1 | """Class Domain - |
---|
2 | 1D interval domains for finite-volume computations of |
---|
3 | the shallow water wave equation. |
---|
4 | |
---|
5 | This module contains a specialisation of class Domain from module domain.py |
---|
6 | consisting of methods specific to the Shallow Water Wave Equation |
---|
7 | |
---|
8 | |
---|
9 | U_t + E_x = S |
---|
10 | |
---|
11 | where |
---|
12 | |
---|
13 | U = [w, uh] |
---|
14 | E = [uh, u^2h + gh^2/2] |
---|
15 | S represents source terms forcing the system |
---|
16 | (e.g. gravity, friction, wind stress, ...) |
---|
17 | |
---|
18 | and _t, _x, _y denote the derivative with respect to t, x and y respectiely. |
---|
19 | |
---|
20 | The quantities are |
---|
21 | |
---|
22 | symbol variable name explanation |
---|
23 | x x horizontal distance from origin [m] |
---|
24 | z elevation elevation of bed on which flow is modelled [m] |
---|
25 | h height water height above z [m] |
---|
26 | w stage absolute water level, w = z+h [m] |
---|
27 | u speed in the x direction [m/s] |
---|
28 | uh xmomentum momentum in the x direction [m^2/s] |
---|
29 | |
---|
30 | eta mannings friction coefficient [to appear] |
---|
31 | nu wind stress coefficient [to appear] |
---|
32 | |
---|
33 | The conserved quantities are w, uh |
---|
34 | |
---|
35 | For details see e.g. |
---|
36 | Christopher Zoppou and Stephen Roberts, |
---|
37 | Catastrophic Collapse of Water Supply Reservoirs in Urban Areas, |
---|
38 | Journal of Hydraulic Engineering, vol. 127, No. 7 July 1999 |
---|
39 | |
---|
40 | |
---|
41 | John Jakeman, Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
---|
42 | Geoscience Australia, 2006 |
---|
43 | """ |
---|
44 | |
---|
45 | |
---|
46 | from anuga_1d.generic.generic_domain import * |
---|
47 | from sww_boundary_conditions import * |
---|
48 | from sww_forcing_terms import * |
---|
49 | |
---|
50 | #Shallow water domain |
---|
51 | class Domain(Generic_domain): |
---|
52 | |
---|
53 | def __init__(self, coordinates, boundary = None, tagged_elements = None): |
---|
54 | |
---|
55 | conserved_quantities = ['stage', 'xmomentum'] |
---|
56 | evolved_quantities = ['stage', 'xmomentum', 'elevation', 'height', 'velocity'] |
---|
57 | other_quantities = ['friction'] |
---|
58 | Generic_domain.__init__(self, |
---|
59 | coordinates = coordinates, |
---|
60 | boundary = boundary, |
---|
61 | conserved_quantities = conserved_quantities, |
---|
62 | evolved_quantities = evolved_quantities, |
---|
63 | other_quantities = other_quantities, |
---|
64 | tagged_elements = tagged_elements) |
---|
65 | |
---|
66 | from anuga_1d.config import minimum_allowed_height, g, h0 |
---|
67 | self.minimum_allowed_height = minimum_allowed_height |
---|
68 | self.g = g |
---|
69 | self.h0 = h0 |
---|
70 | |
---|
71 | #forcing terms not included in 1d domain ?WHy? |
---|
72 | self.forcing_terms.append(gravity) |
---|
73 | #self.forcing_terms.append(manning_friction) |
---|
74 | #print "\nI have Removed forcing terms line 64 1dsw" |
---|
75 | |
---|
76 | |
---|
77 | #Stored output |
---|
78 | self.store = True |
---|
79 | self.format = 'sww' |
---|
80 | self.smooth = True |
---|
81 | |
---|
82 | |
---|
83 | #Reduction operation for get_vertex_values |
---|
84 | from anuga_1d.generic.util import mean |
---|
85 | self.reduction = mean |
---|
86 | #self.reduction = min #Looks better near steep slopes |
---|
87 | |
---|
88 | self.set_quantities_to_be_stored(['stage','xmomentum']) |
