[7909] | 1 | """Class Domain - 1D domains for finite-volume computations of |
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| 2 | the shallow water wave equation |
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| 3 | |
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| 4 | |
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| 5 | Copyright 2004 |
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| 6 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 7 | Geoscience Australia |
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| 8 | """ |
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| 9 | |
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| 10 | from generic_boundary_conditions import * |
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| 11 | |
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| 12 | |
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| 13 | class Domain: |
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| 14 | |
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| 15 | def __init__(self, |
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| 16 | coordinates, |
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| 17 | boundary = None, |
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| 18 | conserved_quantities = None, |
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| 19 | evolved_quantities = None, |
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| 20 | other_quantities = None, |
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| 21 | tagged_elements = None): |
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| 22 | """ |
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| 23 | Build 1D elements from x coordinates |
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| 24 | """ |
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| 25 | |
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| 26 | from Numeric import Float, Int |
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| 27 | from numpy import array, zeros |
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| 28 | |
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| 29 | from config import timestepping_method |
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| 30 | from config import CFL |
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| 31 | |
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| 32 | #Store Points |
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| 33 | self.coordinates = array(coordinates) |
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| 34 | |
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| 35 | |
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| 36 | #Register number of Elements |
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| 37 | self.number_of_elements = N = len(self.coordinates)-1 |
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| 38 | |
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| 39 | self.beta = 1.0 |
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| 40 | self.set_limiter("minmod_kurganov") |
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| 41 | self.set_CFL(CFL) |
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| 42 | self.set_timestepping_method(timestepping_method) |
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| 43 | |
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| 44 | self.wet_nodes = zeros((N,2), Int) # should this be here |
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| 45 | |
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| 46 | #Allocate space for neighbour and boundary structures |
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| 47 | self.neighbours = zeros((N, 2), Int) |
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| 48 | self.neighbour_vertices = zeros((N, 2), Int) |
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| 49 | self.number_of_boundaries = zeros(N, Int) |
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| 50 | self.surrogate_neighbours = zeros((N, 2), Int) |
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| 51 | |
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| 52 | #Allocate space for geometric quantities |
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| 53 | self.vertices = zeros((N, 2), Float) |
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| 54 | self.centroids = zeros(N, Float) |
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| 55 | self.areas = zeros(N, Float) |
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| 56 | self.max_speed_array = zeros(N, Float) |
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| 57 | self.normals = zeros((N, 2), Float) |
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| 58 | |
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| 59 | for i in range(N): |
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| 60 | xl = self.coordinates[i] |
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| 61 | xr = self.coordinates[i+1] |
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| 62 | self.vertices[i,0] = xl |
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| 63 | self.vertices[i,1] = xr |
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| 64 | |
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| 65 | centroid = (xl+xr)/2.0 |
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| 66 | self.centroids[i] = centroid |
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| 67 | |
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| 68 | msg = 'Coordinates should be ordered, smallest to largest' |
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| 69 | assert xr>xl, msg |
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| 70 | |
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| 71 | #The normal vectors |
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| 72 | # - point outward from each edge |
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| 73 | # - are orthogonal to the edge |
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| 74 | # - have unit length |
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| 75 | # - Are enumerated by left vertex then right vertex normals |
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| 76 | |
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| 77 | nl = -1.0 |
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| 78 | nr = 1.0 |
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| 79 | self.normals[i,:] = [nl, nr] |
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| 80 | self.areas[i] = (xr-xl) |
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| 81 | |
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| 82 | #Initialise Neighbours (-1 means that it is a boundary neighbour) |
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| 83 | self.neighbours[i, :] = [-1, -1] |
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| 84 | #Initialise vertex ids of neighbours |
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| 85 | #In case of boundaries this slot is not used |
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| 86 | self.neighbour_vertices[i, :] = [-1, -1] |
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| 87 | |
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| 88 | self.build_vertexlist() |
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| 89 | |
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| 90 | #Build neighbour structure |
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| 91 | self.build_neighbour_structure() |
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| 92 | |
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| 93 | #Build surrogate neighbour structure |
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| 94 | self.build_surrogate_neighbour_structure() |
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| 95 | |
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| 96 | #Build boundary dictionary mapping (id, vertex) to symbolic tags |
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| 97 | self.build_boundary_dictionary(boundary) |
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| 98 | |
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| 99 | #Build tagged element dictionary mapping (tag) to array of elements |
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| 100 | self.build_tagged_elements_dictionary(tagged_elements) |
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| 101 | |
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| 102 | from quantity import Quantity, Conserved_quantity |
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| 103 | |
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| 104 | #List of quantity names entering the conservation equations |
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| 105 | #(Must be a subset of quantities) |
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| 106 | if conserved_quantities is None: |
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| 107 | self.conserved_quantities = [] |
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| 108 | else: |
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| 109 | self.conserved_quantities = conserved_quantities |
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| 110 | |
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| 111 | if evolved_quantities is None: |
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| 112 | self.evolved_quantities = self.conserved_quantities |
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| 113 | else: |
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| 114 | self.evolved_quantities = evolved_quantities |
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| 115 | |
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| 116 | if other_quantities is None: |
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| 117 | self.other_quantities = [] |
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| 118 | else: |
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| 119 | self.other_quantities = other_quantities |
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| 120 | |
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| 121 | |
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| 122 | #Build dictionary of Quantity instances keyed by quantity names |
