1 | #!/usr/bin/env python |
---|
2 | |
---|
3 | import unittest |
---|
4 | from math import sqrt, pi |
---|
5 | |
---|
6 | |
---|
7 | from shallow_water_domain import * |
---|
8 | from Numeric import allclose, array, ones, Float |
---|
9 | |
---|
10 | |
---|
11 | class Test_Shallow_Water(unittest.TestCase): |
---|
12 | def setUp(self): |
---|
13 | self.points = [0.0, 1.0, 2.0, 3.0] |
---|
14 | self.vertex_values = [[1.0,2.0],[4.0,5.0],[-1.0,2.0]] |
---|
15 | |
---|
16 | def tearDown(self): |
---|
17 | pass |
---|
18 | #print " Tearing down" |
---|
19 | |
---|
20 | |
---|
21 | def test_creation(self): |
---|
22 | domain = Domain(self.points) |
---|
23 | assert allclose(domain.centroids, [0.5, 1.5, 2.5]) |
---|
24 | |
---|
25 | def test_compute_fluxes(self): |
---|
26 | """ |
---|
27 | Compare shallow_water_domain flux calculation against a previous |
---|
28 | Python implementation (defined in this file) |
---|
29 | """ |
---|
30 | domain = Domain(self.points) |
---|
31 | domain.set_quantity('stage',2.0) |
---|
32 | domain.set_boundary({'exterior' : Reflective_boundary(domain)}) |
---|
33 | |
---|
34 | stage_ud, xmom_ud = compute_fluxes_python(domain) |
---|
35 | |
---|
36 | domain.compute_fluxes() |
---|
37 | |
---|
38 | #print doamin.quantities['xmomentum'].explicit_update |
---|
39 | #print compute_fluxes_python(domain) |
---|
40 | |
---|
41 | assert allclose( domain.quantities['stage'].explicit_update, stage_ud ) |
---|
42 | assert allclose( domain.quantities['xmomentum'].explicit_update, xmom_ud ) |
---|
43 | |
---|
44 | |
---|
45 | def test_local_flux_function(self): |
---|
46 | normal = 1.0 |
---|
47 | ql = array([1.0, 2.0],Float) |
---|
48 | qr = array([1.0, 2.0],Float) |
---|
49 | zl = 0.0 |
---|
50 | zr = 0.0 |
---|
51 | |
---|
52 | edgeflux, maxspeed = flux_function(normal, ql,qr,zl,zr) |
---|
53 | |
---|
54 | assert allclose(array([2.0, 8.9],Float), edgeflux) |
---|
55 | assert allclose(5.1304951685, maxspeed) |
---|
56 | |
---|
57 | normal = -1.0 |
---|
58 | ql = array([1.0, 2.0],Float) |
---|
59 | qr = array([1.0, 2.0],Float) |
---|
60 | zl = 0.0 |
---|
61 | zr = 0.0 |
---|
62 | |
---|
63 | edgeflux, maxspeed = flux_function(normal, ql,qr,zl,zr) |
---|
64 | |
---|
65 | assert allclose(array([-2.0, -8.9],Float), edgeflux) |
---|
66 | assert allclose(5.1304951685, maxspeed) |
---|
67 | |
---|
68 | def test_domain_flux_function(self): |
---|
69 | normal = 1.0 |
---|
70 | ql = array([1.0, 2.0],Float) |
---|
71 | qr = array([1.0, 2.0],Float) |
---|
72 | zl = 0.0 |
---|
73 | zr = 0.0 |
---|
74 | |
---|
75 | edgeflux, maxspeed = flux_function(normal, ql,qr,zl,zr) |
---|
76 | |
---|
77 | #print edgeflux |
---|
78 | |
---|
79 | from shallow_water_domain import flux_function as domain_flux_function |
---|
80 | |
---|
81 | domainedgeflux, domainmaxspeed = domain_flux_function(normal, ql,qr,zl,zr) |
---|
82 | |
---|
83 | #print domainedgeflux |
---|
84 | |
---|
85 | assert allclose(domainedgeflux, edgeflux) |
---|
