| 1 | """Class Domain - |
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| 2 | 2D triangular 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 + G_y = 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, vh] |
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| 14 | E = [uh, u^2h + gh^2/2, uvh] |
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| 15 | G = [vh, uvh, v^2h + gh^2/2] |
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| 16 | S represents source terms forcing the system |
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| 17 | (e.g. gravity, friction, wind stress, ...) |
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| 18 | |
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| 19 | and _t, _x, _y denote the derivative with respect to t, x and y respectively. |
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| 20 | |
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| 21 | The quantities are |
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| 22 | |
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| 23 | symbol variable name explanation |
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| 24 | x x horizontal distance from origin [m] |
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| 25 | y y vertical distance from origin [m] |
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| 26 | z elevation elevation of bed on which flow is modelled [m] |
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| 27 | h height water height above z [m] |
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| 28 | w stage absolute water level, w = z+h [m] |
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| 29 | u speed in the x direction [m/s] |
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| 30 | v speed in the y direction [m/s] |
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| 31 | uh xmomentum momentum in the x direction [m^2/s] |
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| 32 | vh ymomentum momentum in the y 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, vh |
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| 38 | |
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| 39 | |
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| 40 | For details see e.g. |
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| 41 | Christopher Zoppou and Stephen Roberts, |
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| 42 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
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| 43 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
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| 44 | |
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| 45 | |
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| 46 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 47 | Geoscience Australia, 2004 |
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| 48 | """ |
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| 49 | |
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| 50 | #Subversion keywords: |
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| 51 | # |
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| 52 | #$LastChangedDate: 2005-02-08 06:17:25 +0000 (Tue, 08 Feb 2005) $ |
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| 53 | #$LastChangedRevision: 850 $ |
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| 54 | #$LastChangedBy: ole $ |
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| 55 | |
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| 56 | |
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| 57 | from domain import * |
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| 58 | from region import * |
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| 59 | Generic_domain = Domain #Rename |
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| 60 | |
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| 61 | class Domain(Generic_domain): |
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| 62 | |
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| 63 | def __init__(self, coordinates, vertices, boundary = None, |
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| 64 | tagged_elements = None): |
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| 65 | |
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| 66 | conserved_quantities = ['stage', 'xmomentum', 'ymomentum'] |
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| 67 | other_quantities = ['elevation', 'friction'] |
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| 68 | |
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| 69 | Generic_domain.__init__(self, coordinates, vertices, boundary, |
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| 70 | conserved_quantities, other_quantities, |
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| 71 | tagged_elements) |
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| 72 | |
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| 73 | from config import minimum_allowed_height, g |
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| 74 | self.minimum_allowed_height = minimum_allowed_height |
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| 75 | self.g = g |
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| 76 | |
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| 77 | self.forcing_terms.append(gravity) |
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| 78 | self.forcing_terms.append(manning_friction) |
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| 79 | |
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| 80 | #Realtime visualisation |
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| 81 | self.visualise = False |
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| 82 | |
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| 83 | #Stored output |
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| 84 | self.store = False |
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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 | #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'] |
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| 94 | |
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| 95 | |
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| 96 | #Establish shortcuts to relevant quantities (for efficiency) |
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| 97 | #self.w = self.quantities['stage'] |
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| 98 | #self.uh = self.quantities['xmomentum'] |
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| 99 | #self.vh = self.quantities['ymomentum'] |
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| 100 | #self.z = self.quantities['elevation'] |
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| 101 | #self.eta = self.quantities['friction'] |
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| 102 | |
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| 103 | def check_integrity(self): |
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| 104 | Generic_domain.check_integrity(self) |
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| 105 | |
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| 106 | #Check that we are solving the shallow water wave equation |
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| 107 | |
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| 108 | msg = 'First conserved quantity must be "stage"' |
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| 109 | assert self.conserved_quantities[0] == 'stage', msg |
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| 110 | msg = 'Second conserved quantity must be "xmomentum"' |
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| 111 | assert self.conserved_quantities[1] == 'xmomentum', msg |
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| 112 | msg = 'Third conserved quantity must be "ymomentum"' |
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| 113 | assert self.conserved_quantities[2] == 'ymomentum', msg |
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| 114 | |
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| 115 | |
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| 116 | def compute_fluxes(self): |
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| 117 | #Call correct module function |
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| 118 | #(either from this module or C-extension) |
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| 119 | compute_fluxes(self) |
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| 120 | |
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| 121 | def distribute_to_vertices_and_edges(self): |
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| 122 | #Call correct module function |
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| 123 | #(either from this module or C-extension) |