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| 123 | self.quantities = {} |
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| 124 | |
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| 125 | #FIXME: remove later - maybe OK, though.... |
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| 126 | for name in self.evolved_quantities: |
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| 127 | self.quantities[name] = Quantity(self) |
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| 128 | for name in self.other_quantities: |
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| 129 | self.quantities[name] = Quantity(self) |
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| 130 | |
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| 131 | #Create an empty list for explicit forcing terms |
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| 132 | self.forcing_terms = [] |
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| 133 | |
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| 134 | #Defaults |
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| 135 | from config import max_smallsteps, beta_w, beta_h, epsilon, CFL |
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| 136 | self.beta_w = beta_w |
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| 137 | self.beta_h = beta_h |
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| 138 | self.epsilon = epsilon |
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| 139 | |
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| 140 | #FIXME: Maybe have separate orders for h-limiter and w-limiter? |
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| 141 | #Or maybe get rid of order altogether and use beta_w and beta_h |
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| 142 | self.default_order = 1 |
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| 143 | self.order = self.default_order |
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| 144 | |
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| 145 | self.default_time_order = 1 |
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| 146 | self.time_order = self.default_time_order |
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| 147 | |
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| 148 | self.smallsteps = 0 |
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| 149 | self.max_smallsteps = max_smallsteps |
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| 150 | self.number_of_steps = 0 |
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| 151 | self.number_of_first_order_steps = 0 |
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| 152 | |
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| 153 | #Model time |
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| 154 | self.time = 0.0 |
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| 155 | self.finaltime = None |
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| 156 | self.min_timestep = self.max_timestep = 0.0 |
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| 157 | self.starttime = 0 #Physical starttime if any (0 is 1 Jan 1970 00:00:00) |
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| 158 | #Checkpointing and storage |
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| 159 | from config import default_datadir |
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| 160 | self.set_datadir(default_datadir) |
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| 161 | self.filename = 'domain_avalanche' |
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| 162 | self.checkpoint = False |
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| 163 | self.shock_detector = zeros(N+1, Float) |
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| 164 | |
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| 165 | def __len__(self): |
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| 166 | return self.number_of_elements |
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| 167 | |
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| 168 | def build_vertexlist(self): |
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| 169 | """Build vertexlist index by vertex ids and for each entry (point id) |
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| 170 | build a list of (triangles, vertex_id) pairs that use the point |
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| 171 | as vertex. |
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| 172 | |
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| 173 | Preconditions: |
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| 174 | self.coordinates and self.triangles are defined |
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| 175 | |
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| 176 | Postcondition: |
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| 177 | self.vertexlist is built |
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| 178 | """ |
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| 179 | from numpy import array |
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| 180 | |
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| 181 | vertexlist = [None]*len(self.coordinates) |
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| 182 | for i in range(self.number_of_elements): |
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| 183 | a = i |
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| 184 | b = i + 1 |
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| 185 | |
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| 186 | #Register the vertices v as lists of |
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| 187 | #(triangle_id, vertex_id) tuples associated with them |
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| 188 | #This is used for smoothing |
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| 189 | #for vertex_id, v in enumerate([a,b,c]): |
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| 190 | for vertex_id, v in enumerate([a,b]): |
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| 191 | if vertexlist[v] is None: |
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| 192 | vertexlist[v] = [] |
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| 193 | |
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| 194 | vertexlist[v].append( (i, vertex_id) ) |
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| 195 | |
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| 196 | self.vertexlist = vertexlist |
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| 197 | |
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| 198 | |
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| 199 | def build_neighbour_structure(self): |
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| 200 | """Update all registered triangles to point to their neighbours. |
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| 201 | |
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| 202 | Also, keep a tally of the number of boundaries for each triangle |
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| 203 | |
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| 204 | Postconditions: |
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| 205 | neighbours and neighbour_edges is populated |
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| 206 | neighbours and neighbour_vertices is populated |
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| 207 | number_of_boundaries integer array is defined. |
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| 208 | """ |
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| 209 | |
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| 210 | #Step 1: |
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| 211 | #Build dictionary mapping from segments (2-tuple of points) |
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| 212 | #to left hand side edge (facing neighbouring triangle) |
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| 213 | |
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| 214 | N = self.number_of_elements |
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| 215 | neighbourdict = {} |
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| 216 | l_vertex = 0 |
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| 217 | r_vertex = 1 |
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| 218 | for i in range(N): |
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| 219 | |
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| 220 | #Register all segments as keys mapping to current triangle |
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| 221 | #and segment id |
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| 222 | a = self.vertices[i,0] |
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| 223 | b = self.vertices[i,1] |
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| 224 | |
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| 225 | neighbourdict[a,l_vertex] = (i, 0) #(id, vertex) |
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| 226 | neighbourdict[b,r_vertex] = (i, 1) #(id, vertex) |
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| 227 | |
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| 228 | |
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| 229 | #Step 2: |
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| 230 | #Go through triangles again, but this time |
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| 231 | #reverse direction of segments and lookup neighbours. |
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| 232 | for i in range(N): |
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| 233 | a = self.vertices[i,0] |
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| 234 | b = self.vertices[i,1] |
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| 235 | |
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| 236 | self.number_of_boundaries[i] = 2 |
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| 237 | if neighbourdict.has_key((b,l_vertex)): |
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| 238 | self.neighbours[i, 1] = neighbourdict[b,l_vertex][0] |
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| 239 | self.neighbour_vertices[i, 1] = neighbourdict[b,l_vertex][1] |
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| 240 | self.number_of_boundaries[i] -= 1 |