---|
89 | |
---|
90 | self.__doc__ = 'sww_vel_domain' |
---|
91 | |
---|
92 | self.check_integrity() |
---|
93 | |
---|
94 | |
---|
95 | |
---|
96 | def check_integrity(self): |
---|
97 | |
---|
98 | #Check that we are solving the shallow water wave equation |
---|
99 | |
---|
100 | msg = 'First conserved quantity must be "stage"' |
---|
101 | assert self.conserved_quantities[0] == 'stage', msg |
---|
102 | msg = 'Second conserved quantity must be "xmomentum"' |
---|
103 | assert self.conserved_quantities[1] == 'xmomentum', msg |
---|
104 | |
---|
105 | msg = 'First evolved quantity must be "stage"' |
---|
106 | assert self.evolved_quantities[0] == 'stage', msg |
---|
107 | msg = 'Second evolved quantity must be "xmomentum"' |
---|
108 | assert self.evolved_quantities[1] == 'xmomentum', msg |
---|
109 | msg = 'Third evolved quantity must be "elevation"' |
---|
110 | assert self.evolved_quantities[2] == 'elevation', msg |
---|
111 | msg = 'Fourth evolved quantity must be "height"' |
---|
112 | assert self.evolved_quantities[3] == 'height', msg |
---|
113 | msg = 'Fifth evolved quantity must be "velocity"' |
---|
114 | assert self.evolved_quantities[4] == 'velocity', msg |
---|
115 | |
---|
116 | Generic_domain.check_integrity(self) |
---|
117 | |
---|
118 | def compute_fluxes(self): |
---|
119 | #Call correct module function |
---|
120 | #(either from this module or C-extension) |
---|
121 | compute_fluxes_vel(self) |
---|
122 | |
---|
123 | def distribute_to_vertices_and_edges(self): |
---|
124 | #Call correct module function |
---|
125 | #(either from this module or C-extension) |
---|
126 | distribute_to_vertices_and_edges_limit_w_u(self) |
---|
127 | |
---|
128 | |
---|
129 | #=============== End of Shallow Water Domain =============================== |
---|
130 | #----------------------------------- |
---|
131 | # Compute fluxes interface |
---|
132 | #----------------------------------- |
---|
133 | def compute_fluxes(domain): |
---|
134 | """ |
---|
135 | Python version of compute fluxes (local_compute_fluxes) |
---|
136 | is available in test_shallow_water_vel_domain.py |
---|
137 | """ |
---|
138 | |
---|
139 | |
---|
140 | from numpy import zeros |
---|
141 | import sys |
---|
142 | |
---|
143 | |
---|
144 | timestep = float(sys.maxint) |
---|
145 | |
---|
146 | stage = domain.quantities['stage'] |
---|
147 | xmom = domain.quantities['xmomentum'] |
---|
148 | bed = domain.quantities['elevation'] |
---|
149 | |
---|
150 | |
---|
151 | from anuga_1d.sww_flow.sww_vel_comp_flux_ext import compute_fluxes_ext |
---|
152 | |
---|
153 | domain.flux_timestep = compute_fluxes_ext(timestep,domain,stage,xmom,bed) |
---|
154 | |
---|
155 | |
---|
156 | #----------------------------------- |
---|
157 | # Compute flux definition with vel |
---|
158 | #----------------------------------- |
---|
159 | def compute_fluxes_vel(domain): |
---|
160 | from Numeric import zeros, Float |
---|
161 | import sys |
---|
162 | |
---|
163 | |
---|
164 | timestep = float(sys.maxint) |
---|
165 | |
---|
166 | stage = domain.quantities['stage'] |
---|
167 | xmom = domain.quantities['xmomentum'] |
---|
168 | bed = domain.quantities['elevation'] |
---|
169 | height = domain.quantities['height'] |
---|
170 | velocity = domain.quantities['velocity'] |
---|
171 | |
---|
172 | |
---|
173 | from anuga_1d.sww.sww_vel_comp_flux_ext import compute_fluxes_vel_ext |
---|
174 | |
---|