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| 124 | distribute_to_vertices_and_edges(self) |
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| 125 | |
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| 126 | |
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| 127 | #FIXME: Under construction |
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| 128 | # def set_defaults(self): |
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| 129 | # """Set default values for uninitialised quantities. |
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| 130 | # This is specific to the shallow water wave equation |
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| 131 | # Defaults for 'elevation', 'friction', 'xmomentum' and 'ymomentum' |
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| 132 | # are 0.0. Default for 'stage' is whatever the value of 'elevation'. |
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| 133 | # """ |
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| 134 | |
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| 135 | # for name in self.other_quantities + self.conserved_quantities: |
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| 136 | # print name |
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| 137 | # print self.quantities.keys() |
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| 138 | # if not self.quantities.has_key(name): |
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| 139 | # if name == 'stage': |
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| 140 | |
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| 141 | # if self.quantities.has_key('elevation'): |
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| 142 | # z = self.quantities['elevation'].vertex_values |
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| 143 | # self.set_quantity(name, z) |
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| 144 | # else: |
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| 145 | # self.set_quantity(name, 0.0) |
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| 146 | # else: |
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| 147 | # self.set_quantity(name, 0.0) |
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| 148 | |
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| 149 | |
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| 150 | |
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| 151 | # #Lift negative heights up |
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| 152 | # #z = self.quantities['elevation'].vertex_values |
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| 153 | # #w = self.quantities['stage'].vertex_values |
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| 154 | |
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| 155 | # #h = w-z |
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| 156 | |
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| 157 | # #for k in range(h.shape[0]): |
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| 158 | # # for i in range(3): |
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| 159 | # # if h[k, i] < 0.0: |
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| 160 | # # w[k, i] = z[k, i] |
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| 161 | |
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| 162 | |
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| 163 | # #self.quantities['stage'].interpolate() |
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| 164 | |
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| 165 | |
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| 166 | |
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| 167 | def evolve(self, yieldstep = None, finaltime = None): |
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| 168 | """Specialisation of basic evolve method from parent class |
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| 169 | """ |
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| 170 | |
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| 171 | #Call check integrity here rather than from user scripts |
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| 172 | #self.check_integrity() |
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| 173 | |
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| 174 | #Initialise real time viz if requested |
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| 175 | if self.visualise is True and self.time == 0.0: |
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| 176 | import realtime_visualisation as visualise |
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| 177 | visualise.create_surface(self) |
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| 178 | |
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| 179 | #Store model data, e.g. for visualisation |
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| 180 | if self.store is True and self.time == 0.0: |
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| 181 | self.initialise_storage() |
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| 182 | #print 'Storing results in ' + self.writer.filename |
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| 183 | else: |
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| 184 | #print 'Results will not be stored.' |
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| 185 | #print 'To store results set domain.store = True' |
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| 186 | pass |
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| 187 | #FIXME: Diagnostic output should be controlled by |
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| 188 | # a 'verbose' flag living in domain (or in a parent class) |
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| 189 | |
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| 190 | #Call basic machinery from parent class |
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| 191 | for t in Generic_domain.evolve(self, yieldstep, finaltime): |
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| 192 | #Real time viz |
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| 193 | if self.visualise is True: |
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| 194 | visualise.update(self) |
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| 195 | |
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| 196 | #Store model data, e.g. for subsequent visualisation |
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| 197 | if self.store is True: |
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| 198 | #self.store_timestep(['stage', 'xmomentum', 'ymomentum']) |
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| 199 | self.store_timestep(self.quantities_to_be_stored) |
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| 200 | |
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| 201 | #FIXME: Could maybe be taken from specified list |
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| 202 | #of 'store every step' quantities |
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| 203 | |
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| 204 | #Pass control on to outer loop for more specific actions |
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| 205 | yield(t) |
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| 206 | |
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| 207 | |
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| 208 | def initialise_storage(self): |
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| 209 | """Create and initialise self.writer object for storing data. |
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| 210 | Also, save x,y and bed elevation |
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| 211 | """ |
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| 212 | |
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| 213 | import data_manager |
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| 214 | |
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| 215 | #Initialise writer |
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| 216 | self.writer = data_manager.get_dataobject(self, mode = 'w') |
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| 217 | |
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| 218 | #Store vertices and connectivity |
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| 219 | self.writer.store_connectivity() |
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| 220 | |
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| 221 | |
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| 222 | def store_timestep(self, name): |
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| 223 | """Store named quantity and time. |
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| 224 | |
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| 225 | Precondition: |