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| 241 | |
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| 242 | if neighbourdict.has_key((a,r_vertex)): |
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| 243 | self.neighbours[i, 0] = neighbourdict[a,r_vertex][0] |
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| 244 | self.neighbour_vertices[i, 0] = neighbourdict[a,r_vertex][1] |
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| 245 | self.number_of_boundaries[i] -= 1 |
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| 246 | |
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| 247 | def build_surrogate_neighbour_structure(self): |
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| 248 | """Build structure where each triangle edge points to its neighbours |
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| 249 | if they exist. Otherwise point to the triangle itself. |
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| 250 | |
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| 251 | The surrogate neighbour structure is useful for computing gradients |
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| 252 | based on centroid values of neighbours. |
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| 253 | |
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| 254 | Precondition: Neighbour structure is defined |
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| 255 | Postcondition: |
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| 256 | Surrogate neighbour structure is defined: |
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| 257 | surrogate_neighbours: i0, i1, i2 where all i_k >= 0 point to |
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| 258 | triangles. |
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| 259 | |
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| 260 | """ |
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| 261 | |
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| 262 | N = self.number_of_elements |
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| 263 | for i in range(N): |
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| 264 | #Find all neighbouring volumes that are not boundaries |
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| 265 | #for k in range(3): |
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| 266 | for k in range(2): |
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| 267 | if self.neighbours[i, k] < 0: |
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| 268 | self.surrogate_neighbours[i, k] = i #Point this triangle |
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| 269 | else: |
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| 270 | self.surrogate_neighbours[i, k] = self.neighbours[i, k] |
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| 271 | |
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| 272 | def build_boundary_dictionary(self, boundary = None): |
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| 273 | """Build or check the dictionary of boundary tags. |
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| 274 | self.boundary is a dictionary of tags, |
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| 275 | keyed by volume id and edge: |
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| 276 | { (id, edge): tag, ... } |
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| 277 | |
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| 278 | Postconditions: |
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| 279 | self.boundary is defined. |
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| 280 | """ |
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| 281 | |
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| 282 | from config import default_boundary_tag |
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| 283 | |
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| 284 | if boundary is None: |
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| 285 | boundary = {} |
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| 286 | for vol_id in range(self.number_of_elements): |
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| 287 | for vertex_id in range(0, 2): |
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| 288 | if self.neighbours[vol_id, vertex_id] < 0: |
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| 289 | boundary[(vol_id, vertex_id)] = default_boundary_tag |
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| 290 | else: |
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| 291 | #Check that all keys in given boundary exist |
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| 292 | #for vol_id, edge_id in boundary.keys(): |
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| 293 | for vol_id, vertex_id in boundary.keys(): |
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| 294 | msg = 'Segment (%d, %d) does not exist' %(vol_id, vertex_id) |
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| 295 | a, b = self.neighbours.shape |
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| 296 | assert vol_id < a and vertex_id < b, msg |
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| 297 | |
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| 298 | #FIXME: This assert violates internal boundaries (delete it) |
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| 299 | #msg = 'Segment (%d, %d) is not a boundary' %(vol_id, edge_id) |
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| 300 | #assert self.neighbours[vol_id, edge_id] < 0, msg |
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| 301 | |
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| 302 | #Check that all boundary segments are assigned a tag |
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| 303 | for vol_id in range(self.number_of_elements): |
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| 304 | for vertex_id in range(0, 2): |
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| 305 | if self.neighbours[vol_id, vertex_id] < 0: |
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| 306 | if not boundary.has_key( (vol_id, vertex_id) ): |
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| 307 | msg = 'WARNING: Given boundary does not contain ' |
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| 308 | msg += 'tags for vertex (%d, %d). '\ |
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| 309 | %(vol_id, vertex_id) |
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| 310 | msg += 'Assigning default tag (%s).'\ |
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| 311 | %default_boundary_tag |
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| 312 | boundary[ (vol_id, vertex_id) ] =\ |
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| 313 | default_boundary_tag |
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| 314 | |
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| 315 | self.boundary = boundary |
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| 316 | |
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| 317 | def build_tagged_elements_dictionary(self, tagged_elements = None): |
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| 318 | """Build the dictionary of element tags. |
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| 319 | self.tagged_elements is a dictionary of element arrays, |
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| 320 | keyed by tag: |
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| 321 | { (tag): [e1, e2, e3..] } |
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| 322 | |
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| 323 | Postconditions: |
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| 324 | self.element_tag is defined |
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| 325 | """ |
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| 326 | from Numeric import Int |
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| 327 | from numpy import array |
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| 328 | |
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| 329 | if tagged_elements is None: |
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| 330 | tagged_elements = {} |
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| 331 | else: |
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| 332 | #Check that all keys in given boundary exist |
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| 333 | for tag in tagged_elements.keys(): |
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| 334 | tagged_elements[tag] = array(tagged_elements[tag]).astype(Int) |
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| 335 | |
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| 336 | msg = 'Not all elements exist. ' |
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| 337 | assert max(tagged_elements[tag]) < self.number_of_elements, msg |
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| 338 | self.tagged_elements = tagged_elements |
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| 339 | |
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| 340 | |
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| 341 | def set_quantities_to_be_stored(self, q): |
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| 342 | """Specify which quantities will be stored in the sww file. |
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| 343 | |
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| 344 | q must be either: |
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| 345 | - the name of a quantity |
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| 346 | - a list of quantity names |
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| 347 | - None |
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| 348 | |
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| 349 | In the two first cases, the named quantities will be stored at each |
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| 350 | yieldstep |
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| 351 | (This is in addition to the quantities elevation and friction) |
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| 352 | If q is None, storage will be switched off altogether. |
