |
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| 114 | msg = 'Third evolved quantity must be "elevation"' |
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| 115 | assert self.evolved_quantities[2] == 'elevation', msg |
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| 116 | msg = 'Fourth evolved quantity must be "height"' |
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| 117 | assert self.evolved_quantities[3] == 'height', msg |
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| 118 | msg = 'Fifth evolved quantity must be "velocity"' |
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| 119 | assert self.evolved_quantities[4] == 'velocity', msg |
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| 120 | msg = 'Fifth evolved quantity must be "width"' |
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| 121 | assert self.evolved_quantities[5] == 'width', msg |
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| 122 | |
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| 123 | Generic_Domain.check_integrity(self) |
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| 124 | |
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| 125 | def compute_fluxes(self): |
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| 126 | #Call correct module function |
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| 127 | #(either from this module or C-extension) |
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| 128 | compute_fluxes_channel(self) |
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| 129 | |
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| 130 | def distribute_to_vertices_and_edges(self): |
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| 131 | #Call correct module function |
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| 132 | #(either from this module or C-extension) |
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| 133 | distribute_to_vertices_and_edges_limit_a_d(self) |
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| 134 | |
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| 135 | |
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| 136 | #=============== End of Channel Domain =============================== |
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| 137 | |
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| 138 | #----------------------------------- |
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| 139 | # Compute flux definition with channel |
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| 140 | #----------------------------------- |
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| 141 | def compute_fluxes_channel(domain): |
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| 142 | from Numeric import zeros, Float |
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| 143 | import sys |
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| 144 | |
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| 145 | |
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| 146 | timestep = float(sys.maxint) |
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| 147 | |
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| 148 | area = domain.quantities['area'] |
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| 149 | discharge = domain.quantities['discharge'] |
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| 150 | bed = domain.quantities['elevation'] |
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| 151 | height = domain.quantities['height'] |
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| 152 | velocity = domain.quantities['velocity'] |
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| 153 | width = domain.quantities['width'] |
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| 154 | |
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| 155 | |
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| 156 | from channel_domain_ext import compute_fluxes_channel_ext |
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| 157 | domain.flux_timestep = compute_fluxes_channel_ext(timestep,domain,area,discharge,bed,height,velocity,width) |
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| 158 | |
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| 159 | #----------------------------------------------------------------------- |
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| 160 | # Distribute to verticies with stage reconstructed and then extrapolated |
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| 161 | #----------------------------------------------------------------------- |
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| 162 | def distribute_to_vertices_and_edges_limit_a_d(domain): |
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| 163 | |
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| 164 | #Remove very thin layers of water |
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| 165 | #protect_against_infinitesimal_and_negative_heights(domain) |
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| 166 | |
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| 167 | |
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| 168 | |
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| 169 | import sys |
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| 170 | from Numeric import zeros, Float |
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| 171 | from config import epsilon, h0 |
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| 172 | ## linearb(domain) |
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| 173 | |
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| 174 | |
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| 175 | |
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| 176 | |
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| 177 | N = domain.number_of_elements |
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| 178 | |
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| 179 | #Shortcuts |
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| 180 | Area = domain.quantities['area'] |
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| 181 | Discharge = domain.quantities['discharge'] |
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| 182 | Bed = domain.quantities['elevation'] |
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| 183 | Height = domain.quantities['height'] |
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| 184 | Velocity = domain.quantities['velocity'] |
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| 185 | Width = domain.quantities['width'] |
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| 186 | Stage = domain.quantities['stage'] |
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| 187 | |
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| 188 | #Arrays |
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| 189 | a_C = Area.centroid_values |
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| 190 | d_C = Discharge.centroid_values |
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| 191 | z_C = Bed.centroid_values |
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| 192 | h_C = Height.centroid_values |
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| 193 | u_C = Velocity.centroid_values |
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| 194 | b_C = Width.centroid_values |
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| 195 | w_C = Stage.centroid_values |
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| 196 | |
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| 197 | if domain.setstageflag: |