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| 226 | self.write has been initialised |
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| 227 | """ |
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| 228 | self.writer.store_timestep(name) |
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| 229 | |
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| 230 | |
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| 231 | #Rotation of momentum vector |
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| 232 | def rotate(q, normal, direction = 1): |
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| 233 | """Rotate the momentum component q (q[1], q[2]) |
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| 234 | from x,y coordinates to coordinates based on normal vector. |
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| 235 | |
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| 236 | If direction is negative the rotation is inverted. |
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| 237 | |
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| 238 | Input vector is preserved |
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| 239 | |
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| 240 | This function is specific to the shallow water wave equation |
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| 241 | """ |
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| 242 | |
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| 243 | from Numeric import zeros, Float |
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| 244 | |
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| 245 | assert len(q) == 3,\ |
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| 246 | 'Vector of conserved quantities must have length 3'\ |
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| 247 | 'for 2D shallow water equation' |
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| 248 | |
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| 249 | try: |
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| 250 | l = len(normal) |
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| 251 | except: |
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| 252 | raise 'Normal vector must be an Numeric array' |
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| 253 | |
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| 254 | assert l == 2, 'Normal vector must have 2 components' |
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| 255 | |
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| 256 | |
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| 257 | n1 = normal[0] |
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| 258 | n2 = normal[1] |
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| 259 | |
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| 260 | r = zeros(len(q), Float) #Rotated quantities |
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| 261 | r[0] = q[0] #First quantity, height, is not rotated |
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| 262 | |
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| 263 | if direction == -1: |
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| 264 | n2 = -n2 |
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| 265 | |
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| 266 | |
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| 267 | r[1] = n1*q[1] + n2*q[2] |
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| 268 | r[2] = -n2*q[1] + n1*q[2] |
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| 269 | |
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| 270 | return r |
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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 | # Flux computation |
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| 276 | def flux_function(normal, ql, qr, zl, zr): |
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| 277 | """Compute fluxes between volumes for the shallow water wave equation |
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| 278 | cast in terms of w = h+z using the 'central scheme' as described in |
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| 279 | |
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| 280 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
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| 281 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
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| 282 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
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| 283 | |
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| 284 | The implemented formula is given in equation (3.15) on page 714 |
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| 285 | |
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| 286 | Conserved quantities w, uh, vh are stored as elements 0, 1 and 2 |
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| 287 | in the numerical vectors ql an qr. |
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| 288 | |
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| 289 | Bed elevations zl and zr. |
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| 290 | """ |
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| 291 | |
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| 292 | from config import g, epsilon |
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| 293 | from math import sqrt |
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| 294 | from Numeric import array |
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| 295 | |
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| 296 | #Align momentums with x-axis |
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| 297 | q_left = rotate(ql, normal, direction = 1) |
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| 298 | q_right = rotate(qr, normal, direction = 1) |
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| 299 | |
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| 300 | z = (zl+zr)/2 #Take average of field values |
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| 301 | |
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| 302 | w_left = q_left[0] #w=h+z |
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| 303 | h_left = w_left-z |
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| 304 | uh_left = q_left[1] |
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| 305 | |
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| 306 | if h_left < epsilon: |
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| 307 | u_left = 0.0 #Could have been negative |
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| 308 | h_left = 0.0 |
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| 309 | else: |
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| 310 | u_left = uh_left/h_left |
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| 311 | |
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| 312 | |
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| 313 | w_right = q_right[0] #w=h+z |
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| 314 | h_right = w_right-z |
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| 315 | uh_right = q_right[1] |
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| 316 | |
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| 317 | |
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| 318 | if h_right < epsilon: |
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| 319 | u_right = 0.0 #Could have been negative |
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| 320 | h_right = 0.0 |
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| 321 | else: |
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| 322 | u_right = uh_right/h_right |
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| 323 | |
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| 324 | vh_left = q_left[2] |
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| 325 | vh_right = q_right[2] |
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| 326 | |
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| 327 | soundspeed_left = sqrt(g*h_left) |
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| 328 | soundspeed_right = sqrt(g*h_right) |
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| 329 | |
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| 330 | #Maximal wave speed |
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| 331 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
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| 332 | |
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| 333 | #Minimal wave speed |
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| 334 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
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| 335 | |