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| 353 | """ |
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| 354 | |
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| 355 | |
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| 356 | if q is None: |
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| 357 | self.quantities_to_be_stored = [] |
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| 358 | self.store = False |
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| 359 | return |
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| 360 | |
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| 361 | if isinstance(q, basestring): |
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| 362 | q = [q] # Turn argument into a list |
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| 363 | |
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| 364 | #Check correcness |
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| 365 | for quantity_name in q: |
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| 366 | msg = 'Quantity %s is not a valid conserved quantity' %quantity_name |
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| 367 | assert quantity_name in self.conserved_quantities, msg |
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| 368 | |
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| 369 | self.quantities_to_be_stored = q |
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| 370 | |
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| 371 | |
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| 372 | |
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| 373 | |
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| 374 | |
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| 375 | def get_boundary_tags(self): |
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| 376 | """Return list of available boundary tags |
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| 377 | """ |
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| 378 | |
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| 379 | tags = {} |
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| 380 | for v in self.boundary.values(): |
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| 381 | tags[v] = 1 |
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| 382 | |
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| 383 | return tags.keys() |
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| 384 | |
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| 385 | def get_vertex_coordinates(self, obj = False): |
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| 386 | """Return all vertex coordinates. |
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| 387 | Return all vertex coordinates for all triangles as an Nx6 array |
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| 388 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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| 389 | |
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| 390 | if obj is True, the x/y pairs are returned in a 3*N x 2 array. |
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| 391 | FIXME, we might make that the default. |
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| 392 | FIXME Maybe use keyword: continuous = False for this condition? |
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| 393 | |
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| 394 | |
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| 395 | """ |
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| 396 | |
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| 397 | if obj is True: |
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| 398 | from numpy import concatenate, reshape |
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| 399 | V = self.vertices |
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| 400 | N = V.shape[0] |
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| 401 | return reshape(V, (N, 2)) |
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| 402 | else: |
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| 403 | return self.vertices |
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| 404 | |
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| 405 | def get_conserved_quantities(self, vol_id, vertex=None):#, edge=None): |
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| 406 | """Get conserved quantities at volume vol_id |
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| 407 | |
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| 408 | If vertex is specified use it as index for vertex values |
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| 409 | If edge is specified use it as index for edge values |
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| 410 | If neither are specified use centroid values |
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| 411 | If both are specified an exeception is raised |
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| 412 | |
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| 413 | Return value: Vector of length == number_of_conserved quantities |
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| 414 | |
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| 415 | """ |
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| 416 | |
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| 417 | from Numeric import Float |
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| 418 | from numpy import zeros |
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| 419 | q = zeros( len(self.conserved_quantities), Float) |
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| 420 | for i, name in enumerate(self.conserved_quantities): |
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| 421 | Q = self.quantities[name] |
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| 422 | if vertex is not None: |
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| 423 | q[i] = Q.vertex_values[vol_id, vertex] |
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| 424 | else: |
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| 425 | q[i] = Q.centroid_values[vol_id] |
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| 426 | |
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| 427 | return q |
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| 428 | |
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| 429 | |
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| 430 | def get_evolved_quantities(self, vol_id, vertex=None):#, edge=None): |
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| 431 | """Get evolved quantities at volume vol_id |
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| 432 | |
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| 433 | If vertex is specified use it as index for vertex values |
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| 434 | If edge is specified use it as index for edge values |
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| 435 | If neither are specified use centroid values |
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| 436 | If both are specified an exeception is raised |
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| 437 | |
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| 438 | Return value: Vector of length == number_of_evolved quantities |
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| 439 | |
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| 440 | """ |
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| 441 | |
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| 442 | from Numeric import Float |
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| 443 | from numpy import zeros |
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| 444 | q = zeros( len(self.evolved_quantities), Float) |
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| 445 | |
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| 446 | for i, name in enumerate(self.evolved_quantities): |
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| 447 | Q = self.quantities[name] |
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| 448 | if vertex is not None: |
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| 449 | q[i] = Q.vertex_values[vol_id, vertex] |
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| 450 | else: |
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| 451 | q[i] = Q.centroid_values[vol_id] |
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| 452 | |
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| 453 | return q |
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| 454 | |
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| 455 | |
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| 456 | def get_centroids(self): |
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| 457 | """Return all coordinates of centroids |
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| 458 | Return x coordinate of centroid for each element as a N array |
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| 459 | """ |
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| 460 | |
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| 461 | return self.centroids |
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| 462 | |
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| 463 | def get_vertices(self): |
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| 464 | """Return all coordinates of centroids |
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| 465 | Return x coordinate of centroid for each element as a N array |
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| 466 | """ |
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| 467 | |
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| 468 | return self.vertices |
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| 469 | |
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| 470 | def get_coordinate(self, elem_id, vertex=None): |
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| 471 | """Return coordinate of centroid, |
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| 472 | or left or right vertex. |
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| 473 | Left vertex (vertex=0). Right vertex (vertex=1) |
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| 474 | """ |
