-
Notifications
You must be signed in to change notification settings - Fork 7
/
flux.c
273 lines (248 loc) · 10.1 KB
/
flux.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "flux.h"
//f_select[0] = 0 -> not compute f+, =1 -> compute f+
//f_select[1] = 0 -> not compute f-, =1 -> compute f-
//f_select[2] = 0 -> not compute df+, =1 -> compute df+
//f_select[3] = 0 -> not compute df-, =1 -> compute df-
// ==================================================================================================
//NOTE : BOTH FLUX VECTORS AND JACOBIANS SHOULD BE ALLOCATED PRIOR TO THIS FUNCTION WITH calloc() TO ENSURE INITIAL ZEROOO!!!
// ==================================================================================================
int calc_van_leer(double *Q, double *fvl_p, double *fvl_m, double **d_fvl_p, double **d_fvl_m, int neqs, double gamma, double *n_hat, int *f_select)
{
int i, j;
double sign_pm = 1., p2 = 0.;
double length = 0.;
double nx, ny;
double rho, u, v, u_bar, e, P, c;
double *d_rho_dQi = (double *)calloc(neqs , sizeof(double));
double *d_u_dQi = (double *)calloc(neqs , sizeof(double));
double *d_v_dQi = (double *)calloc(neqs , sizeof(double));
double *d_e_dQi = (double *)calloc(neqs , sizeof(double));
double *d_P_dQi = (double *)calloc(neqs , sizeof(double));
double *d_c_dQi = (double *)calloc(neqs , sizeof(double));
double *d_ubar_dQi = (double *)calloc(neqs , sizeof(double));
//step 1: calculating primitive variables
length = sqrt(n_hat[0] * n_hat[0]+ n_hat[1] * n_hat[1]);
nx = n_hat[0]/length;
ny = n_hat[1]/length;
rho = Q[0];
u = Q[1] / Q[0];
v = Q[2] / Q[0];
e = Q[3];
u_bar = u * nx + v * ny;
P = (gamma - 1.) * e - .5 * (gamma - 1.) *rho * ( u*u + v*v);
c = sqrt(gamma * P/ rho);
//step 2: filling the flux van leer (fvl) vector ASAP
if(u_bar >= c)
{
if(f_select[0] || f_select[2])
{
fvl_p[0] = length * rho* u_bar;
fvl_p[1] = length * (rho * u * u_bar + nx * P);
fvl_p[2] = length * (rho * v * u_bar + ny * P);
fvl_p[3] = length * (e+P)* u_bar;
}
if(f_select[1] || f_select[3])
{
fvl_m[0] = 0.;
fvl_m[1] = 0.;
fvl_m[2] = 0.;
fvl_m[3] = 0.;
}
}
else if(u_bar <= (-c))
{
if(f_select[1] || f_select[3])
{
fvl_m[0] = length * rho* u_bar;
fvl_m[1] = length * (rho * u * u_bar + nx * P);
fvl_m[2] = length * (rho * v * u_bar + ny * P);
fvl_m[3] = length * (e+P)* u_bar;
}
if(f_select[0] || f_select[2])
{
fvl_p[0] = 0.;
fvl_p[1] = 0.;
fvl_p[2] = 0.;
fvl_p[3] = 0.;
}
}
else
{
if(f_select[0] || f_select[2])
{
fvl_p[0] = length * .250 * rho*c* pow((u_bar/c + 1.) , 2.);
fvl_p[1] = fvl_p[0] * (nx/gamma*(-u_bar + 2. * c) + u);
fvl_p[2] = fvl_p[0] * (ny/gamma*(-u_bar + 2. * c) + v);
fvl_p[3] = fvl_p[0] * ( (-(gamma-1)*u_bar*u_bar + 2.*(gamma-1.)*u_bar*c+2.*c*c)/ (gamma*gamma - 1.) + (u*u + v*v)*.5 );
}
if(f_select[1] || f_select[3])
{
fvl_m[0] = length * -.250 * rho*c* pow((u_bar/c - 1.) , 2.);
fvl_m[1] = fvl_m[0] * (nx/gamma*(-u_bar - 2. * c) + u);
fvl_m[2] = fvl_m[0] * (ny/gamma*(-u_bar - 2. * c) + v);
fvl_m[3] = fvl_m[0] * ( (-(gamma-1)*u_bar*u_bar - 2.*(gamma-1.)*u_bar*c+2.*c*c)/ (gamma*gamma - 1.) + (u*u + v*v)*.5 );
}
}
if(f_select[2] || f_select[3]) //at least one of the Jacobians are needed to be computed
{
//step 3: calculating derivatives of primitive variables
d_rho_dQi[0] = 1.; d_rho_dQi[1] = 0.; d_rho_dQi[2] = 0.; d_rho_dQi[3] = 0.;
d_u_dQi[0] = -Q[1]/(Q[0]*Q[0]); d_u_dQi[1] = 1./Q[0]; d_u_dQi[2] = 0.; d_u_dQi[3] = 0.;
d_v_dQi[0] = -Q[2]/(Q[0]*Q[0]); d_v_dQi[1] = 0.; d_v_dQi[2] = 1./Q[0]; d_v_dQi[3] = 0.;
d_e_dQi[0] = 0.; d_e_dQi[1] = 0.; d_e_dQi[2] = 0.; d_e_dQi[3] = 1.;
//step 4: calculating derivatives of physical variables P, c, u_bar
for( i = 0; i < neqs; i++)
{
d_P_dQi[i] = (gamma-1.) * (d_e_dQi[i] - .5 * d_rho_dQi[i] *(u*u + v*v) - rho * (u * d_u_dQi[i] + v * d_v_dQi[i]));
d_c_dQi[i] = gamma/2. * (d_P_dQi[i] * rho - d_rho_dQi[i] * P) / (rho * rho * c);
d_ubar_dQi[i] = d_u_dQi[i] * nx + d_v_dQi[i] * ny;
}
//step 5: using chain-rule to finish the job.