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| 336 | #Flux computation |
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| 337 | flux_left = array([u_left*h_left, |
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| 338 | u_left*uh_left + 0.5*g*h_left**2, |
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| 339 | u_left*vh_left]) |
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| 340 | flux_right = array([u_right*h_right, |
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| 341 | u_right*uh_right + 0.5*g*h_right**2, |
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| 342 | u_right*vh_right]) |
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| 343 | |
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| 344 | denom = s_max-s_min |
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| 345 | if denom == 0.0: |
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| 346 | edgeflux = array([0.0, 0.0, 0.0]) |
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| 347 | max_speed = 0.0 |
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| 348 | else: |
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| 349 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
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| 350 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
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| 351 | |
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| 352 | edgeflux = rotate(edgeflux, normal, direction=-1) |
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| 353 | max_speed = max(abs(s_max), abs(s_min)) |
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| 354 | |
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| 355 | return edgeflux, max_speed |
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| 356 | |
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| 357 | |
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| 358 | def compute_fluxes(domain): |
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| 359 | """Compute all fluxes and the timestep suitable for all volumes |
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| 360 | in domain. |
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| 361 | |
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| 362 | Compute total flux for each conserved quantity using "flux_function" |
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| 363 | |
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| 364 | Fluxes across each edge are scaled by edgelengths and summed up |
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| 365 | Resulting flux is then scaled by area and stored in |
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| 366 | explicit_update for each of the three conserved quantities |
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| 367 | stage, xmomentum and ymomentum |
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| 368 | |
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| 369 | The maximal allowable speed computed by the flux_function for each volume |
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| 370 | is converted to a timestep that must not be exceeded. The minimum of |
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| 371 | those is computed as the next overall timestep. |
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| 372 | |
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| 373 | Post conditions: |
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| 374 | domain.explicit_update is reset to computed flux values |
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| 375 | domain.timestep is set to the largest step satisfying all volumes. |
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| 376 | """ |
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| 377 | |
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| 378 | import sys |
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| 379 | from Numeric import zeros, Float |
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| 380 | |
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| 381 | N = domain.number_of_elements |
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| 382 | |
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| 383 | #Shortcuts |
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| 384 | Stage = domain.quantities['stage'] |
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| 385 | Xmom = domain.quantities['xmomentum'] |
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| 386 | Ymom = domain.quantities['ymomentum'] |
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| 387 | Bed = domain.quantities['elevation'] |
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| 388 | |
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| 389 | #Arrays |
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| 390 | stage = Stage.edge_values |
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| 391 | xmom = Xmom.edge_values |
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| 392 | ymom = Ymom.edge_values |
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| 393 | bed = Bed.edge_values |
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| 394 | |
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| 395 | stage_bdry = Stage.boundary_values |
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| 396 | xmom_bdry = Xmom.boundary_values |
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| 397 | ymom_bdry = Ymom.boundary_values |
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| 398 | |
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| 399 | flux = zeros(3, Float) #Work array for summing up fluxes |
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| 400 | |
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| 401 | #Loop |
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| 402 | timestep = float(sys.maxint) |
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| 403 | for k in range(N): |
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| 404 | |
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| 405 | flux[:] = 0. #Reset work array |
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| 406 | for i in range(3): |
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| 407 | #Quantities inside volume facing neighbour i |
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| 408 | ql = [stage[k, i], xmom[k, i], ymom[k, i]] |
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| 409 | zl = bed[k, i] |
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| 410 | |
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| 411 | #Quantities at neighbour on nearest face |
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| 412 | n = domain.neighbours[k,i] |
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| 413 | if n < 0: |
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| 414 | m = -n-1 #Convert negative flag to index |
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| 415 | qr = [stage_bdry[m], xmom_bdry[m], ymom_bdry[m]] |
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| 416 | zr = zl #Extend bed elevation to boundary |
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| 417 | else: |
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| 418 | m = domain.neighbour_edges[k,i] |
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| 419 | qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
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| 420 | zr = bed[n, m] |
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| 421 | |
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| 422 | |
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| 423 | #Outward pointing normal vector |
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| 424 | normal = domain.normals[k, 2*i:2*i+2] |
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| 425 | |
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| 426 | #Flux computation using provided function |
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| 427 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
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| 428 | flux -= edgeflux * domain.edgelengths[k,i] |
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| 429 | |
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| 430 | #Update optimal_timestep |
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| 431 | try: |
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| 432 | timestep = min(timestep, domain.radii[k]/max_speed) |
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| 433 | except ZeroDivisionError: |
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| 434 | pass |
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| 435 | |
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| 436 | #Normalise by area and store for when all conserved |