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| 475 | |
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| 476 | if vertex is None: |
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| 477 | return self.centroids[elem_id] |
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| 478 | else: |
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| 479 | return self.vertices[elem_id,vertex] |
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| 480 | |
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| 481 | def get_area(self, elem_id): |
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| 482 | """Return area of element id |
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| 483 | """ |
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| 484 | |
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| 485 | return self.areas[elem_id] |
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| 486 | |
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| 487 | def get_quantity(self, name, location='vertices', indices = None): |
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| 488 | """Get values for named quantity |
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| 489 | |
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| 490 | name: Name of quantity |
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| 491 | |
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| 492 | In case of location == 'centroids' the dimension values must |
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| 493 | be a list of a Numerical array of length N, N being the number |
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| 494 | of elements. Otherwise it must be of dimension Nx3. |
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| 495 | |
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| 496 | Indices is the set of element ids that the operation applies to. |
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| 497 | |
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| 498 | The values will be stored in elements following their |
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| 499 | internal ordering. |
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| 500 | """ |
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| 501 | |
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| 502 | return self.quantities[name].get_values( location, indices = indices) |
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| 503 | |
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| 504 | def get_centroid_coordinates(self): |
---|
| 505 | """Return all centroid coordinates. |
---|
| 506 | Return all centroid coordinates for all triangles as an Nx2 array |
---|
| 507 | (ordered as x0, y0 for each triangle) |
---|
| 508 | """ |
---|
| 509 | return self.centroids |
---|
| 510 | |
---|
| 511 | |
---|
| 512 | def get_timestepping_method(self): |
---|
| 513 | return self.timestepping_method |
---|
| 514 | |
---|
| 515 | def set_timestepping_method(self,timestepping_method): |
---|
| 516 | |
---|
| 517 | if timestepping_method in ['euler', 'rk2', 'rk3']: |
---|
| 518 | self.timestepping_method = timestepping_method |
---|
| 519 | return |
---|
| 520 | |
---|
| 521 | msg = '%s is an incorrect timestepping type'% timestepping_method |
---|
| 522 | raise Exception, msg |
---|
| 523 | |
---|
| 524 | |
---|
| 525 | def set_quantity(self, name, *args, **kwargs): |
---|
| 526 | """Set values for named quantity |
---|
| 527 | |
---|
| 528 | |
---|
| 529 | One keyword argument is documented here: |
---|
| 530 | expression = None, # Arbitrary expression |
---|
| 531 | |
---|
| 532 | expression: |
---|
| 533 | Arbitrary expression involving quantity names |
---|
| 534 | |
---|
| 535 | See Quantity.set_values for further documentation. |
---|
| 536 | """ |
---|
| 537 | #Do the expression stuff |
---|
| 538 | if kwargs.has_key('expression'): |
---|
| 539 | expression = kwargs['expression'] |
---|
| 540 | del kwargs['expression'] |
---|
| 541 | |
---|
| 542 | Q = self.create_quantity_from_expression(expression) |
---|
| 543 | kwargs['quantity'] = Q |
---|
| 544 | |
---|
| 545 | #Assign values |
---|
| 546 | self.quantities[name].set_values(*args, **kwargs) |
---|
| 547 | |
---|
| 548 | def set_boundary(self, boundary_map): |
---|
| 549 | """Associate boundary objects with tagged boundary segments. |
---|
| 550 | |
---|
| 551 | Input boundary_map is a dictionary of boundary objects keyed |
---|
| 552 | by symbolic tags to matched against tags in the internal dictionary |
---|
| 553 | self.boundary. |
---|
| 554 | |
---|
| 555 | As result one pointer to a boundary object is stored for each vertex |
---|
| 556 | in the list self.boundary_objects. |
---|
| 557 | More entries may point to the same boundary object |
---|
| 558 | |
---|
| 559 | Schematically the mapping is from two dictionaries to one list |
---|
| 560 | where the index is used as pointer to the boundary_values arrays |
---|
| 561 | within each quantity. |
---|
| 562 | |
---|
| 563 | self.boundary: (vol_id, edge_id): tag |
---|
| 564 | boundary_map (input): tag: boundary_object |
---|
| 565 | ---------------------------------------------- |
---|
| 566 | self.boundary_objects: ((vol_id, edge_id), boundary_object) |
---|
| 567 | |
---|
| 568 | |
---|
| 569 | Pre-condition: |
---|
| 570 | self.boundary has been built. |
---|
| 571 | |
---|
| 572 | Post-condition: |
---|
| 573 | self.boundary_objects is built |
---|
| 574 | |
---|
| 575 | If a tag from the domain doesn't appear in the input dictionary an |
---|
| 576 | exception is raised. |
---|
| 577 | However, if a tag is not used to the domain, no error is thrown. |
---|
| 578 | FIXME: This would lead to implementation of a |
---|
| 579 | default boundary condition |
---|
| 580 | |
---|
| 581 | Note: If a segment is listed in the boundary dictionary and if it is |
---|
| 582 | not None, it *will* become a boundary - |
---|
| 583 | even if there is a neighbouring triangle. |
---|
| 584 | This would be the case for internal boundaries |
---|
| 585 | |
---|
| 586 | Boundary objects that are None will be skipped. |
---|
| 587 | |
---|
| 588 | FIXME: If set_boundary is called multiple times and if Boundary |
---|
| 589 | object is changed into None, the neighbour structure will not be |
---|
| 590 | restored!!! |
---|
| 591 | """ |
---|
| 592 | |
---|
| 593 | self.boundary_objects = [] |
---|
| 594 | self.boundary_map = boundary_map #Store for use with eg. boundary_stats. |
---|
| 595 | |
---|
| 596 | #FIXME: Try to remove the sorting and fix test_mesh.py |
---|
| 597 | x = self.boundary.keys() |
---|
| 598 | x.sort() |
---|
| 599 | |
---|
| 600 | #Loop through edges that lie on the boundary and associate them with |
---|
| 601 | #callable boundary objects depending on their tags |
---|
| 602 | for k, (vol_id, vertex_id) in enumerate(x): |
---|
| 603 | tag = self.boundary[ (vol_id, vertex_id) ] |
---|
| 604 | if boundary_map.has_key(tag): |
---|
| 605 | B = boundary_map[tag] #Get callable boundary object |
---|
| 606 | if B is not None: |
---|
| 607 | #self.boundary_objects.append( ((vol_id, edge_id), B) ) |
---|
| 608 | #self.neighbours[vol_id, edge_id] = -len(self.boundary_objects) |
---|
| 609 | self.boundary_objects.append( ((vol_id, vertex_id), B) ) |
---|
| 610 | self.neighbours[vol_id, vertex_id] = -len(self.boundary_objects) |
---|
| 611 | else: |
---|
| 612 | pass |
---|
| 613 | #FIXME: Check and perhaps fix neighbour structure |
---|
| 614 | |
---|
| 615 | else: |
---|
| 616 | msg = 'ERROR (domain.py): Tag "%s" has not been ' %tag |
---|
| 617 | msg += 'bound to a boundary object.\n' |
---|
| 618 | msg += 'All boundary tags defined in domain must appear ' |
---|
| 619 | msg += 'in the supplied dictionary.\n' |
---|
| 620 | msg += 'The tags are: %s' %self.get_boundary_tags() |
---|
| 621 | raise msg |
---|
| 622 | |
---|
| 623 | |
---|
| 624 | |
---|
| 625 | def check_integrity(self): |
---|
| 626 | #Mesh.check_integrity(self) |
---|
| 627 | for quantity in self.conserved_quantities: |
---|
| 628 | msg = 'Conserved quantities must be a subset of all quantities' |
---|
| 629 | assert quantity in self.quantities, msg |
---|
| 630 | |
---|
| 631 | for quantity in self.evolved_quantities: |
---|
| 632 | msg = 'Evolved quantities must be a subset of all quantities' |
---|
| 633 | assert quantity in self.quantities, msg |
---|
| 634 | |
---|
| 635 | def write_time(self): |
---|
| 636 | print self.timestepping_statistics() |
---|
| 637 | |
---|
| 638 | def get_time(self): |
---|
| 639 | print self.time |
---|
| 640 | |
---|
| 641 | |
---|
| 642 | def timestepping_statistics(self): |
---|
| 643 | """Return string with time stepping statistics for printing or logging |
---|
| 644 | """ |
---|
| 645 | |
---|
| 646 | msg = '' |
---|
| 647 | if self.min_timestep == self.max_timestep: |
---|
| 648 | msg += 'Time = %.4f, delta t = %.8f, steps=%d (%d)'\ |
---|
| 649 | %(self.time, self.min_timestep, self.number_of_steps, |
---|
| 650 | self.number_of_first_order_steps) |
---|
| 651 | elif self.min_timestep > self.max_timestep: |
---|
| 652 | msg += 'Time = %.4f, steps=%d (%d)'\ |
---|
| 653 | %(self.time, self.number_of_steps, |
---|
| 654 | self.number_of_first_order_steps) |
---|
| 655 | else: |
---|
| 656 | msg += 'Time = %.4f, delta t in [%.8f, %.8f], steps=%d (%d)'\ |
---|
| 657 | %(self.time, self.min_timestep, |
---|
| 658 | self.max_timestep, self.number_of_steps, |
---|
| 659 | self.number_of_first_order_steps) |
---|
| 660 | |
---|
| 661 | return msg |
---|
| 662 | |
---|
| 663 | def get_name(self): |
---|
| 664 | return self.filename |
---|
| 665 | |
---|
| 666 | def set_name(self, name): |
---|
| 667 | self.filename = name |
---|
| 668 | |
---|
| 669 | def get_datadir(self): |
---|
| 670 | return self.datadir |
---|
| 671 | |
---|
| 672 | def set_datadir(self, name): |
---|
| 673 | self.datadir = name |
---|
| 674 | |
---|
| 675 | def set_CFL(self, cfl): |
---|
| 676 | if cfl > 1.0: |
---|
| 677 | print 'WARNING: Setting CFL condition to %f which is greater than 1' % cfl |
---|
| 678 | self.CFL = cfl |
---|
| 679 | |
---|
| 680 | def get_CFL(self): |
---|
| 681 | return self.CFL |
---|
| 682 | |
---|
| 683 | def set_filename(self, name): |
---|
| 684 | self.filename = name |
---|
| 685 | |
---|
| 686 | def get_filename(self): |
---|
| 687 | return self.filename |
---|
| 688 | |
---|
| 689 | def get_limiter(self): |
---|
| 690 | return self.limiter |