175 | domain.flux_timestep = compute_fluxes_vel_ext(timestep,domain,stage,xmom,bed,height,velocity) |
---|
176 | |
---|
177 | |
---|
178 | |
---|
179 | #-------------------------------------------------------------------------- |
---|
180 | def distribute_to_vertices_and_edges_limit_w_u(domain): |
---|
181 | """Distribution from centroids to vertices specific to the |
---|
182 | shallow water wave |
---|
183 | equation. |
---|
184 | |
---|
185 | It will ensure that h (w-z) is always non-negative even in the |
---|
186 | presence of steep bed-slopes by taking a weighted average between shallow |
---|
187 | and deep cases. |
---|
188 | |
---|
189 | In addition, all conserved quantities get distributed as per either a |
---|
190 | constant (order==1) or a piecewise linear function (order==2). |
---|
191 | |
---|
192 | FIXME: more explanation about removal of artificial variability etc |
---|
193 | |
---|
194 | Precondition: |
---|
195 | All quantities defined at centroids and bed elevation defined at |
---|
196 | vertices. |
---|
197 | |
---|
198 | Postcondition |
---|
199 | Conserved quantities defined at vertices |
---|
200 | |
---|
201 | """ |
---|
202 | |
---|
203 | |
---|
204 | #Remove very thin layers of water |
---|
205 | #protect_against_infinitesimal_and_negative_heights(domain) |
---|
206 | |
---|
207 | import sys |
---|
208 | from numpy import zeros |
---|
209 | from anuga_1d.config import epsilon, h0 |
---|
210 | |
---|
211 | N = domain.number_of_elements |
---|
212 | |
---|
213 | #Shortcuts |
---|
214 | Stage = domain.quantities['stage'] |
---|
215 | Xmom = domain.quantities['xmomentum'] |
---|
216 | Bed = domain.quantities['elevation'] |
---|
217 | Height = domain.quantities['height'] |
---|
218 | Velocity = domain.quantities['velocity'] |
---|
219 | |
---|
220 | #Arrays |
---|
221 | w_C = Stage.centroid_values |
---|
222 | uh_C = Xmom.centroid_values |
---|
223 | z_C = Bed.centroid_values |
---|
224 | h_C = Height.centroid_values |
---|
225 | u_C = Velocity.centroid_values |
---|
226 | |
---|
227 | #print id(h_C) |
---|
228 | ## for i in range(N): |
---|
229 | ## h_C[i] = w_C[i] - z_C[i] |
---|
230 | ## if h_C[i] <= 1.0e-12: |
---|
231 | ## #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
---|
232 | ## h_C[i] = 0.0 |
---|
233 | ## w_C[i] = z_C[i] |
---|
234 | ## #uh_C[i] = 0.0 |
---|
235 | |
---|
236 | ## # u_C[i] = 0.0 |
---|
237 | ## # else: |
---|
238 | ## # u_C[i] = uh_C[i]/h_C[i] |
---|
239 | |
---|
240 | h0 = 1.0e-12 |
---|
241 | for i in range(N): |
---|
242 | h_C[i] = w_C[i] - z_C[i] |
---|
243 | if h_C[i] < 1.0e-12: |
---|
244 | u_C[i] = 0.0 #Could have been negative |
---|
245 | h_C[i] = 0.0 |
---|
246 | w_C[i] = z_C[i] |
---|
247 | else: |
---|
248 | #u_C[i] = uh_C[i]/(h_C[i] + h0/h_C[i]) |
---|
249 | u_C[i] = uh_C[i]/h_C[i] |
---|
250 | |
---|
251 | for name in [ 'velocity', 'stage' ]: |
---|
252 | Q = domain.quantities[name] |
---|
253 | if domain.order == 1: |
---|
254 | Q.extrapolate_first_order() |
---|
255 | elif domain.order == 2: |
---|
256 | Q.extrapolate_second_order() |
---|
257 | else: |
---|
258 | raise 'Unknown order' |
---|
259 | |
---|
260 | w_V = domain.quantities['stage'].vertex_values |
---|
261 | z_V = domain.quantities['elevation'].vertex_values |
---|
262 | h_V = domain.quantities['height'].vertex_values |
---|
263 | u_V = domain.quantities['velocity'].vertex_values |
---|
264 | uh_V = domain.quantities['xmomentum'].vertex_values |
---|
265 | |
---|
266 | #print w_V |
---|
267 | #print z_V |
---|