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| 437 | #quantities get updated |
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| 438 | flux /= domain.areas[k] |
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| 439 | Stage.explicit_update[k] = flux[0] |
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| 440 | Xmom.explicit_update[k] = flux[1] |
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| 441 | Ymom.explicit_update[k] = flux[2] |
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| 442 | |
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| 443 | |
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| 444 | domain.timestep = timestep |
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| 445 | |
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| 446 | |
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| 447 | def compute_fluxes_c(domain): |
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| 448 | """Wrapper calling C version of compute fluxes |
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| 449 | """ |
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| 450 | |
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| 451 | import sys |
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| 452 | from Numeric import zeros, Float |
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| 453 | |
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| 454 | N = domain.number_of_elements |
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| 455 | |
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| 456 | #Shortcuts |
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| 457 | Stage = domain.quantities['stage'] |
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| 458 | Xmom = domain.quantities['xmomentum'] |
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| 459 | Ymom = domain.quantities['ymomentum'] |
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| 460 | Bed = domain.quantities['elevation'] |
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| 461 | |
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| 462 | timestep = float(sys.maxint) |
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| 463 | from shallow_water_ext import compute_fluxes |
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| 464 | domain.timestep = compute_fluxes(timestep, domain.epsilon, domain.g, |
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| 465 | domain.neighbours, |
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| 466 | domain.neighbour_edges, |
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| 467 | domain.normals, |
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| 468 | domain.edgelengths, |
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| 469 | domain.radii, |
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| 470 | domain.areas, |
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| 471 | Stage.edge_values, |
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| 472 | Xmom.edge_values, |
|---|
| 473 | Ymom.edge_values, |
|---|
| 474 | Bed.edge_values, |
|---|
| 475 | Stage.boundary_values, |
|---|
| 476 | Xmom.boundary_values, |
|---|
| 477 | Ymom.boundary_values, |
|---|
| 478 | Stage.explicit_update, |
|---|
| 479 | Xmom.explicit_update, |
|---|
| 480 | Ymom.explicit_update) |
|---|
| 481 | |
|---|
| 482 | |
|---|
| 483 | #################################### |
|---|
| 484 | # Module functions for gradient limiting (distribute_to_vertices_and_edges) |
|---|
| 485 | |
|---|
| 486 | def distribute_to_vertices_and_edges(domain): |
|---|
| 487 | """Distribution from centroids to vertices specific to the |
|---|
| 488 | shallow water wave |
|---|
| 489 | equation. |
|---|
| 490 | |
|---|
| 491 | It will ensure that h (w-z) is always non-negative even in the |
|---|
| 492 | presence of steep bed-slopes by taking a weighted average between shallow |
|---|
| 493 | and deep cases. |
|---|
| 494 | |
|---|
| 495 | In addition, all conserved quantities get distributed as per either a |
|---|
| 496 | constant (order==1) or a piecewise linear function (order==2). |
|---|
| 497 | |
|---|
| 498 | FIXME: more explanation about removal of artificial variability etc |
|---|
| 499 | |
|---|
| 500 | Precondition: |
|---|
| 501 | All quantities defined at centroids and bed elevation defined at |
|---|
| 502 | vertices. |
|---|
| 503 | |
|---|
| 504 | Postcondition |
|---|
| 505 | Conserved quantities defined at vertices |
|---|
| 506 | |
|---|
| 507 | """ |
|---|
| 508 | |
|---|
| 509 | #Remove very thin layers of water |
|---|
| 510 | protect_against_infinitesimal_and_negative_heights(domain) |
|---|
| 511 | |
|---|
| 512 | #Extrapolate all conserved quantities |
|---|
| 513 | for name in domain.conserved_quantities: |
|---|
| 514 | Q = domain.quantities[name] |
|---|
| 515 | if domain.order == 1: |
|---|
| 516 | Q.extrapolate_first_order() |
|---|
| 517 | elif domain.order == 2: |
|---|
| 518 | Q.extrapolate_second_order() |
|---|
| 519 | Q.limit() |
|---|
| 520 | else: |
|---|
| 521 | raise 'Unknown order' |
|---|
| 522 | |
|---|
| 523 | #Take bed elevation into account when water heights are small |
|---|
| 524 | balance_deep_and_shallow(domain) |
|---|
| 525 | |
|---|
| 526 | #Compute edge values by interpolation |
|---|
| 527 | for name in domain.conserved_quantities: |
|---|
| 528 | Q = domain.quantities[name] |
|---|
| 529 | Q.interpolate_from_vertices_to_edges() |
|---|
| 530 | |
|---|
| 531 | |
|---|
| 532 | |
|---|
| 533 | def dry(domain): |
|---|
| 534 | """Protect against infinitesimal heights and associated high velocities |
|---|
| 535 | at vertices |
|---|
| 536 | """ |
|---|
| 537 | |
|---|
| 538 | #FIXME: Experimental (from old version). Not in use at the moment |
|---|
| 539 | |
|---|
| 540 | #Shortcuts |
|---|
| 541 | wv = domain.quantities['stage'].vertex_values |
|---|
| 542 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 543 | xmomv = domain.quantities['xmomentum'].vertex_values |
|---|
| 544 | ymomv = domain.quantities['ymomentum'].vertex_values |
|---|
| 545 | hv = wv - zv #Water depths at vertices |
|---|
| 546 | |
|---|
| 547 | #Update |
|---|
| 548 | for k in range(domain.number_of_elements): |
|---|
| 549 | hmax = max(hv[k, :]) |
|---|
| 550 | |
|---|
| 551 | if hmax < domain.minimum_allowed_height: |
|---|
| 552 | #Control stage |
|---|
| 553 | wv[k, :] = zv[k, :] |
|---|
| 554 | |
|---|
| 555 | #Control momentum |
|---|
| 556 | xmomv[k,:] = ymomv[k,:] = 0.0 |
|---|
| 557 | |
|---|
| 558 | |
|---|
| 559 | def protect_against_infinitesimal_and_negative_heights(domain): |
|---|
| 560 | """Protect against infinitesimal heights and associated high velocities |
|---|
| 561 | """ |
|---|
| 562 | |
|---|
| 563 | #Shortcuts |
|---|
| 564 | wc = domain.quantities['stage'].centroid_values |
|---|
| 565 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 566 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 567 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 568 | hc = wc - zc #Water depths at centroids |
|---|
| 569 | |
|---|
| 570 | #Update |
|---|
| 571 | for k in range(domain.number_of_elements): |
|---|
| 572 | |
|---|
| 573 | if hc[k] < domain.minimum_allowed_height: |
|---|
| 574 | #Control stage |
|---|
| 575 | wc[k] = zc[k] |
|---|
| 576 | |
|---|
| 577 | #Control momentum |
|---|
| 578 | xmomc[k] = ymomc[k] = 0.0 |
|---|
| 579 | |
|---|
| 580 | |
|---|
| 581 | |
|---|
| 582 | def protect_against_infinitesimal_and_negative_heights_c(domain): |
|---|
| 583 | """Protect against infinitesimal heights and associated high velocities |
|---|
| 584 | """ |
|---|
| 585 | |
|---|
| 586 | #Shortcuts |
|---|
| 587 | wc = domain.quantities['stage'].centroid_values |
|---|
| 588 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 589 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 590 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 591 | |
|---|
| 592 | from shallow_water_ext import protect |
|---|
| 593 | |
|---|
| 594 | protect(domain.minimum_allowed_height, wc, zc, xmomc, ymomc) |
|---|
| 595 | |
|---|
| 596 | |
|---|
| 597 | def balance_deep_and_shallow(domain): |
|---|
| 598 | """Compute linear combination between stage as computed by |
|---|
| 599 | gradient-limiters and stage computed as constant height above bed. |
|---|
| 600 | The former takes precedence when heights are large compared to the |
|---|
| 601 | bed slope while the latter takes precedence when heights are |
|---|
| 602 | relatively small. Anything in between is computed as a balanced |
|---|
| 603 | linear combination in order to avoid numerical disturbances which |
|---|
| 604 | would otherwise appear as a result of hard switching between |
|---|
| 605 | modes. |
|---|
| 606 | """ |
|---|
| 607 | |
|---|
| 608 | #Shortcuts |
|---|
| 609 | wc = domain.quantities['stage'].centroid_values |
|---|
| 610 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 611 | hc = wc - zc |
|---|
| 612 | |
|---|
| 613 | wv = domain.quantities['stage'].vertex_values |
|---|