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| 198 | for i in range(len(a_C)): |
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| 199 | a_C[i]=(w_C[i]-z_C[i])*b_C[i] |
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| 200 | |
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| 201 | domain.setstageflag = False |
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| 202 | |
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| 203 | if domain.discontinousb: |
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| 204 | domain.quantities['width'].extrapolate_second_order() |
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| 205 | |
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| 206 | |
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| 207 | h0 = 1.0e-12 |
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| 208 | #print id(h_C) |
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| 209 | for i in range(N): |
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| 210 | |
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| 211 | if a_C[i] <= h0: |
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| 212 | a_C[i] = 0.0 |
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| 213 | h_C[i] = 0.0 |
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| 214 | d_C[i] = 0.0 |
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| 215 | u_C[i] = 0.0 |
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| 216 | w_C[i] = z_C[i] |
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| 217 | |
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| 218 | |
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| 219 | |
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| 220 | else: |
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| 221 | |
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| 222 | if b_C[i]<=h0: |
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| 223 | a_C[i] = 0.0 |
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| 224 | h_C[i] = 0.0 |
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| 225 | d_C[i] = 0.0 |
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| 226 | u_C[i] = 0.0 |
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| 227 | w_C[i] = z_C[i] |
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| 228 | |
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| 229 | else: |
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| 230 | h_C[i] = a_C[i]/(b_C[i]+h0/b_C[i]) |
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| 231 | w_C[i] = h_C[i]+z_C[i] |
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| 232 | u_C[i] = d_C[i]/(a_C[i]+h0/a_C[i]) |
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| 233 | |
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| 234 | |
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| 235 | |
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| 236 | |
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| 237 | for name in ['velocity','stage']: |
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| 238 | Q = domain.quantities[name] |
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| 239 | if domain.order == 1: |
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| 240 | Q.extrapolate_first_order() |
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| 241 | elif domain.order == 2: |
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| 242 | Q.extrapolate_second_order() |
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| 243 | else: |
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| 244 | raise 'Unknown order' |
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| 245 | a_V = domain.quantities['area'].vertex_values |
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| 246 | w_V = domain.quantities['stage'].vertex_values |
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| 247 | z_V = domain.quantities['elevation'].vertex_values |
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| 248 | h_V = domain.quantities['height'].vertex_values |
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| 249 | u_V = domain.quantities['velocity'].vertex_values |
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| 250 | d_V = domain.quantities['discharge'].vertex_values |
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| 251 | b_V = domain.quantities['width'].vertex_values |
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| 252 | |
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| 253 | |
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| 254 | |
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| 255 | for i in range(len(h_C)): |
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| 256 | for j in range(2): |
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| 257 | ## if b_V[i,j] < h0 : |
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| 258 | ## a_V[i,j]=0 |
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| 259 | ## h_V[i,j]=0 |
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| 260 | ## d_V[i,j]=0 |
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| 261 | ## u_V[i,j]=0 |
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| 262 | ## else: |
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| 263 | |
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| 264 | h_V[i,j] = w_V[i,j]-z_V[i,j] |
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| 265 | if h_V[i,j]<h0: |
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| 266 | h_V[i,j]=0 |
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| 267 | w_V[i,j]=z_V[i,j] |
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| 268 | a_V[i,j] = b_V[i,j]*h_V[i,j] |
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| 269 | d_V[i,j]=u_V[i,j]*a_V[i,j] |
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| 270 | |
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| 271 | |
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| 272 | |
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| 273 | |
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| 274 | |
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| 275 | |
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| 276 | return |
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| 277 | |
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| 278 | |
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| 279 | #-------------------------------------------------------- |
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| 280 | #Boundaries - specific to the shallow_water_vel_domain |
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| 281 | #-------------------------------------------------------- |
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| 282 | class Reflective_boundary(Boundary): |
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| 283 | """Reflective boundary returns same conserved quantities as |
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| 284 | those present in its neighbour volume but reflected. |
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| 285 | |
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| 286 | This class is specific to the shallow water equation as it |
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| 287 | works with the momentum quantities assumed to be the second |
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| 288 | and third conserved quantities. |
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| 289 | """ |
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| 290 | |
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| 291 | def __init__(self, domain = None): |