86 | assert allclose(domainmaxspeed, maxspeed) |
---|
87 | |
---|
88 | |
---|
89 | |
---|
90 | #============================================================================== |
---|
91 | |
---|
92 | def compute_fluxes_python(domain): |
---|
93 | """Compute all fluxes and the timestep suitable for all volumes |
---|
94 | in domain. |
---|
95 | |
---|
96 | Compute total flux for each conserved quantity using "flux_function" |
---|
97 | |
---|
98 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
99 | Resulting flux is then scaled by area and stored in |
---|
100 | explicit_update for each of the three conserved quantities |
---|
101 | stage, xmomentum and ymomentum |
---|
102 | |
---|
103 | The maximal allowable speed computed by the flux_function for each volume |
---|
104 | is converted to a timestep that must not be exceeded. The minimum of |
---|
105 | those is computed as the next overall timestep. |
---|
106 | |
---|
107 | Post conditions: |
---|
108 | domain.explicit_update is reset to computed flux values |
---|
109 | domain.timestep is set to the largest step satisfying all volumes. |
---|
110 | """ |
---|
111 | |
---|
112 | import sys |
---|
113 | from Numeric import zeros, Float |
---|
114 | |
---|
115 | N = domain.number_of_elements |
---|
116 | |
---|
117 | tmp0 = zeros((N,),Float) |
---|
118 | tmp1 = zeros((N,),Float) |
---|
119 | |
---|
120 | #Shortcuts |
---|
121 | Stage = domain.quantities['stage'] |
---|
122 | Xmom = domain.quantities['xmomentum'] |
---|
123 | # Ymom = domain.quantities['ymomentum'] |
---|
124 | Bed = domain.quantities['elevation'] |
---|
125 | |
---|
126 | #Arrays |
---|
127 | #stage = Stage.edge_values |
---|
128 | #xmom = Xmom.edge_values |
---|
129 | # ymom = Ymom.edge_values |
---|
130 | #bed = Bed.edge_values |
---|
131 | |
---|
132 | stage = Stage.vertex_values |
---|
133 | xmom = Xmom.vertex_values |
---|
134 | bed = Bed.vertex_values |
---|
135 | |
---|
136 | #print 'stage edge values', stage |
---|
137 | #print 'xmom edge values', xmom |
---|
138 | #print 'bed values', bed |
---|
139 | |
---|
140 | stage_bdry = Stage.boundary_values |
---|
141 | xmom_bdry = Xmom.boundary_values |
---|
142 | #print 'stage_bdry',stage_bdry |
---|
143 | #print 'xmom_bdry', xmom_bdry |
---|
144 | # ymom_bdry = Ymom.boundary_values |
---|
145 | |
---|
146 | # flux = zeros(3, Float) #Work array for summing up fluxes |
---|
147 | flux = zeros(2, Float) #Work array for summing up fluxes |
---|
148 | ql = zeros(2, Float) |
---|
149 | qr = zeros(2, Float) |
---|
150 | |
---|
151 | #Loop |
---|
152 | timestep = float(sys.maxint) |
---|
153 | enter = True |
---|
154 | for k in range(N): |
---|
155 | |
---|
156 | flux[:] = 0. #Reset work array |
---|
157 | #for i in range(3): |
---|
158 | for i in range(2): |
---|
159 | #Quantities inside volume facing neighbour i |
---|
160 | #ql[0] = stage[k, i] |
---|
161 | #ql[1] = xmom[k, i] |
---|
162 | ql = [stage[k, i], xmom[k, i]] |
---|
163 | zl = bed[k, i] |
---|
164 | |
---|