| 614 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 615 | hv = wv-zv |
|---|
| 616 | |
|---|
| 617 | |
|---|
| 618 | #Computed linear combination between constant stages and and |
|---|
| 619 | #stages parallel to the bed elevation. |
|---|
| 620 | for k in range(domain.number_of_elements): |
|---|
| 621 | #Compute maximal variation in bed elevation |
|---|
| 622 | # This quantitiy is |
|---|
| 623 | # dz = max_i abs(z_i - z_c) |
|---|
| 624 | # and it is independent of dimension |
|---|
| 625 | # In the 1d case zc = (z0+z1)/2 |
|---|
| 626 | # In the 2d case zc = (z0+z1+z2)/3 |
|---|
| 627 | |
|---|
| 628 | dz = max(abs(zv[k,0]-zc[k]), |
|---|
| 629 | abs(zv[k,1]-zc[k]), |
|---|
| 630 | abs(zv[k,2]-zc[k])) |
|---|
| 631 | |
|---|
| 632 | |
|---|
| 633 | hmin = min( hv[k,:] ) |
|---|
| 634 | |
|---|
| 635 | |
|---|
| 636 | #Create alpha in [0,1], where alpha==0 means using shallow |
|---|
| 637 | #first order scheme and alpha==1 means using the stage w as |
|---|
| 638 | #computed by the gradient limiter (1st or 2nd order) |
|---|
| 639 | # |
|---|
| 640 | #If hmin > dz/2 then alpha = 1 and the bed will have no effect |
|---|
| 641 | #If hmin < 0 then alpha = 0 reverting to constant height above bed. |
|---|
| 642 | |
|---|
| 643 | if dz > 0.0: |
|---|
| 644 | alpha = max( min( 2*hmin/dz, 1.0), 0.0 ) |
|---|
| 645 | else: |
|---|
| 646 | #Flat bed |
|---|
| 647 | alpha = 1.0 |
|---|
| 648 | |
|---|
| 649 | |
|---|
| 650 | #Weighted balance between stage parallel to bed elevation |
|---|
| 651 | #(wvi = zvi + hc) and stage as computed by 1st or 2nd |
|---|
| 652 | #order gradient limiter |
|---|
| 653 | #(wvi = zvi + hvi) where i=0,1,2 denotes the vertex ids |
|---|
| 654 | # |
|---|
| 655 | #It follows that the updated wvi is |
|---|
| 656 | # wvi := (1-alpha)*(zvi+hc) + alpha*(zvi+hvi) = |
|---|
| 657 | # zvi + hc + alpha*(hvi - hc) |
|---|
| 658 | # |
|---|
| 659 | #Note that hvi = zc+hc-zvi in the first order case (constant). |
|---|
| 660 | |
|---|
| 661 | if alpha < 1: |
|---|
| 662 | for i in range(3): |
|---|
| 663 | wv[k,i] = zv[k,i] + hc[k] + alpha*(hv[k,i]-hc[k]) |
|---|
| 664 | |
|---|
| 665 | |
|---|
| 666 | #Momentums at centroids |
|---|
| 667 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 668 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 669 | |
|---|
| 670 | #Momentums at vertices |
|---|
| 671 | xmomv = domain.quantities['xmomentum'].vertex_values |
|---|
| 672 | ymomv = domain.quantities['ymomentum'].vertex_values |
|---|
| 673 | |
|---|
| 674 | # Update momentum as a linear combination of |
|---|
| 675 | # xmomc and ymomc (shallow) and momentum |
|---|
| 676 | # from extrapolator xmomv and ymomv (deep). |
|---|
| 677 | xmomv[k,:] = (1-alpha)*xmomc[k] + alpha*xmomv[k,:] |
|---|
| 678 | ymomv[k,:] = (1-alpha)*ymomc[k] + alpha*ymomv[k,:] |
|---|
| 679 | |
|---|
| 680 | |
|---|
| 681 | |
|---|
| 682 | def balance_deep_and_shallow_c(domain): |
|---|
| 683 | """Wrapper for C implementation |
|---|
| 684 | """ |
|---|
| 685 | |
|---|
| 686 | #Shortcuts |
|---|
| 687 | wc = domain.quantities['stage'].centroid_values |
|---|
| 688 | zc = domain.quantities['elevation'].centroid_values |
|---|
| 689 | hc = wc - zc |
|---|
| 690 | |
|---|
| 691 | wv = domain.quantities['stage'].vertex_values |
|---|
| 692 | zv = domain.quantities['elevation'].vertex_values |
|---|
| 693 | hv = wv-zv |
|---|
| 694 | |
|---|
| 695 | #Momentums at centroids |
|---|
| 696 | xmomc = domain.quantities['xmomentum'].centroid_values |
|---|
| 697 | ymomc = domain.quantities['ymomentum'].centroid_values |
|---|
| 698 | |
|---|
| 699 | #Momentums at vertices |
|---|
| 700 | xmomv = domain.quantities['xmomentum'].vertex_values |
|---|
| 701 | ymomv = domain.quantities['ymomentum'].vertex_values |
|---|
| 702 | |
|---|
| 703 | |
|---|
| 704 | |
|---|
| 705 | from shallow_water_ext import balance_deep_and_shallow |
|---|
| 706 | balance_deep_and_shallow(wc, zc, hc, wv, zv, hv, |
|---|
| 707 | xmomc, ymomc, xmomv, ymomv) |
|---|
| 708 | |
|---|
| 709 | |
|---|
| 710 | |
|---|
| 711 | |
|---|
| 712 | ############################################### |
|---|
| 713 | #Boundaries - specific to the shallow water wave equation |
|---|
| 714 | class Reflective_boundary(Boundary): |
|---|
| 715 | """Reflective boundary returns same conserved quantities as |
|---|
| 716 | those present in its neighbour volume but reflected. |
|---|
| 717 | |
|---|
| 718 | This class is specific to the shallow water equation as it |
|---|
| 719 | works with the momentum quantities assumed to be the second |
|---|
| 720 | and third conserved quantities. |
|---|
| 721 | """ |
|---|
| 722 | |
|---|
| 723 | def __init__(self, domain = None): |
|---|
| 724 | Boundary.__init__(self) |
|---|
| 725 | |
|---|
| 726 | if domain is None: |
|---|
| 727 | msg = 'Domain must be specified for reflective boundary' |
|---|
| 728 | raise msg |
|---|
| 729 | |
|---|
| 730 | #Handy shorthands |
|---|
| 731 | self.stage = domain.quantities['stage'].edge_values |
|---|
| 732 | self.xmom = domain.quantities['xmomentum'].edge_values |
|---|
| 733 | self.ymom = domain.quantities['ymomentum'].edge_values |
|---|
| 734 | self.normals = domain.normals |
|---|
| 735 | |
|---|
| 736 | from Numeric import zeros, Float |
|---|
| 737 | self.conserved_quantities = zeros(3, Float) |
|---|
| 738 | |
|---|
| 739 | def __repr__(self): |
|---|
| 740 | return 'Reflective_boundary' |
|---|
| 741 | |
|---|
| 742 | |
|---|
| 743 | def evaluate(self, vol_id, edge_id): |
|---|
| 744 | """Reflective boundaries reverses the outward momentum |
|---|
| 745 | of the volume they serve. |
|---|
| 746 | """ |
|---|
| 747 | |
|---|
| 748 | q = self.conserved_quantities |
|---|
| 749 | q[0] = self.stage[vol_id, edge_id] |
|---|
| 750 | q[1] = self.xmom[vol_id, edge_id] |
|---|
| 751 | q[2] = self.ymom[vol_id, edge_id] |
|---|
| 752 | |
|---|
| 753 | normal = self.normals[vol_id, 2*edge_id:2*edge_id+2] |
|---|
| 754 | |
|---|
| 755 | |
|---|
| 756 | r = rotate(q, normal, direction = 1) |
|---|
| 757 | r[1] = -r[1] |
|---|
| 758 | q = rotate(r, normal, direction = -1) |
|---|
| 759 | |
|---|
| 760 | return q |
|---|
| 761 | |
|---|
| 762 | |
|---|
| 763 | #class Spatio_temporal_boundary(Boundary): |
|---|
| 764 | # """The spatio-temporal boundary, reads values for the conserved |
|---|
| 765 | # quantities from an sww NetCDF file, and returns interpolated values |
|---|
| 766 | # at the midpoints of each associated boundaty segment. |
|---|
| 767 | # Time dependency is interpolated linearly as in util.File_function.# |
|---|
| 768 | # |
|---|
| 769 | # Example: |
|---|
| 770 | # Bf = Spatio_temporal_boundary('source_file.sww', domain) |
|---|
| 771 | # |
|---|
| 772 | # """ |
|---|
| 773 | Spatio_temporal_boundary = File_boundary |
|---|
| 774 | |
|---|
| 775 | |
|---|
| 776 | |
|---|
| 777 | |
|---|
| 778 | ######################### |
|---|
| 779 | #Standard forcing terms: |
|---|
| 780 | # |
|---|
| 781 | def gravity(domain): |
|---|
| 782 | """Apply gravitational pull in the presence of bed slope |
|---|
| 783 | """ |
|---|
| 784 | |
|---|
| 785 | from util import gradient |
|---|
| 786 | from Numeric import zeros, Float, array, sum |
|---|
| 787 | |
|---|
| 788 | xmom = domain.quantities['xmomentum'].explicit_update |
|---|
| 789 | ymom = domain.quantities['ymomentum'].explicit_update |
|---|
| 790 | |
|---|
| 791 | Stage = domain.quantities['stage'] |
|---|
| 792 | Elevation = domain.quantities['elevation'] |
|---|
| 793 | h = Stage.edge_values - Elevation.edge_values |
|---|
| 794 | v = Elevation.vertex_values |
|---|
| 795 | |
|---|
| 796 | x = domain.get_vertex_coordinates() |
|---|
| 797 | g = domain.g |
|---|
| 798 | |
|---|
| 799 | for k in range(domain.number_of_elements): |
|---|
| 800 | avg_h = sum( h[k,:] )/3 |
|---|
| 801 | |
|---|
| 802 | #Compute bed slope |
|---|
| 803 | x0, y0, x1, y1, x2, y2 = x[k,:] |
|---|
| 804 | z0, z1, z2 = v[k,:] |
|---|
| 805 | |
|---|
| 806 | zx, zy = gradient(x0, y0, x1, y1, x2, y2, z0, z1, z2) |
|---|
| 807 | |
|---|
| 808 | #Update momentum |
|---|
| 809 | xmom[k] += -g*zx*avg_h |
|---|
| 810 | ymom[k] += -g*zy*avg_h |
|---|
| 811 | |
|---|
| 812 | |
|---|
| 813 | def gravity_c(domain): |
|---|
| 814 | """Wrapper calling C version |
|---|
| 815 | """ |
|---|
| 816 | |
|---|
| 817 | xmom = domain.quantities['xmomentum'].explicit_update |
|---|
| 818 | ymom = domain.quantities['ymomentum'].explicit_update |
|---|
| 819 | |
|---|
| 820 | Stage = domain.quantities['stage'] |
|---|
| 821 | Elevation = domain.quantities['elevation'] |
|---|
| 822 | h = Stage.edge_values - Elevation.edge_values |
|---|
| 823 | v = Elevation.vertex_values |
|---|
| 824 | |
|---|
| 825 | x = domain.get_vertex_coordinates() |
|---|
| 826 | g = domain.g |
|---|
| 827 | |
|---|
| 828 | |
|---|
| 829 | from shallow_water_ext import gravity |
|---|
| 830 | gravity(g, h, v, x, xmom, ymom) |
|---|
| 831 | |
|---|
| 832 | |
|---|
| 833 | def manning_friction(domain): |
|---|