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| 292 | Boundary.__init__(self) |
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| 293 | |
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| 294 | if domain is None: |
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| 295 | msg = 'Domain must be specified for reflective boundary' |
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| 296 | raise msg |
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| 297 | |
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| 298 | #Handy shorthands |
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| 299 | self.normals = domain.normals |
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| 300 | self.area = domain.quantities['area'].vertex_values |
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| 301 | self.discharge = domain.quantities['discharge'].vertex_values |
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| 302 | self.bed = domain.quantities['elevation'].vertex_values |
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| 303 | self.height = domain.quantities['height'].vertex_values |
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| 304 | self.velocity = domain.quantities['velocity'].vertex_values |
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| 305 | self.width = domain.quantities['width'].vertex_values |
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| 306 | self.stage = domain.quantities['stage'].vertex_values |
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| 307 | |
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| 308 | from Numeric import zeros, Float |
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| 309 | #self.conserved_quantities = zeros(3, Float) |
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| 310 | self.evolved_quantities = zeros(7, Float) |
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| 311 | |
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| 312 | def __repr__(self): |
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| 313 | return 'Reflective_boundary' |
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| 314 | |
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| 315 | |
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| 316 | def evaluate(self, vol_id, edge_id): |
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| 317 | """Reflective boundaries reverses the outward momentum |
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| 318 | of the volume they serve. |
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| 319 | """ |
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| 320 | |
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| 321 | q = self.evolved_quantities |
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| 322 | q[0] = self.area[vol_id, edge_id] |
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| 323 | q[1] = -self.discharge[vol_id, edge_id] |
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| 324 | q[2] = self.bed[vol_id, edge_id] |
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| 325 | q[3] = self.height[vol_id, edge_id] |
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| 326 | q[4] = -self.velocity[vol_id, edge_id] |
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| 327 | q[5] = self.width[vol_id,edge_id] |
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| 328 | q[6] = self.stage[vol_id,edge_id] |
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| 329 | |
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| 330 | #print "In Reflective q ",q |
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| 331 | |
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| 332 | |
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| 333 | return q |
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| 334 | |
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| 335 | class Dirichlet_boundary(Boundary): |
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| 336 | """Dirichlet boundary returns constant values for the |
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| 337 | conserved quantities |
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| 338 | if k>5 and k<15: |
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| 339 | print discharge_ud[k],-g*zx*avg_h*avg_b |
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| 340 | discharge_ud[k] +=-g*zx*avg_h*avg_b """ |
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| 341 | |
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| 342 | |
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| 343 | def __init__(self, evolved_quantities=None): |
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| 344 | Boundary.__init__(self) |
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| 345 | |
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| 346 | if evolved_quantities is None: |
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| 347 | msg = 'Must specify one value for each evolved quantity' |
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| 348 | raise msg |
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| 349 | |
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| 350 | from Numeric import array, Float |
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| 351 | self.evolved_quantities=array(evolved_quantities).astype(Float) |
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| 352 | |
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| 353 | def __repr__(self): |
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| 354 | return 'Dirichlet boundary (%s)' %self.evolved_quantities |
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| 355 | |
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| 356 | def evaluate(self, vol_id=None, edge_id=None): |
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| 357 | return self.evolved_quantities |
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| 358 | |
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| 359 | |
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| 360 | #---------------------------- |
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| 361 | #Standard forcing terms: |
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| 362 | #--------------------------- |
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| 363 | def gravity(domain): |
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| 364 | """Apply gravitational pull in the presence of bed slope |
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| 365 | """ |
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| 366 | |
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| 367 | from util import gradient |
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| 368 | from Numeric import zeros, Float, array, sum |
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| 369 | |
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| 370 | |
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| 371 | |
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| 372 | Area = domain.quantities['area'] |
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| 373 | Discharge = domain.quantities['discharge'] |
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| 374 | Elevation = domain.quantities['elevation'] |
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| 375 | Height = domain.quantities['height'] |
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| 376 | Width = domain.quantities['width'] |
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| 377 | |
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| 378 | discharge_ud = Discharge.explicit_update |