---|
| 691 | |
---|
| 692 | def set_limiter(self,limiter): |
---|
| 693 | |
---|
| 694 | possible_limiters = \ |
---|
| 695 | ['pyvolution', 'minmod_steve', 'minmod', 'minmod_kurganov', 'superbee', 'vanleer', 'vanalbada'] |
---|
| 696 | |
---|
| 697 | if limiter in possible_limiters: |
---|
| 698 | self.limiter = limiter |
---|
| 699 | return |
---|
| 700 | |
---|
| 701 | msg = '%s is an incorrect limiter type.\n'% limiter |
---|
| 702 | msg += 'Possible types are: '+ ", ".join(["%s" % el for el in possible_limiters]) |
---|
| 703 | raise Exception, msg |
---|
| 704 | |
---|
| 705 | |
---|
| 706 | #-------------------------- |
---|
| 707 | # Main components of evolve |
---|
| 708 | #-------------------------- |
---|
| 709 | |
---|
| 710 | def evolve(self, yieldstep = None, |
---|
| 711 | finaltime = None, |
---|
| 712 | duration = None, |
---|
| 713 | skip_initial_step = False): |
---|
| 714 | """Evolve model through time starting from self.starttime. |
---|
| 715 | |
---|
| 716 | |
---|
| 717 | yieldstep: Interval between yields where results are stored, |
---|
| 718 | statistics written and domain inspected or |
---|
| 719 | possibly modified. If omitted the internal predefined |
---|
| 720 | max timestep is used. |
---|
| 721 | Internally, smaller timesteps may be taken. |
---|
| 722 | |
---|
| 723 | duration: Duration of simulation |
---|
| 724 | |
---|
| 725 | finaltime: Time where simulation should end. This is currently |
---|
| 726 | relative time. So it's the same as duration. |
---|
| 727 | |
---|
| 728 | If both duration and finaltime are given an exception is thrown. |
---|
| 729 | |
---|
| 730 | |
---|
| 731 | skip_initial_step: Boolean flag that decides whether the first |
---|
| 732 | yield step is skipped or not. This is useful for example to avoid |
---|
| 733 | duplicate steps when multiple evolve processes are dove tailed. |
---|
| 734 | |
---|
| 735 | |
---|
| 736 | Evolve is implemented as a generator and is to be called as such, e.g. |
---|
| 737 | |
---|
| 738 | for t in domain.evolve(yieldstep, finaltime): |
---|
| 739 | <Do something with domain and t> |
---|
| 740 | |
---|
| 741 | |
---|
| 742 | All times are given in seconds |
---|
| 743 | |
---|
| 744 | """ |
---|
| 745 | |
---|
| 746 | from config import min_timestep, max_timestep, epsilon |
---|
| 747 | |
---|
| 748 | # FIXME: Maybe lump into a larger check prior to evolving |
---|
| 749 | msg = 'Boundary tags must be bound to boundary objects before ' |
---|
| 750 | msg += 'evolving system, ' |
---|
| 751 | msg += 'e.g. using the method set_boundary.\n' |
---|
| 752 | msg += 'This system has the boundary tags %s '\ |
---|
| 753 | %self.get_boundary_tags() |
---|
| 754 | assert hasattr(self, 'boundary_objects'), msg |
---|
| 755 | |
---|
| 756 | if yieldstep is None: |
---|
| 757 | yieldstep = max_timestep |
---|
| 758 | else: |
---|
| 759 | yieldstep = float(yieldstep) |
---|
| 760 | |
---|
| 761 | self._order_ = self.default_order |
---|
| 762 | |
---|
| 763 | if finaltime is not None and duration is not None: |
---|
| 764 | # print 'F', finaltime, duration |
---|
| 765 | msg = 'Only one of finaltime and duration may be specified' |
---|
| 766 | raise msg |
---|
| 767 | else: |
---|
| 768 | if finaltime is not None: |
---|
| 769 | self.finaltime = float(finaltime) |
---|
| 770 | if duration is not None: |
---|
| 771 | self.finaltime = self.starttime + float(duration) |
---|
| 772 | |
---|
| 773 | N = len(self) # Number of triangles |
---|
| 774 | self.yieldtime = 0.0 # Track time between 'yields' |
---|
| 775 | |
---|
| 776 | # Initialise interval of timestep sizes (for reporting only) |
---|
| 777 | self.min_timestep = max_timestep |
---|
| 778 | self.max_timestep = min_timestep |
---|
| 779 | self.number_of_steps = 0 |
---|
| 780 | self.number_of_first_order_steps = 0 |
---|
| 781 | |
---|
| 782 | |
---|
| 783 | # Update ghosts |
---|
| 784 | self.update_ghosts() |
---|
| 785 | |
---|
| 786 | # Initial update of vertex and edge values |
---|
| 787 | self.distribute_to_vertices_and_edges() |
---|
| 788 | |
---|
| 789 | # Update extrema if necessary (for reporting) |
---|
| 790 | self.update_extrema() |
---|
| 791 | |
---|
| 792 | # Initial update boundary values |
---|
| 793 | self.update_boundary() |
---|
| 794 | |
---|
| 795 | # Or maybe restore from latest checkpoint |
---|
| 796 | if self.checkpoint is True: |
---|
| 797 | self.goto_latest_checkpoint() |
---|
| 798 | |
---|
| 799 | if skip_initial_step is False: |
---|
| 800 | yield(self.time) # Yield initial values |
---|
| 801 | |
---|
| 802 | while True: |
---|
| 803 | |
---|
| 804 | # Evolve One Step, using appropriate timestepping method |
---|
| 805 | if self.get_timestepping_method() == 'euler': |
---|
| 806 | self.evolve_one_euler_step(yieldstep,finaltime) |
---|
| 807 | |
---|
| 808 | elif self.get_timestepping_method() == 'rk2': |
---|
| 809 | self.evolve_one_rk2_step(yieldstep,finaltime) |
---|
| 810 | |
---|
| 811 | elif self.get_timestepping_method() == 'rk3': |
---|
| 812 | self.evolve_one_rk3_step(yieldstep,finaltime) |
---|
| 813 | |
---|
| 814 | # Update extrema if necessary (for reporting) |
---|
| 815 | self.update_extrema() |
---|
| 816 | self.yieldtime += self.timestep |
---|
| 817 | self.number_of_steps += 1 |
---|
| 818 | if self._order_ == 1: |
---|
| 819 | self.number_of_first_order_steps += 1 |
---|
| 820 | |
---|
| 821 | |
---|
| 822 | # Yield results |
---|
| 823 | if finaltime is not None and self.time >= finaltime-epsilon: |
---|
| 824 | |
---|
| 825 | if self.time > finaltime: |
---|
| 826 | msg = 'WARNING (domain.py): time overshot finaltime. ' |
---|
| 827 | msg += 'Contact Ole.Nielsen@ga.gov.au' |
---|
| 828 | raise Exception, msg |
---|
| 829 | |
---|
| 830 | |
---|
| 831 | # Yield final time and stop |
---|
| 832 | self.time = finaltime |
---|
| 833 | yield(self.time) |
---|
| 834 | break |
---|
| 835 | |
---|
| 836 | if self.yieldtime >= yieldstep-0.5*min_timestep: |
---|
| 837 | # Yield (intermediate) time and allow inspection of domain |
---|
| 838 | |
---|
| 839 | if self.checkpoint is True: |
---|
| 840 | self.store_checkpoint() |
---|
| 841 | self.delete_old_checkpoints() |
---|
| 842 | |
---|
| 843 | # Pass control on to outer loop for more specific actions |
---|
| 844 | print "Checking here.........,Sudi." |
---|
| 845 | yield(self.time) |
---|
| 846 | |
---|
| 847 | # Reinitialise |
---|
| 848 | self.yieldtime = 0.0 |
---|
| 849 | self.min_timestep = max_timestep |
---|
| 850 | self.max_timestep = min_timestep |
---|
| 851 | self.number_of_steps = 0 |
---|
| 852 | self.number_of_first_order_steps = 0 |
---|
| 853 | |
---|
| 854 | if finaltime is not None and self.time >= finaltime-0.5*min_timestep: |
---|
| 855 | break |
---|
| 856 | |
---|
| 857 | |
---|
| 858 | def evolve_one_euler_step(self, yieldstep, finaltime): |
---|
| 859 | """ |
---|
| 860 | One Euler Time Step |
---|
| 861 | Q^{n+1} = E(h) Q^n |
---|
| 862 | """ |
---|
| 863 | |
---|
| 864 | # Back up evolved (ALL) quantities, Sudi 13 July 2010 |
---|
| 865 | self.backup_evolved_quantities() |
---|
| 866 | |
---|
| 867 | # Compute fluxes across each element edge |
---|
| 868 | self.compute_fluxes() |
---|
| 869 | |
---|
| 870 | # Update timestep to fit yieldstep and finaltime |
---|
| 871 | self.update_timestep(yieldstep, finaltime) |
---|
| 872 | |
---|
| 873 | # Update conserved quantities |
---|
| 874 | self.update_conserved_quantities() |
---|
| 875 | |
---|
| 876 | # Update ghosts |
---|
| 877 | self.update_ghosts() |
---|
| 878 | |
---|
| 879 | # Update vertex and edge values |
---|
| 880 | self.distribute_to_vertices_and_edges() |
---|
| 881 | |
---|
| 882 | # Update boundary values |
---|
| 883 | self.update_boundary() |
---|
| 884 | |
---|
| 885 | # Update time |
---|
| 886 | self.time += self.timestep |
---|
| 887 | |
---|
| 888 | # Detect shock, Sudi 13 July 2010 |
---|
| 889 | self.detect_shock() |
---|
| 890 | |
---|
| 891 | |
---|
| 892 | |
---|
| 893 | def evolve_one_rk2_step(self, yieldstep, finaltime): |
---|
| 894 | """ |
---|
| 895 | One 2nd order RK timestep |
---|
| 896 | Q^{n+1} = 0.5 Q^n + 0.5 E(h)^2 Q^n |
---|
| 897 | """ |
---|
| 898 | |
---|
| 899 | # Save initial conserved quantities values |
---|
| 900 | self.backup_conserved_quantities() |
---|
| 901 | |
---|
| 902 | # Back up non_conserved (ehv) quantities, Sudi 13 July 2010 |
---|
| 903 | self.backup_ehv_quantities() |
---|
| 904 | |
---|
| 905 | #-------------------------------------- |
---|
| 906 | # First euler step |
---|
| 907 | #-------------------------------------- |
---|
| 908 | |
---|
| 909 | # Compute fluxes across each element edge |
---|
| 910 | self.compute_fluxes() |
---|
| 911 | |
---|
| 912 | # Update timestep to fit yieldstep and finaltime |
---|
| 913 | self.update_timestep(yieldstep, finaltime) |
---|
| 914 | |
---|
| 915 | # Update conserved quantities |
---|
| 916 | self.update_conserved_quantities() |
---|
| 917 | |
---|
| 918 | # Update ghosts |
---|
| 919 | self.update_ghosts() |
---|
| 920 | |
---|
| 921 | # Update vertex and edge values |
---|
| 922 | self.distribute_to_vertices_and_edges() |
---|
| 923 | |
---|
| 924 | # Update boundary values |
---|
| 925 | self.update_boundary() |
---|
| 926 | |
---|
| 927 | # Update time |
---|
| 928 | self.time += self.timestep |
---|
| 929 | |
---|
| 930 | #------------------------------------ |
---|
| 931 | # Second Euler step |
---|
| 932 | #------------------------------------ |
---|
| 933 | |
---|
| 934 | # Compute fluxes across each element edge |
---|
| 935 | self.compute_fluxes() |
---|
| 936 | |
---|
| 937 | # Update conserved quantities |
---|
| 938 | self.update_conserved_quantities() |
---|
| 939 | |
---|
| 940 | #------------------------------------ |
---|
| 941 | # Combine initial and final values |
---|
| 942 | # of conserved quantities and cleanup |
---|
| 943 | #------------------------------------ |
---|
| 944 | |
---|
| 945 | # Combine steps |
---|
| 946 | self.saxpy_conserved_quantities(0.5, 0.5) |
---|
| 947 | |
---|
| 948 | #----------------------------------- |
---|
| 949 | # clean up vertex values |
---|
| 950 | #----------------------------------- |
---|
| 951 | |
---|
| 952 | # Update ghosts |
---|
| 953 | self.update_ghosts() |
---|
| 954 | |
---|
| 955 | # Update vertex and edge values |
---|
| 956 | self.distribute_to_vertices_and_edges() |
---|
| 957 | |
---|
| 958 | # Update boundary values |
---|
| 959 | self.update_boundary() |
---|
| 960 | |
