1 | """Class Domain - |
---|
2 | 2D triangular domains for finite-volume computations of |
---|
3 | the advection equation. |
---|
4 | |
---|
5 | This module contains a specialisation of class Domain from module domain.py |
---|
6 | consisting of methods specific to the advection equantion |
---|
7 | |
---|
8 | The equation is |
---|
9 | |
---|
10 | u_t + (v_1 u)_x + (v_2 u)_y = 0 |
---|
11 | |
---|
12 | There is only one conserved quantity, the stage u |
---|
13 | |
---|
14 | The advection equation is a very simple specialisation of the generic |
---|
15 | domain and may serve as an instructive example or a test of other |
---|
16 | components such as visualisation. |
---|
17 | |
---|
18 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
---|
19 | Geoscience Australia, 2004 |
---|
20 | """ |
---|
21 | |
---|
22 | |
---|
23 | #import logging, logging.config |
---|
24 | #logger = logging.getLogger('advection') |
---|
25 | #logger.setLevel(logging.WARNING) |
---|
26 | # |
---|
27 | #try: |
---|
28 | # logging.config.fileConfig('log.ini') |
---|
29 | #except: |
---|
30 | # pass |
---|
31 | |
---|
32 | |
---|
33 | from anuga.abstract_2d_finite_volumes.domain import * |
---|
34 | Generic_domain = Domain # Rename |
---|
35 | |
---|
36 | class Domain(Generic_domain): |
---|
37 | |
---|
38 | def __init__(self, |
---|
39 | coordinates, |
---|
40 | vertices, |
---|
41 | boundary = None, |
---|
42 | tagged_elements = None, |
---|
43 | geo_reference = None, |
---|
44 | use_inscribed_circle=False, |
---|
45 | velocity = None, |
---|
46 | full_send_dict=None, |
---|
47 | ghost_recv_dict=None, |
---|
48 | processor=0, |
---|
49 | numproc=1 |
---|
50 | ): |
---|
51 | |
---|
52 | conserved_quantities = ['stage'] |
---|
53 | other_quantities = [] |
---|
54 | Generic_domain.__init__(self, |
---|
55 | source=coordinates, |
---|
56 | triangles=vertices, |
---|
57 | boundary=boundary, |
---|
58 | conserved_quantities=conserved_quantities, |
---|
59 | other_quantities=other_quantities, |
---|
60 | tagged_elements=tagged_elements, |
---|
61 | geo_reference=geo_reference, |
---|
62 | use_inscribed_circle=use_inscribed_circle, |
---|
63 | full_send_dict=full_send_dict, |
---|
64 | ghost_recv_dict=ghost_recv_dict, |
---|
65 | processor=processor, |
---|
66 | numproc=numproc) |
---|
67 | |
---|
68 | import Numeric |
---|
69 | if velocity is None: |
---|
70 | self.velocity = Numeric.array([1,0],'d') |
---|
71 | else: |
---|
72 | self.velocity = Numeric.array(velocity,'d') |
---|
73 | |
---|
74 | #Only first is implemented for advection |
---|
75 | self.default_order = self.order = 1 |
---|
76 | |
---|
77 | self.smooth = True |
---|
78 | |
---|
79 | def check_integrity(self): |
---|
80 | Generic_domain.check_integrity(self) |
---|
81 | |
---|
82 | msg = 'Conserved quantity must be "stage"' |
---|
83 | assert self.conserved_quantities[0] == 'stage', msg |
---|
84 | |
---|
85 | |
---|
86 | def flux_function(self, normal, ql, qr, zl=None, zr=None): |
---|
87 | """Compute outward flux as inner product between velocity |
---|
88 | vector v=(v_1, v_2) and normal vector n. |
---|
89 | |
---|
90 | if <n,v> > 0 flux direction is outward bound and its magnitude is |
---|
91 | determined by the quantity inside volume: ql. |
---|
92 | Otherwise it is inbound and magnitude is determined by the |
---|
93 | quantity outside the volume: qr. |
---|
94 | """ |
---|
95 | |
---|
96 | v1 = self.velocity[0] |
---|
97 | v2 = self.velocity[1] |
---|
98 | |
---|
99 | |
---|
100 | normal_velocity = v1*normal[0] + v2*normal[1] |
---|
101 | |
---|
102 | if normal_velocity < 0: |
---|
103 | flux = qr * normal_velocity |
---|
104 | else: |
---|
105 | flux = ql * normal_velocity |
---|
106 | |
---|
107 | max_speed = abs(normal_velocity) |
---|
108 | return flux, max_speed |
---|
109 | |
---|
110 | |
---|
111 | |
---|
112 | def compute_fluxes(self): |
---|
113 | """Compute all fluxes and the timestep suitable for all volumes |
---|
114 | in domain. |
---|
115 | |
---|
116 | Compute total flux for each conserved quantity using "flux_function" |
---|
117 | |
---|
118 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
119 | Resulting flux is then scaled by area and stored in |
---|
120 | domain.explicit_update |
---|
121 | |
---|
122 | The maximal allowable speed computed by the flux_function |
---|
123 | for each volume |
---|
124 | is converted to a timestep that must not be exceeded. The minimum of |
---|
125 | those is computed as the next overall timestep. |
---|
126 | |
---|
127 | Post conditions: |
---|
128 | domain.explicit_update is reset to computed flux values |
---|
129 | domain.timestep is set to the largest step satisfying all volumes. |
---|
130 | """ |
---|
131 | |
---|
132 | import sys |
---|
133 | from Numeric import zeros, Float |
---|
134 | from anuga.config import max_timestep |
---|
135 | |
---|
136 | |
---|
137 | huge_timestep = float(sys.maxint) |