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| 379 | |
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| 380 | |
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| 381 | |
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| 382 | h = Height.vertex_values |
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| 383 | b = Width.vertex_values |
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| 384 | a = Area.vertex_values |
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| 385 | z = Elevation.vertex_values |
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| 386 | |
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| 387 | x = domain.get_vertex_coordinates() |
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| 388 | g = domain.g |
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| 389 | for k in range(domain.number_of_elements): |
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| 390 | avg_h = 0.5*(h[k,0] + h[k,1]) |
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| 391 | avg_b = 0.5*(b[k,0] + b[k,1]) |
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| 392 | |
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| 393 | #Compute bed slope |
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| 394 | x0, x1 = x[k,:] |
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| 395 | z0, z1 = z[k,:] |
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| 396 | zx = gradient(x0, x1, z0, z1) |
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| 397 | |
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| 398 | #Update momentum (explicit update is reset to source values) |
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| 399 | discharge_ud[k]+= -g*zx*avg_h*avg_b |
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| 400 | |
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| 401 | |
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| 402 | def boundary_stress(domain): |
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| 403 | |
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| 404 | |
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| 405 | from util import gradient |
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| 406 | from Numeric import zeros, Float, array, sum |
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| 407 | |
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| 408 | |
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| 409 | |
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| 410 | Area = domain.quantities['area'] |
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| 411 | Discharge = domain.quantities['discharge'] |
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| 412 | Elevation = domain.quantities['elevation'] |
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| 413 | Height = domain.quantities['height'] |
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| 414 | Width = domain.quantities['width'] |
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| 415 | |
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| 416 | discharge_ud = Discharge.explicit_update |
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| 417 | |
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| 418 | |
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| 419 | |
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| 420 | h = Height.vertex_values |
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| 421 | b = Width.vertex_values |
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| 422 | a = Area.vertex_values |
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| 423 | z = Elevation.vertex_values |
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| 424 | |
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| 425 | x = domain.get_vertex_coordinates() |
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| 426 | g = domain.g |
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| 427 | |
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| 428 | for k in range(domain.number_of_elements): |
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| 429 | avg_h = 0.5*(h[k,0] + h[k,1]) |
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| 430 | |
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| 431 | |
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| 432 | #Compute bed slope |
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| 433 | x0, x1 = x[k,:] |
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| 434 | b0, b1 = b[k,:] |
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| 435 | bx = gradient(x0, x1, b0, b1) |
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| 436 | |
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| 437 | #Update momentum (explicit update is reset to source values) |
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| 438 | discharge_ud[k] += 0.5*g*bx*avg_h*avg_h |
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| 439 | #stage_ud[k] = 0.0 |
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| 440 | |
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| 441 | |
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| 442 | def manning_friction(domain): |
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| 443 | """Apply (Manning) friction to water momentum |
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| 444 | """ |
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| 445 | |
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| 446 | from math import sqrt |
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| 447 | |
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| 448 | w = domain.quantities['stage'].centroid_values |
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| 449 | z = domain.quantities['elevation'].centroid_values |
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| 450 | h = w-z |
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| 451 | |
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| 452 | uh = domain.quantities['xmomentum'].centroid_values |
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| 453 | #vh = domain.quantities['ymomentum'].centroid_values |
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| 454 | eta = domain.quantities['friction'].centroid_values |
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| 455 | |
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| 456 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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| 457 | #ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
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| 458 | |
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| 459 | N = domain.number_of_elements |
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| 460 | eps = domain.minimum_allowed_height |
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| 461 | g = domain.g |
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| 462 | |
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| 463 | for k in range(N): |
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| 464 | if eta[k] >= eps: |
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| 465 | if h[k] >= eps: |
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| 466 | #S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
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| 467 | S = -g * eta[k]**2 * uh[k] |
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| 468 | S /= h[k]**(7.0/3) |
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| 469 | |
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| 470 | #Update momentum |