| 834 | """Apply (Manning) friction to water momentum |
|---|
| 835 | """ |
|---|
| 836 | |
|---|
| 837 | from math import sqrt |
|---|
| 838 | |
|---|
| 839 | w = domain.quantities['stage'].centroid_values |
|---|
| 840 | z = domain.quantities['elevation'].centroid_values |
|---|
| 841 | h = w-z |
|---|
| 842 | |
|---|
| 843 | uh = domain.quantities['xmomentum'].centroid_values |
|---|
| 844 | vh = domain.quantities['ymomentum'].centroid_values |
|---|
| 845 | eta = domain.quantities['friction'].centroid_values |
|---|
| 846 | |
|---|
| 847 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
|---|
| 848 | ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
|---|
| 849 | |
|---|
| 850 | N = domain.number_of_elements |
|---|
| 851 | eps = domain.minimum_allowed_height |
|---|
| 852 | g = domain.g |
|---|
| 853 | |
|---|
| 854 | for k in range(N): |
|---|
| 855 | if eta[k] >= eps: |
|---|
| 856 | if h[k] >= eps: |
|---|
| 857 | S = -g * eta[k]**2 * sqrt((uh[k]**2 + vh[k]**2)) |
|---|
| 858 | S /= h[k]**(7.0/3) |
|---|
| 859 | |
|---|
| 860 | #Update momentum |
|---|
| 861 | xmom_update[k] += S*uh[k] |
|---|
| 862 | ymom_update[k] += S*vh[k] |
|---|
| 863 | |
|---|
| 864 | |
|---|
| 865 | def manning_friction_c(domain): |
|---|
| 866 | """Wrapper for c version |
|---|
| 867 | """ |
|---|
| 868 | |
|---|
| 869 | |
|---|
| 870 | xmom = domain.quantities['xmomentum'] |
|---|
| 871 | ymom = domain.quantities['ymomentum'] |
|---|
| 872 | |
|---|
| 873 | w = domain.quantities['stage'].centroid_values |
|---|
| 874 | z = domain.quantities['elevation'].centroid_values |
|---|
| 875 | |
|---|
| 876 | uh = xmom.centroid_values |
|---|
| 877 | vh = ymom.centroid_values |
|---|
| 878 | eta = domain.quantities['friction'].centroid_values |
|---|
| 879 | |
|---|
| 880 | xmom_update = xmom.semi_implicit_update |
|---|
| 881 | ymom_update = ymom.semi_implicit_update |
|---|
| 882 | |
|---|
| 883 | N = domain.number_of_elements |
|---|
| 884 | eps = domain.minimum_allowed_height |
|---|
| 885 | g = domain.g |
|---|
| 886 | |
|---|
| 887 | from shallow_water_ext import manning_friction |
|---|
| 888 | manning_friction(g, eps, w, z, uh, vh, eta, xmom_update, ymom_update) |
|---|
| 889 | |
|---|
| 890 | |
|---|
| 891 | def linear_friction(domain): |
|---|
| 892 | """Apply linear friction to water momentum |
|---|
| 893 | |
|---|
| 894 | Assumes quantity: 'linear_friction' to be present |
|---|
| 895 | """ |
|---|
| 896 | |
|---|
| 897 | from math import sqrt |
|---|
| 898 | |
|---|
| 899 | w = domain.quantities['stage'].centroid_values |
|---|
| 900 | z = domain.quantities['elevation'].centroid_values |
|---|
| 901 | h = w-z |
|---|
| 902 | |
|---|
| 903 | uh = domain.quantities['xmomentum'].centroid_values |
|---|
| 904 | vh = domain.quantities['ymomentum'].centroid_values |
|---|
| 905 | tau = domain.quantities['linear_friction'].centroid_values |
|---|
| 906 | |
|---|
| 907 | xmom_update = domain.quantities['xmomentum'].semi_implicit_update |
|---|
| 908 | ymom_update = domain.quantities['ymomentum'].semi_implicit_update |
|---|
| 909 | |
|---|
| 910 | N = domain.number_of_elements |
|---|
| 911 | eps = domain.minimum_allowed_height |
|---|
| 912 | |
|---|
| 913 | for k in range(N): |
|---|
| 914 | if tau[k] >= eps: |
|---|
| 915 | if h[k] >= eps: |
|---|
| 916 | S = -tau[k]/h[k] |
|---|
| 917 | |
|---|
| 918 | #Update momentum |
|---|
| 919 | xmom_update[k] += S*uh[k] |
|---|
| 920 | ymom_update[k] += S*vh[k] |
|---|
| 921 | |
|---|
| 922 | |
|---|
| 923 | |
|---|
| 924 | def check_forcefield(f): |
|---|
| 925 | """Check that f is either |
|---|
| 926 | 1: a callable object f(t,x,y), where x and y are vectors |
|---|
| 927 | and that it returns an array or a list of same length |
|---|
| 928 | as x and y |
|---|
| 929 | 2: a scalar |
|---|
| 930 | """ |
|---|
| 931 | |
|---|
| 932 | from Numeric import ones, Float, array |
|---|
| 933 | |
|---|
| 934 | |
|---|
| 935 | if callable(f): |
|---|
| 936 | N = 3 |
|---|
| 937 | x = ones(3, Float) |
|---|
| 938 | y = ones(3, Float) |
|---|
| 939 | try: |
|---|
| 940 | q = f(1.0, x, y) |
|---|
| 941 | except Exception, e: |
|---|
| 942 | msg = 'Function %s could not be executed:\n%s' %(f, e) |
|---|
| 943 | raise msg |
|---|
| 944 | |
|---|
| 945 | try: |
|---|
| 946 | q = array(q).astype(Float) |
|---|
| 947 | except: |
|---|
| 948 | msg = 'Return value from vector function %s could ' %f |
|---|
| 949 | msg += 'not be converted into a Numeric array of floats.\n' |
|---|
| 950 | msg += 'Specified function should return either list or array.' |
|---|
| 951 | raise msg |
|---|
| 952 | |
|---|
| 953 | msg = 'Return vector from function %s' %f |
|---|
| 954 | msg += 'must have same lenght as input vectors' |
|---|
| 955 | assert len(q) == N, msg |
|---|
| 956 | |
|---|
| 957 | else: |
|---|
| 958 | try: |
|---|
| 959 | f = float(f) |
|---|
| 960 | except: |
|---|
| 961 | msg = 'Force field %s must be either a scalar' %f |
|---|
| 962 | msg += ' or a vector function' |
|---|
| 963 | raise msg |
|---|
| 964 | return f |
|---|
| 965 | |
|---|
| 966 | |
|---|
| 967 | class Wind_stress: |
|---|
| 968 | """Apply wind stress to water momentum in terms of |
|---|
| 969 | wind speed [m/s] and wind direction [degrees] |
|---|
| 970 | """ |
|---|
| 971 | |
|---|
| 972 | def __init__(self, *args, **kwargs): |
|---|
| 973 | """Initialise windfield from wind speed s [m/s] |
|---|
| 974 | and wind direction phi [degrees] |
|---|
| 975 | |
|---|
| 976 | Inputs v and phi can be either scalars or Python functions, e.g. |
|---|
| 977 | |
|---|
| 978 | W = Wind_stress(10, 178) |
|---|
| 979 | |
|---|
| 980 | #FIXME - 'normal' degrees are assumed for now, i.e. the |
|---|
| 981 | vector (1,0) has zero degrees. |
|---|
| 982 | We may need to convert from 'compass' degrees later on and also |
|---|
| 983 | map from True north to grid north. |
|---|
| 984 | |
|---|
| 985 | Arguments can also be Python functions of t,x,y as in |
|---|
| 986 | |
|---|
| 987 | def speed(t,x,y): |
|---|
| 988 | ... |
|---|
| 989 | return s |
|---|
| 990 | |
|---|
| 991 | def angle(t,x,y): |
|---|
| 992 | ... |
|---|
| 993 | return phi |
|---|
| 994 | |
|---|
| 995 | where x and y are vectors. |
|---|
| 996 | |
|---|
| 997 | and then pass the functions in |
|---|
| 998 | |
|---|
| 999 | W = Wind_stress(speed, angle) |
|---|
| 1000 | |
|---|
| 1001 | The instantiated object W can be appended to the list of |
|---|
| 1002 | forcing_terms as in |
|---|
| 1003 | |
|---|
| 1004 | Alternatively, one vector valued function for (speed, angle) |
|---|
| 1005 | can be applied, providing both quantities simultaneously. |
|---|
| 1006 | As in |
|---|
| 1007 | W = Wind_stress(F), where returns (speed, angle) for each t. |
|---|
| 1008 | |
|---|
| 1009 | domain.forcing_terms.append(W) |
|---|
| 1010 | """ |
|---|
| 1011 | |
|---|
| 1012 | from config import rho_a, rho_w, eta_w |
|---|
| 1013 | from Numeric import array, Float |
|---|
| 1014 | |
|---|
| 1015 | if len(args) == 2: |
|---|
| 1016 | s = args[0] |
|---|
| 1017 | phi = args[1] |
|---|
| 1018 | elif len(args) == 1: |
|---|
| 1019 | #Assume vector function returning (s, phi)(t,x,y) |
|---|
| 1020 | vector_function = args[0] |
|---|
| 1021 | s = lambda t,x,y: vector_function(t,x,y)[0] |
|---|
| 1022 | phi = lambda t,x,y: vector_function(t,x,y)[1] |
|---|
| 1023 | else: |
|---|
| 1024 | #Assume info is in 2 keyword arguments |
|---|
| 1025 | |
|---|
| 1026 | if len(kwargs) == 2: |
|---|
| 1027 | s = kwargs['s'] |
|---|
| 1028 | phi = kwargs['phi'] |
|---|
| 1029 | else: |
|---|
| 1030 | raise 'Assumes two keyword arguments: s=..., phi=....' |
|---|
| 1031 | |
|---|
| 1032 | self.speed = check_forcefield(s) |
|---|
| 1033 | self.phi = check_forcefield(phi) |
|---|
| 1034 | |
|---|
| 1035 | self.const = eta_w*rho_a/rho_w |
|---|
| 1036 | |
|---|
| 1037 | |
|---|
| 1038 | def __call__(self, domain): |
|---|
| 1039 | """Evaluate windfield based on values found in domain |
|---|
| 1040 | """ |
|---|
| 1041 | |
|---|
| 1042 | from math import pi, cos, sin, sqrt |
|---|
| 1043 | from Numeric import Float, ones, ArrayType |
|---|
| 1044 | |
|---|
| 1045 | xmom_update = domain.quantities['xmomentum'].explicit_update |
|---|
| 1046 | ymom_update = domain.quantities['ymomentum'].explicit_update |
|---|
| 1047 | |
|---|
| 1048 | N = domain.number_of_elements |
|---|
| 1049 | t = domain.time |
|---|
| 1050 | |
|---|
| 1051 | if callable(self.speed): |
|---|
| 1052 | xc = domain.get_centroid_coordinates() |
|---|
| 1053 | s_vec = self.speed(t, xc[:,0], xc[:,1]) |
|---|
| 1054 | else: |
|---|
| 1055 | #Assume s is a scalar |
|---|
| 1056 | |
|---|
| 1057 | try: |
|---|
| 1058 | s_vec = self.speed * ones(N, Float) |
|---|
| 1059 | except: |
|---|
| 1060 | msg = 'Speed must be either callable or a scalar: %s' %self.s |
|---|
| 1061 | raise msg |
|---|
| 1062 | |
|---|
| 1063 | |
|---|
| 1064 | if callable(self.phi): |
|---|
| 1065 | xc = domain.get_centroid_coordinates() |
|---|
| 1066 | phi_vec = self.phi(t, xc[:,0], xc[:,1]) |
|---|
| 1067 | else: |