---|
138 | Stage = self.quantities['stage'] |
---|
139 | |
---|
140 | """ |
---|
141 | print "======================================" |
---|
142 | print "BEFORE compute_fluxes" |
---|
143 | print "stage_update",Stage.explicit_update |
---|
144 | print "stage_edge",Stage.edge_values |
---|
145 | print "stage_bdry",Stage.boundary_values |
---|
146 | print "neighbours",self.neighbours |
---|
147 | print "neighbour_edges",self.neighbour_edges |
---|
148 | print "normals",self.normals |
---|
149 | print "areas",self.areas |
---|
150 | print "radii",self.radii |
---|
151 | print "edgelengths",self.edgelengths |
---|
152 | print "tri_full_flag",self.tri_full_flag |
---|
153 | print "huge_timestep",huge_timestep |
---|
154 | print "max_timestep",max_timestep |
---|
155 | print "velocity",self.velocity |
---|
156 | """ |
---|
157 | |
---|
158 | import advection_ext |
---|
159 | self.flux_timestep = advection_ext.compute_fluxes(self, Stage, huge_timestep, max_timestep) |
---|
160 | |
---|
161 | |
---|
162 | |
---|
163 | def evolve(self, |
---|
164 | yieldstep = None, |
---|
165 | finaltime = None, |
---|
166 | duration = None, |
---|
167 | skip_initial_step = False): |
---|
168 | |
---|
169 | """Specialisation of basic evolve method from parent class |
---|
170 | """ |
---|
171 | |
---|
172 | #Call basic machinery from parent class |
---|
173 | for t in Generic_domain.evolve(self, |
---|
174 | yieldstep=yieldstep, |
---|
175 | finaltime=finaltime, |
---|
176 | duration=duration, |
---|
177 | skip_initial_step=skip_initial_step): |
---|
178 | |
---|
179 | #Pass control on to outer loop for more specific actions |
---|
180 | yield(t) |
---|
181 | |
---|
182 | |
---|
183 | |
---|
184 | |
---|
185 | def compute_fluxes_python(self): |
---|
186 | """Compute all fluxes and the timestep suitable for all volumes |
---|
187 | in domain. |
---|
188 | |
---|
189 | Compute total flux for each conserved quantity using "flux_function" |
---|
190 | |
---|
191 | Fluxes across each edge are scaled by edgelengths and summed up |
---|
192 | Resulting flux is then scaled by area and stored in |
---|
193 | domain.explicit_update |
---|
194 | |
---|
195 | The maximal allowable speed computed by the flux_function |
---|
196 | for each volume |
---|
197 | is converted to a timestep that must not be exceeded. The minimum of |
---|
198 | those is computed as the next overall timestep. |
---|
199 | |
---|
200 | Post conditions: |
---|
201 | domain.explicit_update is reset to computed flux values |
---|
202 | domain.timestep is set to the largest step satisfying all volumes. |
---|
203 | """ |
---|
204 | |
---|
205 | import sys |
---|
206 | from Numeric import zeros, Float |
---|
207 | from anuga.config import max_timestep |
---|
208 | |
---|
209 | N = len(self) |
---|
210 | |
---|
211 | neighbours = self.neighbours |
---|
212 | neighbour_edges = self.neighbour_edges |
---|
213 | normals = self.normals |
---|
214 | |
---|
215 | areas = self.areas |
---|
216 | radii = self.radii |
---|
217 | edgelengths = self.edgelengths |
---|
218 | |
---|
219 | timestep = max_timestep #FIXME: Get rid of this |
---|
220 | |
---|
221 | #Shortcuts |
---|
222 | Stage = self.quantities['stage'] |
---|
223 | |
---|
224 | #Arrays |
---|
225 | stage = Stage.edge_values |
---|
226 | |
---|
227 | stage_bdry = Stage.boundary_values |
---|
228 | |
---|
229 | flux = zeros(1, Float) #Work array for summing up fluxes |
---|
230 | |
---|
231 | #Loop |
---|
232 | for k in range(N): |
---|
233 | optimal_timestep = float(sys.maxint) |
---|
234 | |
---|
235 | flux[:] = 0. #Reset work array |
---|
236 | for i in range(3): |
---|
237 | #Quantities inside volume facing neighbour i |
---|
238 | ql = stage[k, i] |
---|
239 | |
---|
240 | #Quantities at neighbour on nearest face |
---|
241 | n = neighbours[k,i] |
---|
242 | if n < 0: |
---|
243 | m = -n-1 #Convert neg flag to index |
---|
244 | qr = stage_bdry[m] |
---|
245 | else: |
---|
246 | m = neighbour_edges[k,i] |
---|
247 | qr = stage[n, m] |
---|
248 | |
---|
249 | |
---|
250 | #Outward pointing normal vector |
---|
251 | normal = normals[k, 2*i:2*i+2] |
---|
252 | |
---|
253 | #Flux computation using provided function |
---|
254 | edgeflux, max_speed = self.flux_function(normal, ql, qr) |
---|
255 | flux -= edgeflux * edgelengths[k,i] |
---|
256 | |
---|
257 | #Update optimal_timestep |
---|
258 | if self.tri_full_flag[k] == 1 : |
---|
259 | try: |
---|
260 | optimal_timestep = min(optimal_timestep, radii[k]/max_speed) |
---|
261 | except ZeroDivisionError: |
---|
262 | pass |
---|
263 | |
---|
264 | #Normalise by area and store for when all conserved |
---|
265 | #quantities get updated |
---|
266 | flux /= areas[k] |
---|
267 | Stage.explicit_update[k] = flux[0] |
---|
268 | |
---|
269 | timestep = min(timestep, optimal_timestep) |
---|
270 | |
---|
271 | self.timestep = timestep |
---|
272 | |
---|