---|
| 961 | # Detect shock, Sudi 13 July 2010 |
---|
| 962 | self.detect_shock() |
---|
| 963 | |
---|
| 964 | |
---|
| 965 | |
---|
| 966 | def evolve_one_rk3_step(self, yieldstep, finaltime): |
---|
| 967 | """ |
---|
| 968 | One 3rd order RK timestep |
---|
| 969 | Q^(1) = 3/4 Q^n + 1/4 E(h)^2 Q^n (at time t^n + h/2) |
---|
| 970 | Q^{n+1} = 1/3 Q^n + 2/3 E(h) Q^(1) (at time t^{n+1}) |
---|
| 971 | """ |
---|
| 972 | |
---|
| 973 | # Save initial initial conserved quantities values |
---|
| 974 | self.backup_conserved_quantities() |
---|
| 975 | |
---|
| 976 | # Back up non_conserved (ehv) quantities, Sudi 13 July 2010 |
---|
| 977 | self.backup_ehv_quantities() |
---|
| 978 | |
---|
| 979 | initial_time = self.time |
---|
| 980 | |
---|
| 981 | #-------------------------------------- |
---|
| 982 | # First euler step |
---|
| 983 | #-------------------------------------- |
---|
| 984 | |
---|
| 985 | # Compute fluxes across each element edge |
---|
| 986 | self.compute_fluxes() |
---|
| 987 | |
---|
| 988 | # Update timestep to fit yieldstep and finaltime |
---|
| 989 | self.update_timestep(yieldstep, finaltime) |
---|
| 990 | |
---|
| 991 | # Update conserved quantities |
---|
| 992 | self.update_conserved_quantities() |
---|
| 993 | |
---|
| 994 | # Update ghosts |
---|
| 995 | self.update_ghosts() |
---|
| 996 | |
---|
| 997 | # Update vertex and edge values |
---|
| 998 | self.distribute_to_vertices_and_edges() |
---|
| 999 | |
---|
| 1000 | # Update boundary values |
---|
| 1001 | self.update_boundary() |
---|
| 1002 | |
---|
| 1003 | # Update time |
---|
| 1004 | self.time += self.timestep |
---|
| 1005 | |
---|
| 1006 | #------------------------------------ |
---|
| 1007 | # Second Euler step |
---|
| 1008 | #------------------------------------ |
---|
| 1009 | |
---|
| 1010 | # Compute fluxes across each element edge |
---|
| 1011 | self.compute_fluxes() |
---|
| 1012 | |
---|
| 1013 | # Update conserved quantities |
---|
| 1014 | self.update_conserved_quantities() |
---|
| 1015 | |
---|
| 1016 | #------------------------------------ |
---|
| 1017 | #Combine steps to obtain intermediate |
---|
| 1018 | #solution at time t^n + 0.5 h |
---|
| 1019 | #------------------------------------ |
---|
| 1020 | |
---|
| 1021 | # Combine steps |
---|
| 1022 | self.saxpy_conserved_quantities(0.25, 0.75) |
---|
| 1023 | |
---|
| 1024 | # Update ghosts |
---|
| 1025 | self.update_ghosts() |
---|
| 1026 | |
---|
| 1027 | # Update vertex and edge values |
---|
| 1028 | self.distribute_to_vertices_and_edges() |
---|
| 1029 | |
---|
| 1030 | # Update boundary values |
---|
| 1031 | self.update_boundary() |
---|
| 1032 | |
---|
| 1033 | # Set substep time |
---|
| 1034 | self.time = initial_time + self.timestep*0.5 |
---|
| 1035 | |
---|
| 1036 | #------------------------------------ |
---|
| 1037 | # Third Euler step |
---|
| 1038 | #------------------------------------ |
---|
| 1039 | |
---|
| 1040 | # Compute fluxes across each element edge |
---|
| 1041 | self.compute_fluxes() |
---|
| 1042 | |
---|
| 1043 | # Update conserved quantities |
---|
| 1044 | self.update_conserved_quantities() |
---|
| 1045 | |
---|
| 1046 | #------------------------------------ |
---|
| 1047 | # Combine final and initial values |
---|
| 1048 | # and cleanup |
---|
| 1049 | #------------------------------------ |
---|
| 1050 | |
---|
| 1051 | # Combine steps |
---|
| 1052 | self.saxpy_conserved_quantities(2.0/3.0, 1.0/3.0) |
---|
| 1053 | |
---|
| 1054 | # Update ghosts |
---|
| 1055 | self.update_ghosts() |
---|
| 1056 | |
---|
| 1057 | # Update vertex and edge values |
---|
| 1058 | self.distribute_to_vertices_and_edges() |
---|
| 1059 | |
---|
| 1060 | # Update boundary values |
---|
| 1061 | self.update_boundary() |
---|
| 1062 | |
---|
| 1063 | # Set new time |
---|
| 1064 | self.time = initial_time + self.timestep |
---|
| 1065 | |
---|
| 1066 | # Detect shock, Sudi 13 July 2010 |
---|
| 1067 | self.detect_shock() |
---|
| 1068 | |
---|
| 1069 | |
---|
| 1070 | def backup_conserved_quantities(self): |
---|
| 1071 | N = len(self) # Number_of_triangles |
---|
| 1072 | |
---|
| 1073 | # Backup conserved_quantities centroid values |
---|
| 1074 | for name in self.conserved_quantities: |
---|
| 1075 | Q = self.quantities[name] |
---|
| 1076 | Q.backup_centroid_values() |
---|
| 1077 | |
---|
| 1078 | def backup_evolved_quantities(self): |
---|
| 1079 | N = len(self) # Number_of_triangles |
---|
| 1080 | |
---|
| 1081 | # Backup evolved_quantities centroid values |
---|
| 1082 | for name in self.evolved_quantities: |
---|
| 1083 | Q = self.quantities[name] |
---|
| 1084 | Q.backup_centroid_values() |
---|
| 1085 | |
---|
| 1086 | def backup_ehv_quantities(self): |
---|
| 1087 | N = len(self) # Number_of_triangles |
---|
| 1088 | |
---|
| 1089 | # Backup NON-conserved_quantities centroid values |
---|
| 1090 | for name in ['elevation', 'height', 'velocity']: |
---|
| 1091 | Q = self.quantities[name] |
---|
| 1092 | Q.backup_centroid_values() |
---|
| 1093 | |
---|
| 1094 | def detect_shock(self): |
---|
| 1095 | h_prev = self.quantities['height'].centroid_backup_values |
---|
| 1096 | h_now = self.quantities['height'].centroid_values |
---|
| 1097 | u_prev = self.quantities['velocity'].centroid_backup_values |
---|
| 1098 | u_now = self.quantities['velocity'].centroid_values |
---|
| 1099 | Ver = self.vertices |
---|
| 1100 | N = len(Ver) |
---|
| 1101 | E = self.shock_detector |
---|
| 1102 | E[0] = E[N] = E[N-1] = 0.0 |
---|
| 1103 | #from parameters import points |
---|
| 1104 | for i in range(N-2): |
---|
| 1105 | k = i+1 |
---|
| 1106 | interval = Ver[k] |
---|
| 1107 | dx = interval[1]-interval[0] |
---|
| 1108 | dt = self.timestep |
---|
| 1109 | E[k] = 0.5 * dx *(h_now[k] - h_prev[k] + h_now[k+1] - h_prev[k+1]) |
---|
| 1110 | E[k] += 0.5 * dt *(h_prev[k+1]*u_prev[k+1] - h_prev[k]*u_prev[k] |
---|
| 1111 | + h_now[k+1]*u_now[k+1] - h_now[k]*u_now[k]) |
---|
| 1112 | self.shock_detector[:] = abs(E) |
---|
| 1113 | |
---|
| 1114 | def saxpy_conserved_quantities(self,a,b): |
---|
| 1115 | N = len(self) #number_of_triangles |
---|
| 1116 | |
---|
| 1117 | # Backup conserved_quantities centroid values |
---|
| 1118 | for name in self.conserved_quantities: |
---|
| 1119 | Q = self.quantities[name] |
---|
| 1120 | Q.saxpy_centroid_values(a,b) |
---|
| 1121 | |
---|
| 1122 | def solve_inhomogenous_second_order(self,yieldstep, finaltime): |
---|
| 1123 | |
---|
| 1124 | #Update timestep to fit yieldstep and finaltime |
---|
| 1125 | self.update_timestep(yieldstep, finaltime) |
---|
| 1126 | #Compute forcing terms |
---|
| 1127 | self.compute_forcing_terms() |
---|
| 1128 | #Update conserved quantities |
---|
| 1129 | self.update_conserved_quantities(0.5*self.timestep) |
---|
| 1130 | #Update vertex and edge values |
---|
| 1131 | self.distribute_to_vertices_and_edges() |
---|
| 1132 | #Update boundary values |
---|
| 1133 | self.update_boundary() |
---|
| 1134 | |
---|
| 1135 | def solve_homogenous_second_order(self,yieldstep,finaltime): |
---|
| 1136 | """Use Shu Second order timestepping to update |
---|
| 1137 | conserved quantities |
---|
| 1138 | |
---|
| 1139 | q^{n+1/2} = q^{n}+0.5*dt*F^{n} |
---|
| 1140 | q^{n+1} = q^{n}+dt*F^{n+1/2} |
---|
| 1141 | """ |
---|
| 1142 | import copy |
---|
| 1143 | from Numeric import Float |
---|
| 1144 | from numpy import zeros |
---|
| 1145 | |
---|
| 1146 | N = self.number_of_elements |
---|
| 1147 | |
---|
| 1148 | self.compute_fluxes() |
---|
| 1149 | #Update timestep to fit yieldstep and finaltime |
---|
| 1150 | self.update_timestep(yieldstep, finaltime) |
---|
| 1151 | #Compute forcing terms |
---|
| 1152 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
| 1153 | #ADDING THIS WILL NEED TO REMOVE ZEROING IN COMPUTE_FORCING |
---|
| 1154 | #self.compute_forcing_terms() |
---|
| 1155 | |
---|
| 1156 | QC = zeros((N,len(self.conserved_quantities)),Float) |
---|
| 1157 | QF = zeros((N,len(self.conserved_quantities)),Float) |
---|
| 1158 | |
---|
| 1159 | i = 0 |
---|
| 1160 | for name in self.conserved_quantities: |
---|
| 1161 | Q = self.quantities[name] |
---|
| 1162 | #Store the centroid values at time t^n |
---|
| 1163 | QC[:,i] = copy.copy(Q.centroid_values) |
---|
| 1164 | QF[:,i] = copy.copy(Q.explicit_update) |
---|
| 1165 | #Update conserved quantities |
---|
| 1166 | Q.update(self.timestep) |
---|
| 1167 | i+=1 |
---|
| 1168 | |
---|
| 1169 | #Update vertex and edge values |
---|
| 1170 | self.distribute_to_vertices_and_edges() |
---|
| 1171 | #Update boundary values |
---|
| 1172 | self.update_boundary() |
---|
| 1173 | |
---|
| 1174 | self.compute_fluxes() |
---|
| 1175 | self.update_timestep(yieldstep, finaltime) |
---|
| 1176 | #Compute forcing terms |
---|
| 1177 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
| 1178 | #self.compute_forcing_terms() |
---|
| 1179 | |
---|
| 1180 | i = 0 |
---|
| 1181 | for name in self.conserved_quantities: |
---|
| 1182 | Q = self.quantities[name] |
---|
| 1183 | Q.centroid_values = QC[:,i] |
---|
| 1184 | Q.explicit_update = 0.5*(Q.explicit_update+QF[:,i]) |
---|
| 1185 | #Update conserved quantities |
---|
| 1186 | Q.update(self.timestep) |
---|
| 1187 | i+=1 |
---|
| 1188 | |
---|
| 1189 | #Update vertex and edge values |
---|
| 1190 | self.distribute_to_vertices_and_edges() |
---|
| 1191 | #Update boundary values |
---|
| 1192 | self.update_boundary() |
---|
| 1193 | |
---|
| 1194 | def solve_homogenous_second_order_harten(self,yieldstep,finaltime): |
---|
| 1195 | """Use Harten Second order timestepping to update |
---|
| 1196 | conserved quantities |
---|
| 1197 | |
---|
| 1198 | q^{n+1/2} = q^{n}+0.5*dt*F^{n} |
---|
| 1199 | q^{n+1} = q^{n}+dt*F^{n+1/2} |
---|
| 1200 | """ |
---|
| 1201 | import copy |
---|
| 1202 | from Numeric import Float |
---|
| 1203 | from numpy import zeros |
---|
| 1204 | |
---|
| 1205 | N = self.number_of_elements |
---|
| 1206 | |
---|
| 1207 | self.compute_fluxes() |
---|
| 1208 | #Update timestep to fit yieldstep and finaltime |
---|
| 1209 | self.update_timestep(yieldstep, finaltime) |
---|
| 1210 | #Compute forcing terms |
---|
| 1211 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
| 1212 | #ADDING THIS WILL NEED TO REMOVE ZEROING IN COMPUTE_FORCING |
---|
| 1213 | #self.compute_forcing_terms() |
---|
| 1214 | |
---|
| 1215 | QC = zeros((N,len(self.conserved_quantities)),Float) |
---|
| 1216 | |
---|
| 1217 | i = 0 |
---|