268 | |
---|
269 | h_V[:,:] = w_V - z_V |
---|
270 | for i in range(len(h_C)): |
---|
271 | for j in range(2): |
---|
272 | if h_V[i,j] < 0.0 : |
---|
273 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
---|
274 | dh = h_V[i,j] |
---|
275 | h_V[i,j] = 0.0 |
---|
276 | w_V[i,j] = z_V[i,j] |
---|
277 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
---|
278 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
---|
279 | |
---|
280 | uh_V[:,:] = u_V * h_V |
---|
281 | |
---|
282 | |
---|
283 | return |
---|
284 | |
---|
285 | #--------------------------------------------------------------------------- |
---|
286 | def distribute_to_vertices_and_edges_limit_w_uh(domain): |
---|
287 | """Distribution from centroids to vertices specific to the |
---|
288 | shallow water wave equation. |
---|
289 | |
---|
290 | In addition, all conserved quantities get distributed as per either a |
---|
291 | constant (order==1) or a piecewise linear function (order==2). |
---|
292 | |
---|
293 | Precondition: |
---|
294 | All quantities defined at centroids and bed elevation defined at |
---|
295 | vertices. |
---|
296 | |
---|
297 | Postcondition |
---|
298 | Conserved quantities defined at vertices |
---|
299 | |
---|
300 | """ |
---|
301 | |
---|
302 | import sys |
---|
303 | from numpy import zeros |
---|
304 | from anuga_1d.config import epsilon, h0 |
---|
305 | |
---|
306 | N = domain.number_of_elements |
---|
307 | |
---|
308 | #Shortcuts |
---|
309 | Stage = domain.quantities['stage'] |
---|
310 | Xmom = domain.quantities['xmomentum'] |
---|
311 | Bed = domain.quantities['elevation'] |
---|
312 | Height = domain.quantities['height'] |
---|
313 | Velocity = domain.quantities['velocity'] |
---|
314 | |
---|
315 | #Arrays |
---|
316 | w_C = Stage.centroid_values |
---|
317 | uh_C = Xmom.centroid_values |
---|
318 | z_C = Bed.centroid_values |
---|
319 | h_C = Height.centroid_values |
---|
320 | u_C = Velocity.centroid_values |
---|
321 | |
---|
322 | |
---|
323 | for i in range(N): |
---|
324 | h_C[i] = w_C[i] - z_C[i] |
---|
325 | if h_C[i] <= 1.0e-6: |
---|
326 | #print 'h_C[%d]= %15.5e\n' % (i,h_C[i]) |
---|
327 | h_C[i] = 0.0 |
---|
328 | w_C[i] = z_C[i] |
---|
329 | uh_C[i] = 0.0 |
---|
330 | |
---|
331 | for name in [ 'stage', 'xmomentum']: |
---|
332 | Q = domain.quantities[name] |
---|
333 | if domain.order == 1: |
---|
334 | Q.extrapolate_first_order() |
---|
335 | elif domain.order == 2: |
---|
336 | Q.extrapolate_second_order() |
---|
337 | else: |
---|
338 | raise 'Unknown order' |
---|
339 | |
---|
340 | w_V = domain.quantities['stage'].vertex_values |
---|
341 | z_V = domain.quantities['elevation'].vertex_values |
---|
342 | h_V = domain.quantities['height'].vertex_values |
---|
343 | u_V = domain.quantities['velocity'].vertex_values |
---|
344 | uh_V = domain.quantities['xmomentum'].vertex_values |
---|
345 | |
---|
346 | h_V[:,:] = w_V - z_V |
---|
347 | |
---|
348 | for i in range(len(h_C)): |
---|
349 | for j in range(2): |
---|
350 | if h_V[i,j] < 0.0 : |
---|
351 | #print 'h_V[%d,%d] = %f \n' % (i,j,h_V[i,j]) |
---|
352 | dh = h_V[i,j] |
---|
353 | h_V[i,j] = 0.0 |
---|
354 | w_V[i,j] = z_V[i,j] |
---|
355 | h_V[i,(j+1)%2] = h_V[i,(j+1)%2] + dh |
---|
356 | w_V[i,(j+1)%2] = w_V[i,(j+1)%2] + dh |
---|
357 | u_V[i,j] = 0.0 |
---|
358 | if h_V[i,j] < h0: |
---|
359 | u_V[i,j] |
---|
360 | else: |
---|
361 | u_V[i,j] = uh_V[i,j]/(h_V[i,j] + h0/h_V[i,j]) |
---|
362 | |
---|
363 | |
---|