165 | #Quantities at neighbour on nearest face |
---|
166 | n = domain.neighbours[k,i] |
---|
167 | if n < 0: |
---|
168 | m = -n-1 #Convert negative flag to index |
---|
169 | qr[0] = stage_bdry[m] |
---|
170 | qr[1] = xmom_bdry[m] |
---|
171 | zr = zl #Extend bed elevation to boundary |
---|
172 | else: |
---|
173 | #m = domain.neighbour_edges[k,i] |
---|
174 | m = domain.neighbour_vertices[k,i] |
---|
175 | #print i, ' ' , m |
---|
176 | #qr = [stage[n, m], xmom[n, m], ymom[n, m]] |
---|
177 | qr[0] = stage[n, m] |
---|
178 | qr[1] = xmom[n, m] |
---|
179 | zr = bed[n, m] |
---|
180 | |
---|
181 | |
---|
182 | #Outward pointing normal vector |
---|
183 | normal = domain.normals[k, i] |
---|
184 | |
---|
185 | #Flux computation using provided function |
---|
186 | #edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
187 | #print 'ql',ql |
---|
188 | #print 'qr',qr |
---|
189 | |
---|
190 | |
---|
191 | edgeflux, max_speed = flux_function(normal, ql, qr, zl, zr) |
---|
192 | |
---|
193 | #print 'edgeflux', edgeflux |
---|
194 | |
---|
195 | # THIS IS THE LINE TO DEAL WITH LEFT AND RIGHT FLUXES |
---|
196 | # flux = edgefluxleft - edgefluxright |
---|
197 | flux -= edgeflux #* domain.edgelengths[k,i] |
---|
198 | #Update optimal_timestep |
---|
199 | try: |
---|
200 | #timestep = min(timestep, 0.5*domain.radii[k]/max_speed) |
---|
201 | timestep = min(timestep, domain.cfl*0.5*domain.areas[k]/max_speed) |
---|
202 | except ZeroDivisionError: |
---|
203 | pass |
---|
204 | |
---|
205 | #Normalise by area and store for when all conserved |
---|
206 | #quantities get updated |
---|
207 | flux /= domain.areas[k] |
---|
208 | |
---|
209 | #Stage.explicit_update[k] = flux[0] |
---|
210 | tmp0[k] = flux[0] |
---|
211 | tmp1[k] = flux[1] |
---|
212 | |
---|
213 | |
---|
214 | return tmp0, tmp1 |
---|
215 | |
---|
216 | |
---|
217 | def flux_function(normal, ql, qr, zl, zr): |
---|
218 | """Compute fluxes between volumes for the shallow water wave equation |
---|
219 | cast in terms of w = h+z using the 'central scheme' as described in |
---|
220 | |
---|
221 | Kurganov, Noelle, Petrova. 'Semidiscrete Central-Upwind Schemes For |
---|
222 | Hyperbolic Conservation Laws and Hamilton-Jacobi Equations'. |
---|
223 | Siam J. Sci. Comput. Vol. 23, No. 3, pp. 707-740. |
---|
224 | |
---|
225 | The implemented formula is given in equation (3.15) on page 714 |
---|
226 | |
---|
227 | Conserved quantities w, uh, are stored as elements 0 and 1 |
---|
228 | in the numerical vectors ql an qr. |
---|
229 | |
---|
230 | Bed elevations zl and zr. |
---|
231 | """ |
---|
232 | |
---|
233 | from config import g, epsilon |
---|
234 | from math import sqrt |
---|
235 | from Numeric import array |
---|
236 | |
---|
237 | #print 'ql',ql |
---|
238 | |
---|
239 | #Align momentums with x-axis |
---|
240 | #q_left = rotate(ql, normal, direction = 1) |
---|
241 | #q_right = rotate(qr, normal, direction = 1) |
---|
242 | q_left = ql |
---|
243 | q_left[1] = q_left[1]*normal |