// starting filling row by row ..
if(u_bar >= c)
{
if(f_select[2])
{
// d_fvl_p
for( j = 0; j < neqs; j++)
{
d_fvl_p[0][j] = length*(d_rho_dQi[j]*u_bar + rho*d_ubar_dQi[j]);
d_fvl_p[1][j] = length * (d_rho_dQi[j] * u * u_bar+ rho * d_u_dQi[j] * u_bar+ rho * u * d_ubar_dQi[j] + nx * d_P_dQi[j]);
d_fvl_p[2][j] = length * (d_rho_dQi[j] * v * u_bar+ rho * d_v_dQi[j] * u_bar+ rho * v * d_ubar_dQi[j] + ny * d_P_dQi[j]);
d_fvl_p[3][j] = length * ( (d_e_dQi[j]+d_P_dQi[j])* u_bar + (e+P)* d_ubar_dQi[j] );
}
}
if(f_select[3])
{
// d_fvl_m
for( j = 0; j < neqs; j++)
{
d_fvl_m[0][j] = 0.;
d_fvl_m[1][j] = 0.;
d_fvl_m[2][j] = 0.;
d_fvl_m[3][j] = 0.;
}
}
}
else if(u_bar <= (-c))
{
if(f_select[2])
{
// d_fvl_p
for( j = 0; j < neqs; j++)
{
d_fvl_p[0][j] = 0.;
d_fvl_p[1][j] = 0.;
d_fvl_p[2][j] = 0.;
d_fvl_p[3][j] = 0.;
}
}
if(f_select[3])
{
// d_fvl_m
for( j = 0; j < neqs; j++)
{
d_fvl_m[0][j] = length*(d_rho_dQi[j]*u_bar + rho*d_ubar_dQi[j]);
d_fvl_m[1][j] = length * (d_rho_dQi[j] * u * u_bar+ rho * d_u_dQi[j] * u_bar+ rho * u * d_ubar_dQi[j] + nx * d_P_dQi[j]);
d_fvl_m[2][j] = length * (d_rho_dQi[j] * v * u_bar+ rho * d_v_dQi[j] * u_bar+ rho * v * d_ubar_dQi[j] + ny * d_P_dQi[j]);
d_fvl_m[3][j] = length * ( (d_e_dQi[j]+d_P_dQi[j])* u_bar + (e+P)* d_ubar_dQi[j] );
}
}
}
else
{
if(f_select[2])
{
// d_fvl_p
sign_pm = 1.0;
p2 = pow((u_bar / c + sign_pm * 1.),2.0);
for( j = 0; j < neqs; j++)
{
d_fvl_p[0][j] = length*sign_pm*.25*(d_rho_dQi[j]*c*p2 + rho * d_c_dQi[j] * p2 + 2.*(rho/c)* (u_bar/c + sign_pm * 1.) * (d_ubar_dQi[j]*c-d_c_dQi[j]*u_bar));
d_fvl_p[1][j] = d_fvl_p[0][j] * (nx/gamma * (-u_bar + sign_pm*2.*c)+u) + fvl_p[0] * (nx/gamma*(-d_ubar_dQi[j]+sign_pm* 2.* d_c_dQi[j])+ d_u_dQi[j]);
d_fvl_p[2][j] = d_fvl_p[0][j] * (ny/gamma * (-u_bar + sign_pm*2.*c)+v) + fvl_p[0] * (ny/gamma*(-d_ubar_dQi[j]+sign_pm* 2.* d_c_dQi[j])+ d_v_dQi[j]);
d_fvl_p[3][j] = d_fvl_p[0][j] * ((-(gamma-1.)*u_bar*u_bar+ sign_pm*2.*(gamma-1.)*u_bar*c+2.*c*c)/(gamma*gamma-1.)+.5*(u*u+v*v)) + fvl_p[0] * ((-2.*(gamma-1.)*u_bar*d_ubar_dQi[j]+sign_pm*2.*(gamma-1.)*(d_ubar_dQi[j]*c+u_bar*d_c_dQi[j])+ 4.*c*d_c_dQi[j])/(gamma*gamma-1.)+ u*d_u_dQi[j] + v*d_v_dQi[j]);
}
}
if(f_select[3])
{
// d_fvl_m
sign_pm = -1.0;
p2 = pow((u_bar / c + sign_pm * 1.),2.0);
for( j = 0; j < neqs; j++)
{
d_fvl_m[0][j] = length*sign_pm*.25*(d_rho_dQi[j]*c*p2 + rho * d_c_dQi[j] * p2 + 2.*(rho/c)* (u_bar/c + sign_pm * 1.) * (d_ubar_dQi[j]*c-d_c_dQi[j]*u_bar));