|---|
| 1068 | #Assume phi is a scalar |
|---|
| 1069 | |
|---|
| 1070 | try: |
|---|
| 1071 | phi_vec = self.phi * ones(N, Float) |
|---|
| 1072 | except: |
|---|
| 1073 | msg = 'Angle must be either callable or a scalar: %s' %self.phi |
|---|
| 1074 | raise msg |
|---|
| 1075 | |
|---|
| 1076 | assign_windfield_values(xmom_update, ymom_update, |
|---|
| 1077 | s_vec, phi_vec, self.const) |
|---|
| 1078 | |
|---|
| 1079 | |
|---|
| 1080 | def assign_windfield_values(xmom_update, ymom_update, |
|---|
| 1081 | s_vec, phi_vec, const): |
|---|
| 1082 | """Python version of assigning wind field to update vectors. |
|---|
| 1083 | A c version also exists (for speed) |
|---|
| 1084 | """ |
|---|
| 1085 | from math import pi, cos, sin, sqrt |
|---|
| 1086 | |
|---|
| 1087 | N = len(s_vec) |
|---|
| 1088 | for k in range(N): |
|---|
| 1089 | s = s_vec[k] |
|---|
| 1090 | phi = phi_vec[k] |
|---|
| 1091 | |
|---|
| 1092 | #Convert to radians |
|---|
| 1093 | phi = phi*pi/180 |
|---|
| 1094 | |
|---|
| 1095 | #Compute velocity vector (u, v) |
|---|
| 1096 | u = s*cos(phi) |
|---|
| 1097 | v = s*sin(phi) |
|---|
| 1098 | |
|---|
| 1099 | #Compute wind stress |
|---|
| 1100 | S = const * sqrt(u**2 + v**2) |
|---|
| 1101 | xmom_update[k] += S*u |
|---|
| 1102 | ymom_update[k] += S*v |
|---|
| 1103 | |
|---|
| 1104 | |
|---|
| 1105 | |
|---|
| 1106 | ########################### |
|---|
| 1107 | ########################### |
|---|
| 1108 | #Geometries |
|---|
| 1109 | |
|---|
| 1110 | |
|---|
| 1111 | #FIXME: Rethink this way of creating values. |
|---|
| 1112 | |
|---|
| 1113 | |
|---|
| 1114 | class Weir: |
|---|
| 1115 | """Set a bathymetry for weir with a hole and a downstream gutter |
|---|
| 1116 | x,y are assumed to be in the unit square |
|---|
| 1117 | """ |
|---|
| 1118 | |
|---|
| 1119 | def __init__(self, stage): |
|---|
| 1120 | self.inflow_stage = stage |
|---|
| 1121 | |
|---|
| 1122 | def __call__(self, x, y): |
|---|
| 1123 | from Numeric import zeros, Float |
|---|
| 1124 | from math import sqrt |
|---|
| 1125 | |
|---|
| 1126 | N = len(x) |
|---|
| 1127 | assert N == len(y) |
|---|
| 1128 | |
|---|
| 1129 | z = zeros(N, Float) |
|---|
| 1130 | for i in range(N): |
|---|
| 1131 | z[i] = -x[i]/2 #General slope |
|---|
| 1132 | |
|---|
| 1133 | #Flattish bit to the left |
|---|
| 1134 | if x[i] < 0.3: |
|---|
| 1135 | z[i] = -x[i]/10 |
|---|
| 1136 | |
|---|
| 1137 | #Weir |
|---|
| 1138 | if x[i] >= 0.3 and x[i] < 0.4: |
|---|
| 1139 | z[i] = -x[i]+0.9 |
|---|
| 1140 | |
|---|
| 1141 | #Dip |
|---|
| 1142 | x0 = 0.6 |
|---|
| 1143 | #depth = -1.3 |
|---|
| 1144 | depth = -1.0 |
|---|
| 1145 | #plateaux = -0.9 |
|---|
| 1146 | plateaux = -0.6 |
|---|
| 1147 | if y[i] < 0.7: |
|---|
| 1148 | if x[i] > x0 and x[i] < 0.9: |
|---|
| 1149 | z[i] = depth |
|---|
| 1150 | |
|---|
| 1151 | #RHS plateaux |
|---|
| 1152 | if x[i] >= 0.9: |
|---|
| 1153 | z[i] = plateaux |
|---|
| 1154 | |
|---|
| 1155 | |
|---|
| 1156 | elif y[i] >= 0.7 and y[i] < 1.5: |
|---|
| 1157 | #Restrict and deepen |
|---|
| 1158 | if x[i] >= x0 and x[i] < 0.8: |
|---|
| 1159 | z[i] = depth-(y[i]/3-0.3) |
|---|
| 1160 | #z[i] = depth-y[i]/5 |
|---|
| 1161 | #z[i] = depth |
|---|
| 1162 | elif x[i] >= 0.8: |
|---|
| 1163 | #RHS plateaux |
|---|
| 1164 | z[i] = plateaux |
|---|
| 1165 | |
|---|
| 1166 | elif y[i] >= 1.5: |
|---|
| 1167 | if x[i] >= x0 and x[i] < 0.8 + (y[i]-1.5)/1.2: |
|---|
| 1168 | #Widen up and stay at constant depth |
|---|
| 1169 | z[i] = depth-1.5/5 |
|---|
| 1170 | elif x[i] >= 0.8 + (y[i]-1.5)/1.2: |
|---|
| 1171 | #RHS plateaux |
|---|
| 1172 | z[i] = plateaux |
|---|
| 1173 | |
|---|
| 1174 | |
|---|
| 1175 | #Hole in weir (slightly higher than inflow condition) |
|---|
| 1176 | if x[i] >= 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1177 | z[i] = -x[i]+self.inflow_stage + 0.02 |
|---|
| 1178 | |
|---|
| 1179 | #Channel behind weir |
|---|
| 1180 | x0 = 0.5 |
|---|
| 1181 | if x[i] >= 0.4 and x[i] < x0 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1182 | z[i] = -x[i]+self.inflow_stage + 0.02 |
|---|
| 1183 | |
|---|
| 1184 | if x[i] >= x0 and x[i] < 0.6 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1185 | #Flatten it out towards the end |
|---|
| 1186 | z[i] = -x0+self.inflow_stage + 0.02 + (x0-x[i])/5 |
|---|
| 1187 | |
|---|
| 1188 | #Hole to the east |
|---|
| 1189 | x0 = 1.1; y0 = 0.35 |
|---|
| 1190 | #if x[i] < -0.2 and y < 0.5: |
|---|
| 1191 | if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: |
|---|
| 1192 | z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-1.0 |
|---|
| 1193 | |
|---|
| 1194 | #Tiny channel draining hole |
|---|
| 1195 | if x[i] >= 1.14 and x[i] < 1.2 and y[i] >= 0.4 and y[i] < 0.6: |
|---|
| 1196 | z[i] = -0.9 #North south |
|---|
| 1197 | |
|---|
| 1198 | if x[i] >= 0.9 and x[i] < 1.18 and y[i] >= 0.58 and y[i] < 0.65: |
|---|
| 1199 | z[i] = -1.0 + (x[i]-0.9)/3 #East west |
|---|
| 1200 | |
|---|
| 1201 | |
|---|
| 1202 | |
|---|
| 1203 | #Stuff not in use |
|---|
| 1204 | |
|---|
| 1205 | #Upward slope at inlet to the north west |
|---|
| 1206 | #if x[i] < 0.0: # and y[i] > 0.5: |
|---|
| 1207 | # #z[i] = -y[i]+0.5 #-x[i]/2 |
|---|
| 1208 | # z[i] = x[i]/4 - y[i]**2 + 0.5 |
|---|
| 1209 | |
|---|
| 1210 | #Hole to the west |
|---|
| 1211 | #x0 = -0.4; y0 = 0.35 # center |
|---|
| 1212 | #if sqrt((2*(x[i]-x0))**2 + (2*(y[i]-y0))**2) < 0.2: |
|---|
| 1213 | # z[i] = sqrt(((x[i]-x0))**2 + ((y[i]-y0))**2)-0.2 |
|---|
| 1214 | |
|---|
| 1215 | |
|---|
| 1216 | |
|---|
| 1217 | |
|---|
| 1218 | |
|---|
| 1219 | return z/2 |
|---|
| 1220 | |
|---|
| 1221 | class Weir_simple: |
|---|
| 1222 | """Set a bathymetry for weir with a hole and a downstream gutter |
|---|
| 1223 | x,y are assumed to be in the unit square |
|---|
| 1224 | """ |
|---|
| 1225 | |
|---|
| 1226 | def __init__(self, stage): |
|---|
| 1227 | self.inflow_stage = stage |
|---|
| 1228 | |
|---|
| 1229 | def __call__(self, x, y): |
|---|
| 1230 | from Numeric import zeros, Float |
|---|
| 1231 | |
|---|
| 1232 | N = len(x) |
|---|
| 1233 | assert N == len(y) |
|---|
| 1234 | |
|---|
| 1235 | z = zeros(N, Float) |
|---|
| 1236 | for i in range(N): |
|---|
| 1237 | z[i] = -x[i] #General slope |
|---|
| 1238 | |
|---|
| 1239 | #Flat bit to the left |
|---|
| 1240 | if x[i] < 0.3: |
|---|
| 1241 | z[i] = -x[i]/10 #General slope |
|---|
| 1242 | |
|---|
| 1243 | #Weir |
|---|
| 1244 | if x[i] > 0.3 and x[i] < 0.4: |
|---|
| 1245 | z[i] = -x[i]+0.9 |
|---|
| 1246 | |
|---|
| 1247 | #Dip |
|---|
| 1248 | if x[i] > 0.6 and x[i] < 0.9: |
|---|
| 1249 | z[i] = -x[i]-0.5 #-y[i]/5 |
|---|
| 1250 | |
|---|
| 1251 | #Hole in weir (slightly higher than inflow condition) |
|---|
| 1252 | if x[i] > 0.3 and x[i] < 0.4 and y[i] > 0.2 and y[i] < 0.4: |
|---|
| 1253 | z[i] = -x[i]+self.inflow_stage + 0.05 |
|---|
| 1254 | |
|---|
| 1255 | |
|---|
| 1256 | return z/2 |
|---|
| 1257 | |
|---|
| 1258 | |
|---|
| 1259 | |
|---|
| 1260 | class Constant_height: |
|---|
| 1261 | """Set an initial condition with constant water height, e.g |
|---|
| 1262 | stage s = z+h |
|---|
| 1263 | """ |
|---|
| 1264 | def __init__(self, W, h): |
|---|
| 1265 | self.W = W |
|---|
| 1266 | self.h = h |
|---|
| 1267 | |
|---|
| 1268 | def __call__(self, x, y): |
|---|
| 1269 | if self.W is None: |
|---|
| 1270 | from Numeric import ones, Float |
|---|
| 1271 | return self.h*ones(len(x), Float) |
|---|
| 1272 | else: |
|---|
| 1273 | return self.W(x,y) + self.h |
|---|
| 1274 | |
|---|
| 1275 | |
|---|
| 1276 | |
|---|
| 1277 | ############################################## |
|---|
| 1278 | #Initialise module |
|---|
| 1279 | |
|---|
| 1280 | |
|---|
| 1281 | import compile |
|---|
| 1282 | if compile.can_use_C_extension('shallow_water_ext.c'): |
|---|
| 1283 | #Replace python version with c implementations |
|---|
| 1284 | |
|---|
| 1285 | from shallow_water_ext import rotate, assign_windfield_values |
|---|
| 1286 | compute_fluxes = compute_fluxes_c |
|---|
| 1287 | gravity = gravity_c |
|---|
| 1288 | manning_friction = manning_friction_c |
|---|
| 1289 | balance_deep_and_shallow = balance_deep_and_shallow_c |
|---|
| 1290 | protect_against_infinitesimal_and_negative_heights = protect_against_infinitesimal_and_negative_heights_c |
|---|
| 1291 | |
|---|
| 1292 | |
|---|
| 1293 | #distribute_to_vertices_and_edges = distribute_to_vertices_and_edges_c |
|---|
| 1294 | |
|---|
| 1295 | |
|---|
| 1296 | #Optimisation with psyco |
|---|
| 1297 | from config import use_psyco |
|---|
| 1298 | if use_psyco: |
|---|
| 1299 | try: |
|---|
| 1300 | import psyco |
|---|
| 1301 | except: |
|---|
| 1302 | msg = 'WARNING: psyco (speedup) could not import'+\ |
|---|
| 1303 | ', you may want to consider installing it' |
|---|
| 1304 | print msg |
|---|
| 1305 | else: |
|---|
| 1306 | psyco.bind(Domain.distribute_to_vertices_and_edges) |
|---|
| 1307 | psyco.bind(Domain.compute_fluxes) |
|---|
| 1308 | |
|---|
| 1309 | if __name__ == "__main__": |
|---|
| 1310 | pass |
|---|