---|
244 | q_right = qr |
---|
245 | q_right[1] = q_right[1]*normal |
---|
246 | |
---|
247 | #z = (zl+zr)/2 #Take average of field values |
---|
248 | z = 0.5*(zl+zr) #Take average of field values |
---|
249 | |
---|
250 | w_left = q_left[0] #w=h+z |
---|
251 | h_left = w_left-z |
---|
252 | uh_left = q_left[1] |
---|
253 | |
---|
254 | if h_left < epsilon: |
---|
255 | u_left = 0.0 #Could have been negative |
---|
256 | h_left = 0.0 |
---|
257 | else: |
---|
258 | u_left = uh_left/h_left |
---|
259 | |
---|
260 | |
---|
261 | w_right = q_right[0] #w=h+z |
---|
262 | h_right = w_right-z |
---|
263 | uh_right = q_right[1] |
---|
264 | |
---|
265 | |
---|
266 | if h_right < epsilon: |
---|
267 | u_right = 0.0 #Could have been negative |
---|
268 | h_right = 0.0 |
---|
269 | else: |
---|
270 | u_right = uh_right/h_right |
---|
271 | |
---|
272 | #vh_left = q_left[2] |
---|
273 | #vh_right = q_right[2] |
---|
274 | |
---|
275 | #print h_right |
---|
276 | #print u_right |
---|
277 | #print h_left |
---|
278 | #print u_right |
---|
279 | |
---|
280 | soundspeed_left = sqrt(g*h_left) |
---|
281 | soundspeed_right = sqrt(g*h_right) |
---|
282 | |
---|
283 | #Maximal wave speed |
---|
284 | s_max = max(u_left+soundspeed_left, u_right+soundspeed_right, 0) |
---|
285 | |
---|
286 | #Minimal wave speed |
---|
287 | s_min = min(u_left-soundspeed_left, u_right-soundspeed_right, 0) |
---|
288 | |
---|
289 | #Flux computation |
---|
290 | |
---|
291 | #flux_left = array([u_left*h_left, |
---|
292 | # u_left*uh_left + 0.5*g*h_left**2]) |
---|
293 | #flux_right = array([u_right*h_right, |
---|
294 | # u_right*uh_right + 0.5*g*h_right**2]) |
---|
295 | flux_left = array([u_left*h_left, |
---|
296 | u_left*uh_left + 0.5*g*h_left*h_left]) |
---|
297 | flux_right = array([u_right*h_right, |
---|
298 | u_right*uh_right + 0.5*g*h_right*h_right]) |
---|
299 | |
---|
300 | denom = s_max-s_min |
---|
301 | if denom == 0.0: |
---|
302 | edgeflux = array([0.0, 0.0]) |
---|
303 | max_speed = 0.0 |
---|
304 | else: |
---|
305 | edgeflux = (s_max*flux_left - s_min*flux_right)/denom |
---|
306 | edgeflux += s_max*s_min*(q_right-q_left)/denom |
---|
307 | |
---|
308 | edgeflux[1] = edgeflux[1]*normal |
---|
309 | |
---|
310 | max_speed = max(abs(s_max), abs(s_min)) |
---|
311 | |
---|
312 | return edgeflux, max_speed |
---|
313 | |
---|
314 | |
---|
315 | #------------------------------------------------------------- |
---|
316 | if __name__ == "__main__": |
---|
317 | suite = unittest.makeSuite(Test_Shallow_Water, 'test') |
---|
318 | #suite = unittest.makeSuite(Test_Quantity, 'test_set_values_from_file_using_polygon') |
---|
319 | |
---|
320 | #suite = unittest.makeSuite(Test_Quantity, 'test_set_vertex_values_using_general_interface_with_subset') |
---|
321 | #print "restricted test" |
---|
322 | #suite = unittest.makeSuite(Test_Quantity,'verbose_test_set_values_from_UTM_pts') |
---|
323 | runner = unittest.TextTestRunner() |
---|
324 | runner.run(suite) |
---|