d_fvl_m[1][j] = d_fvl_m[0][j] * (nx/gamma * (-u_bar + sign_pm*2.*c)+u) + fvl_m[0] * (nx/gamma*(-d_ubar_dQi[j]+sign_pm* 2.* d_c_dQi[j])+ d_u_dQi[j]);
d_fvl_m[2][j] = d_fvl_m[0][j] * (ny/gamma * (-u_bar + sign_pm*2.*c)+v) + fvl_m[0] * (ny/gamma*(-d_ubar_dQi[j]+sign_pm* 2.* d_c_dQi[j])+ d_v_dQi[j]);
d_fvl_m[3][j] = d_fvl_m[0][j] * ((-(gamma-1.)*u_bar*u_bar+ sign_pm*2.*(gamma-1.)*u_bar*c+2.*c*c)/(gamma*gamma-1.)+.5*(u*u+v*v)) + fvl_m[0] * ((-2.*(gamma-1.)*u_bar*d_ubar_dQi[j]+sign_pm*2.*(gamma-1.)*(d_ubar_dQi[j]*c+u_bar*d_c_dQi[j])+ 4.*c*d_c_dQi[j])/(gamma*gamma-1.)+ u*d_u_dQi[j] + v*d_v_dQi[j]);
}
}
}
}
/* clean - up*/
free(d_rho_dQi);
free(d_u_dQi);
free(d_v_dQi);
free(d_e_dQi);
free(d_P_dQi);
free(d_c_dQi);
free(d_ubar_dQi);
//completed successfully!
return 0;
}
//computes wall flux and Jacobians
int calc_wall_flux(double *Q, double *fw, double **d_fw, int neqs, double gamma, double *n_hat)
{
int i, j;
double length = 0.;
double nx, ny;
double rho, u, v, u_bar, e, P, c;
double *d_rho_dQi = (double *)calloc(neqs , sizeof(double));
double *d_u_dQi = (double *)calloc(neqs , sizeof(double));
double *d_v_dQi = (double *)calloc(neqs , sizeof(double));
double *d_e_dQi = (double *)calloc(neqs , sizeof(double));
double *d_P_dQi = (double *)calloc(neqs , sizeof(double));
//step 1: calculating primitive variables
length = sqrt(n_hat[0] * n_hat[0]+ n_hat[1] * n_hat[1]);
nx = n_hat[0]/length;
ny = n_hat[1]/length;
rho = Q[0];
u = Q[1] / Q[0];
v = Q[2] / Q[0];
e = Q[3];
u_bar = u * nx + v * ny;
P = (gamma - 1.) * e - .5 * (gamma - 1.) *rho * ( u*u + v*v);
c = sqrt(gamma * P/ rho);
//calculate wall flux here
fw[0] = 0.;
fw[1] = length * (nx * P);
fw[2] = length * (ny * P);
fw[3] = 0.;
//calculating derivatives of primitive variables
d_rho_dQi[0] = 1.; d_rho_dQi[1] = 0.; d_rho_dQi[2] = 0.; d_rho_dQi[3] = 0.;
d_u_dQi[0] = -Q[1]/(Q[0]*Q[0]); d_u_dQi[1] = 1./Q[0]; d_u_dQi[2] = 0.; d_u_dQi[3] = 0.;
d_v_dQi[0] = -Q[2]/(Q[0]*Q[0]); d_v_dQi[1] = 0.; d_v_dQi[2] = 1./Q[0]; d_v_dQi[3] = 0.;
d_e_dQi[0] = 0.; d_e_dQi[1] = 0.; d_e_dQi[2] = 0.; d_e_dQi[3] = 1.;
//calculating derivatives of P
for( i = 0; i < neqs; i++)
d_P_dQi[i] = (gamma-1.) * (d_e_dQi[i] - .5 * d_rho_dQi[i] *(u*u + v*v) - rho * (u * d_u_dQi[i] + v * d_v_dQi[i]));
// filling d_fw
for( j = 0; j < neqs; j++)
{
d_fw[0][j] = 0.;
d_fw[1][j] = length * nx * d_P_dQi[j];
d_fw[2][j] = length * ny * d_P_dQi[j];
d_fw[3][j] = 0.;
}
/* clean - up*/
free(d_rho_dQi);
free(d_u_dQi);
free(d_v_dQi);
free(d_e_dQi);
free(d_P_dQi);
//completed successfully!
return 0;
}