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| 471 | xmom_update[k] += S*uh[k] |
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| 472 | #ymom_update[k] += S*vh[k] |
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| 473 | |
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| 474 | def linear_friction(domain): |
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| 475 | """Apply linear friction to water momentum |
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| 476 | |
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| 477 | Assumes quantity: 'linear_friction' to be present |
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| 478 | """ |
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| 479 | |
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| 480 | from math import sqrt |
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| 481 | |
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| 482 | w = domain.quantities['stage'].centroid_values |
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| 483 | z = domain.quantities['elevation'].centroid_values |
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| 484 | h = w-z |
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| 485 | |
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| 486 | uh = domain.quantities['xmomentum'].centroid_values |
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| 487 | tau = domain.quantities['linear_friction'].centroid_values |
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| 488 | |
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| 489 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
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| 490 | |
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| 491 | N = domain.number_of_elements |
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| 492 | eps = domain.minimum_allowed_height |
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| 493 | |
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| 494 | for k in range(N): |
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| 495 | if tau[k] >= eps: |
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| 496 | if h[k] >= eps: |
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| 497 | S = -tau[k]/h[k] |
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| 498 | |
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| 499 | #Update momentum |
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| 500 | xmom_update[k] += S*uh[k] |
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| 501 | |
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| 502 | |
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| 503 | |
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| 504 | def check_forcefield(f): |
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| 505 | """Check that f is either |
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| 506 | 1: a callable object f(t,x,y), where x and y are vectors |
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| 507 | and that it returns an array or a list of same length |
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| 508 | as x and y |
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| 509 | 2: a scalar |
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| 510 | """ |
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| 511 | |
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| 512 | from Numeric import ones, Float, array |
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| 513 | |
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| 514 | |
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| 515 | if callable(f): |
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| 516 | #N = 3 |
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| 517 | N = 2 |
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| 518 | #x = ones(3, Float) |
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| 519 | #y = ones(3, Float) |
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| 520 | x = ones(2, Float) |
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| 521 | #y = ones(2, Float) |
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| 522 | |
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| 523 | try: |
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| 524 | #q = f(1.0, x=x, y=y) |
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| 525 | q = f(1.0, x=x) |
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| 526 | except Exception, e: |
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| 527 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
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| 528 | #FIXME: Reconsider this semantics |
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| 529 | raise msg |
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| 530 | |
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| 531 | try: |
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| 532 | q = array(q).astype(Float) |
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| 533 | except: |
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| 534 | msg = 'Return value from vector function %s could ' %f |
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| 535 | msg += 'not be converted into a Numeric array of floats.\n' |
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| 536 | msg += 'Specified function should return either list or array.' |
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| 537 | raise msg |
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| 538 | |
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| 539 | #Is this really what we want? |
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| 540 | msg = 'Return vector from function %s ' %f |
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| 541 | msg += 'must have same lenght as input vectors' |
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| 542 | assert len(q) == N, msg |
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| 543 | |
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| 544 | else: |
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| 545 | try: |
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| 546 | f = float(f) |
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| 547 | except: |
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| 548 | msg = 'Force field %s must be either a scalar' %f |
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| 549 | msg += ' or a vector function' |
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| 550 | raise msg |
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| 551 | return f |
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| 552 | |
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| 553 | def linearb(domain): |
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| 554 | |
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| 555 | bC = domain.quantities['width'].vertex_values |
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| 556 | |
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| 557 | for i in range(len(bC)-1): |
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| 558 | temp= 0.5*(bC[i,1]+bC[i+1,0]) |
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| 559 | bC[i,1]=temp |
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| 560 | bC[i+1,0]=temp |
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| 561 | |
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| 562 | |
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| 563 | |
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