| 1218 | for name in self.conserved_quantities: |
---|
| 1219 | Q = self.quantities[name] |
---|
| 1220 | #Store the centroid values at time t^n |
---|
| 1221 | QC[:,i] = copy.copy(Q.centroid_values) |
---|
| 1222 | #Update conserved quantities |
---|
| 1223 | Q.update(0.5*self.timestep) |
---|
| 1224 | i+=1 |
---|
| 1225 | |
---|
| 1226 | #Update vertex and edge values |
---|
| 1227 | self.distribute_to_vertices_and_edges() |
---|
| 1228 | #Update boundary values |
---|
| 1229 | self.update_boundary() |
---|
| 1230 | |
---|
| 1231 | self.compute_fluxes() |
---|
| 1232 | self.update_timestep(yieldstep, finaltime) |
---|
| 1233 | #Compute forcing terms |
---|
| 1234 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
---|
| 1235 | #self.compute_forcing_terms() |
---|
| 1236 | |
---|
| 1237 | i = 0 |
---|
| 1238 | for name in self.conserved_quantities: |
---|
| 1239 | Q = self.quantities[name] |
---|
| 1240 | Q.centroid_values = QC[:,i] |
---|
| 1241 | #Update conserved quantities |
---|
| 1242 | Q.update(self.timestep) |
---|
| 1243 | i+=1 |
---|
| 1244 | |
---|
| 1245 | #Update vertex and edge values |
---|
| 1246 | self.distribute_to_vertices_and_edges() |
---|
| 1247 | #Update boundary values |
---|
| 1248 | self.update_boundary() |
---|
| 1249 | |
---|
| 1250 | def distribute_to_vertices_and_edges(self): |
---|
| 1251 | """Extrapolate conserved quantities from centroid to |
---|
| 1252 | vertices and edge-midpoints for each volume |
---|
| 1253 | |
---|
| 1254 | Default implementation is straight first order, |
---|
| 1255 | i.e. constant values throughout each element and |
---|
| 1256 | no reference to non-conserved quantities. |
---|
| 1257 | """ |
---|
| 1258 | |
---|
| 1259 | for name in self.conserved_quantities: |
---|
| 1260 | Q = self.quantities[name] |
---|
| 1261 | if self.order == 1: |
---|
| 1262 | Q.extrapolate_first_order() |
---|
| 1263 | elif self.order == 2: |
---|
| 1264 | Q.extrapolate_second_order() |
---|
| 1265 | #Q.limit() |
---|
| 1266 | else: |
---|
| 1267 | raise 'Unknown order' |
---|
| 1268 | |
---|
| 1269 | |
---|
| 1270 | def update_ghosts(self): |
---|
| 1271 | pass |
---|
| 1272 | """ |
---|
| 1273 | n = len(self.quantities['stage'].vertex_values) |
---|
| 1274 | from parameters import bed_slope, cell_len |
---|
| 1275 | |
---|
| 1276 | self.quantities['stage'].centroid_values[n-1] = self.quantities['stage'].boundary_values[1] - 0.5*bed_slope*cell_len |
---|
| 1277 | self.quantities['xmomentum'].centroid_values[n-1] = self.quantities['xmomentum'].boundary_values[1] |
---|
| 1278 | self.quantities['elevation'].centroid_values[n-1] = self.quantities['elevation'].boundary_values[1] - 0.5*bed_slope*cell_len |
---|
| 1279 | self.quantities['height'].centroid_values[n-1] = self.quantities['height'].boundary_values[1] |
---|
| 1280 | self.quantities['velocity'].centroid_values[n-1] = self.quantities['velocity'].boundary_values[1] |
---|
| 1281 | #Below is additional condition, after meeting Steve, to make smooth dry bed. |
---|
| 1282 | self.quantities['stage'].centroid_values[0] = self.quantities['stage'].boundary_values[0] + 0.5*bed_slope*cell_len |
---|
| 1283 | self.quantities['xmomentum'].centroid_values[0] = self.quantities['xmomentum'].boundary_values[0] |
---|
| 1284 | self.quantities['elevation'].centroid_values[0] = self.quantities['elevation'].boundary_values[0] + 0.5*bed_slope*cell_len |
---|
| 1285 | self.quantities['height'].centroid_values[0] = self.quantities['height'].boundary_values[0] |
---|
| 1286 | self.quantities['velocity'].centroid_values[0] = self.quantities['velocity'].boundary_values[0] |
---|
| 1287 | """ |
---|
| 1288 | |
---|
| 1289 | |
---|
| 1290 | def update_boundary(self): |
---|
| 1291 | """Go through list of boundary objects and update boundary values |
---|
| 1292 | for all conserved quantities on boundary. |
---|
| 1293 | """ |
---|
| 1294 | for i, ((vol_id, vertex_id), B) in enumerate(self.boundary_objects): |
---|
| 1295 | q = B.evaluate(vol_id, vertex_id) |
---|
| 1296 | for j, name in enumerate(self.evolved_quantities): |
---|
| 1297 | #print 'name %s j = %f \n'%(name,j) |
---|
| 1298 | Q = self.quantities[name] |
---|
| 1299 | Q.boundary_values[i] = q[j] |
---|
| 1300 | """ |
---|
| 1301 | ##!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
---|
| 1302 | for j, name in enumerate(self.evolved_quantities): |
---|
| 1303 | BV = self.quantities[name].boundary_values |
---|
| 1304 | VV = self.quantities[name].vertex_values |
---|
| 1305 | n = len(VV) |
---|
| 1306 | VV[0,0] = BV[0] |
---|
| 1307 | VV[n-1,1] = BV[1] |
---|
| 1308 | |
---|
| 1309 | |
---|
| 1310 | #Below is for fixing the ghost cell. |
---|
| 1311 | from parameters import bed_slope, cell_len |
---|
| 1312 | n = len(self.quantities['stage'].vertex_values) |
---|
| 1313 | self.quantities['stage'].vertex_values[n-1,0] = self.quantities['stage'].boundary_values[1] - bed_slope*cell_len |
---|
| 1314 | self.quantities['xmomentum'].vertex_values[n-1,0] = self.quantities['xmomentum'].boundary_values[1] |
---|
| 1315 | self.quantities['elevation'].vertex_values[n-1,0] = self.quantities['elevation'].boundary_values[1] - bed_slope*cell_len |
---|
| 1316 | self.quantities['height'].vertex_values[n-1,0] = self.quantities['height'].boundary_values[1] |
---|
| 1317 | self.quantities['velocity'].vertex_values[n-1,0] = self.quantities['velocity'].boundary_values[1] |
---|
| 1318 | #Below is additional condition, after meeting Steve, to make smooth dry bed. |
---|
| 1319 | self.quantities['stage'].vertex_values[0,1] = self.quantities['stage'].boundary_values[0] + bed_slope*cell_len |
---|
| 1320 | self.quantities['xmomentum'].vertex_values[0,1] = self.quantities['xmomentum'].boundary_values[0] |
---|
| 1321 | self.quantities['elevation'].vertex_values[0,1] = self.quantities['elevation'].boundary_values[0] + bed_slope*cell_len |
---|
| 1322 | self.quantities['height'].vertex_values[0,1] = self.quantities['height'].boundary_values[0] |
---|
| 1323 | self.quantities['velocity'].vertex_values[0,1] = self.quantities['velocity'].boundary_values[0] |
---|
| 1324 | """ |
---|
| 1325 | |
---|
| 1326 | def update_timestep(self, yieldstep, finaltime): |
---|
| 1327 | |
---|
| 1328 | from config import min_timestep, max_timestep |
---|
| 1329 | |
---|
| 1330 | # self.timestep is calculated from speed of characteristics |
---|
| 1331 | # Apply CFL condition here |
---|
| 1332 | timestep = min(self.CFL*self.flux_timestep, max_timestep) |
---|
| 1333 | |
---|
| 1334 | #Record maximal and minimal values of timestep for reporting |
---|
| 1335 | self.max_timestep = max(timestep, self.max_timestep) |
---|
| 1336 | self.min_timestep = min(timestep, self.min_timestep) |
---|
| 1337 | |
---|
| 1338 | #Protect against degenerate time steps |
---|
| 1339 | if timestep < min_timestep: |
---|
| 1340 | |
---|
| 1341 | #Number of consecutive small steps taken b4 taking action |
---|
| 1342 | self.smallsteps += 1 |
---|
| 1343 | |
---|
| 1344 | if self.smallsteps > self.max_smallsteps: |
---|
| 1345 | self.smallsteps = 0 #Reset |
---|
| 1346 | |
---|
| 1347 | if self.order == 1: |
---|
| 1348 | msg = 'WARNING: Too small timestep %.16f reached '\ |
---|
| 1349 | %timestep |
---|
| 1350 | msg += 'even after %d steps of 1 order scheme'\ |
---|
| 1351 | %self.max_smallsteps |
---|
| 1352 | print msg |
---|
| 1353 | timestep = min_timestep #Try enforcing min_step |
---|
| 1354 | |
---|
| 1355 | #raise msg |
---|
| 1356 | else: |
---|
| 1357 | #Try to overcome situation by switching to 1 order |
---|
| 1358 | print "changing Order 1" |
---|
| 1359 | self.order = 1 |
---|
| 1360 | |
---|
| 1361 | else: |
---|
| 1362 | self.smallsteps = 0 |
---|
| 1363 | if self.order == 1 and self.default_order == 2: |
---|
| 1364 | self.order = 2 |
---|
| 1365 | |
---|
| 1366 | |
---|
| 1367 | #Ensure that final time is not exceeded |
---|
| 1368 | if finaltime is not None and self.time + timestep > finaltime: |
---|
| 1369 | timestep = finaltime-self.time |
---|
| 1370 | |
---|
| 1371 | #Ensure that model time is aligned with yieldsteps |
---|
| 1372 | if self.yieldtime + timestep > yieldstep: |
---|
| 1373 | timestep = yieldstep-self.yieldtime |
---|
| 1374 | |
---|
| 1375 | self.timestep = timestep |
---|
| 1376 | |
---|
| 1377 | def update_extrema(self): |
---|
| 1378 | pass |
---|
| 1379 | |
---|
| 1380 | def compute_forcing_terms(self): |
---|
| 1381 | """If there are any forcing functions driving the system |
---|
| 1382 | they should be defined in Domain subclass and appended to |
---|
| 1383 | the list self.forcing_terms |
---|
| 1384 | """ |
---|
| 1385 | #Clears explicit_update needed for second order method |
---|
| 1386 | if self.time_order == 2: |
---|
| 1387 | for name in self.conserved_quantities: |
---|
| 1388 | Q = self.quantities[name] |
---|
| 1389 | Q.explicit_update[:] = 0.0 |
---|
| 1390 | |
---|
| 1391 | for f in self.forcing_terms: |
---|
| 1392 | f(self) |
---|
| 1393 | |
---|
| 1394 | |
---|
| 1395 | def update_derived_quantites(self): |
---|
| 1396 | pass |
---|
| 1397 | |
---|
| 1398 | #def update_conserved_quantities(self): |
---|
| 1399 | def update_conserved_quantities(self): |
---|
| 1400 | """Update vectors of conserved quantities using previously |
---|
| 1401 | computed fluxes specified forcing functions. |
---|
| 1402 | """ |
---|
| 1403 | |
---|
| 1404 | from Numeric import Float |
---|
| 1405 | from numpy import ones, sum, equal |
---|
| 1406 | |
---|
| 1407 | N = self.number_of_elements |
---|
| 1408 | d = len(self.conserved_quantities) |
---|
| 1409 | |
---|
| 1410 | timestep = self.timestep |
---|
| 1411 | |
---|
| 1412 | #Compute forcing terms |
---|
| 1413 | self.compute_forcing_terms() |
---|
| 1414 | |
---|
| 1415 | #Update conserved_quantities |
---|
| 1416 | for name in self.conserved_quantities: |
---|
| 1417 | Q = self.quantities[name] |
---|
| 1418 | Q.update(timestep) |
---|
| 1419 | |
---|
| 1420 | |
---|
| 1421 | |
---|
| 1422 | if __name__ == "__main__": |
---|
| 1423 | |
---|
| 1424 | points1 = [0.0, 1.0, 2.0, 3.0] |
---|
| 1425 | D1 = Domain(points1) |
---|
| 1426 | |
---|
| 1427 | print D1.get_coordinate(0) |
---|
| 1428 | print D1.get_coordinate(0,1) |
---|
| 1429 | print 'Number of Elements = ',D1.number_of_elements |
---|
| 1430 | |
---|
| 1431 | try: |
---|
| 1432 | print D1.get_coordinate(3) |
---|
| 1433 | except: |
---|
| 1434 | pass |
---|
| 1435 | else: |
---|
| 1436 | msg = 'Should have raised an out of bounds exception' |
---|
| 1437 | raise msg |
---|