-
Notifications
You must be signed in to change notification settings - Fork 0
/
validation_functions.cpp
149 lines (116 loc) · 6.11 KB
/
validation_functions.cpp
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
#include "functions.h"
// #include <math.h>
/* Calculating flux integral at the center of CV */
void exact_fluxIntegral(double*** FI) {
for (int i = 0; i < IMAX; i++) {
double X = (i + 0.5) * dX;
/* parameters of exact FluxIntegral*/
double Cx = cos(PI * X);
double Sx = sin(PI * X);
double C2x = cos(2 * PI * X);
double S2x = sin(2 * PI * X);
for (int j = 0; j < JMAX; j++) {
double Y = (j + 0.5) * dY;
/* parameters of exact FluxIntegral*/
double Cy = cos(PI * Y);
double Sy = sin(PI * Y);
double C2y = cos(2 * PI * Y);
double S2y = sin(2 * PI * Y);
/* calculating the exact Flux Integral */
FI[i][j][0] = -(PI / Beta) * (u0 * Cx * S2y + v0 * S2x * Cy);
FI[i][j][1] = P0 * PI * Sx * Cy - u0 * u0 * PI * S2x * S2y * S2y
- u0 * v0 * PI * Sx * S2x * (Cy * S2y + 2 * C2y * Sy)
- (u0 * 5.0 * PI * PI * Sx * S2y) / Re;
FI[i][j][2] = P0 * PI * Cx * Sy - v0 * v0 * PI * S2x * S2x * S2y
- u0 * v0 * PI * Sy * S2y * (Cx * S2x + 2 * C2x * Sx)
- (v0 * 5.0 * PI * PI * S2x * Sy) / Re;
}
}
}
/* calculating flux jacobian and flux integral for testing flux jacobian correctness */
void calc_fluxJacobians(double*** Soln, double*** dSoln, double*** RHS) {
/*double FFJ1[IMAX + 2][JMAX + 2][3][3]{}, FFJ2[IMAX + 2][JMAX + 2][3][3]{};
double GFJ1[IMAX + 2][JMAX + 2][3][3]{}, GFJ2[IMAX + 2][JMAX + 2][3][3]{};*/
double**** FFJ1{}, **** FFJ2{};
double**** GFJ1{}, **** GFJ2{};
mem_alloc_fluxJacobian(&FFJ1, &FFJ2, &GFJ1, &GFJ2);
for (int j = 1; j < JMAX + 1; j++) {
for (int i = 1; i < IMAX + 2; i++) {
int I_ = i - 1;
/* Defining Jacobian type 1: F(i+0.5,j)/U(i,j) and F(i-0.5,j)/U(i-1,j) */
FFJ1[i][j][0][0] = 0; FFJ1[i][j][0][1] = 1.0 / (2.0 * Beta); FFJ1[i][j][0][2] = 0;
FFJ1[i][j][1][0] = 0.5; FFJ1[i][j][1][1] = (Soln[I_][j][1] + Soln[I_ + 1][j][1]) / 2.0 + 1.0 / (dX * Re); FFJ1[i][j][1][2] = 0;
FFJ1[i][j][2][0] = 0; FFJ1[i][j][2][1] = (Soln[I_][j][2] + Soln[I_ + 1][j][2]) / 4.0; FFJ1[i][j][2][2] = (Soln[I_][j][1] + Soln[I_ + 1][j][1]) / 4.0 + 1.0 / (dX * Re);
/* Defining Jacobian type 2: F(i+0.5,j)/U(i+1,j) and F(i-0.5,j)/U(i-1,j) */
FFJ2[i][j][0][0] = 0; FFJ2[i][j][0][1] = 1.0 / (2.0 * Beta); FFJ2[i][j][0][2] = 0;
FFJ2[i][j][1][0] = 0.5; FFJ2[i][j][1][1] = (Soln[I_][j][1] + Soln[I_ + 1][j][1]) / 2.0 - 1.0 / (dX * Re); FFJ2[i][j][1][2] = 0;
FFJ2[i][j][2][0] = 0; FFJ2[i][j][2][1] = (Soln[I_][j][2] + Soln[I_ + 1][j][2]) / 4.0; FFJ2[i][j][2][2] = (Soln[I_][j][1] + Soln[I_ + 1][j][1]) / 4.0 - 1.0 / (dX * Re);
}
}
for (int i = 1; i < IMAX + 1; i++) {
for (int j = 1; j < JMAX + 2; j++) {
int J = j - 1;
/* Defining Jacobian type 1: F(i+0.5,j)/U(i,j) */
GFJ1[i][j][0][0] = 0; GFJ1[i][j][0][1] = 0; GFJ1[i][j][0][2] = 1.0 / (2.0 * Beta);
GFJ1[i][j][1][0] = 0; GFJ1[i][j][1][1] = (Soln[i][J][2] + Soln[i][J + 1][2]) / 4.0 + 1.0 / (dY * Re); GFJ1[i][j][1][2] = (Soln[i][J][1] + Soln[i][J + 1][1]) / 4.0;
GFJ1[i][j][2][0] = 0.5; GFJ1[i][j][2][1] = 0; GFJ1[i][j][2][2] = (Soln[i][J][2] + Soln[i][J + 1][2]) / 2.0 + 1.0 / (dY * Re);
/* Defining Jacobian type 2: F(i+0.5,j)/U(i+1,j) */
GFJ2[i][j][0][0] = 0; GFJ2[i][j][0][1] = 0; GFJ2[i][j][0][2] = 1.0 / (2.0 * Beta);
GFJ2[i][j][1][0] = 0; GFJ2[i][j][1][1] = (Soln[i][J][2] + Soln[i][J + 1][2]) / 4.0 - 1.0 / (dY * Re); GFJ2[i][j][1][2] = (Soln[i][J][1] + Soln[i][J + 1][1]) / 4.0;
GFJ2[i][j][2][0] = 0.5; GFJ2[i][j][2][1] = 0; GFJ2[i][j][2][2] = (Soln[i][J][2] + Soln[i][J + 1][2]) / 2.0 - 1.0 / (dY * Re);
}
}
for (int i = 0; i < IMAX; i++) {
for (int j = 0; j < JMAX; j++) {
double Ax{}, Bx{}, Cx{}; //considers the multiplication of delta_U
double Ay{}, By{}, Cy{}; //this one too
for (int k = 0; k < 3; k++) {
int I_ = i + 2;
int Iu = i + 1;
//int k = 0;
Bx = (FFJ1[I_][j + 1][k][0] * dSoln[Iu][j + 1][0] - FFJ2[I_ - 1][j + 1][k][0] * dSoln[Iu][j + 1][0]) / dX;
Bx += (FFJ1[I_][j + 1][k][1] * dSoln[Iu][j + 1][1] - FFJ2[I_ - 1][j + 1][k][1] * dSoln[Iu][j + 1][1]) / dX;
Bx += (FFJ1[I_][j + 1][k][2] * dSoln[Iu][j + 1][2] - FFJ2[I_ - 1][j + 1][k][2] * dSoln[Iu][j + 1][2]) / dX;
Cx = (FFJ2[I_][j + 1][k][0] * dSoln[Iu + 1][j + 1][0]) / dX;
Cx += (FFJ2[I_][j + 1][k][1] * dSoln[Iu + 1][j + 1][1]) / dX;
Cx += (FFJ2[I_][j + 1][k][2] * dSoln[Iu + 1][j + 1][2]) / dX;
Ax = -(FFJ1[I_ - 1][j + 1][k][0] * dSoln[Iu - 1][j + 1][0]) / dX;
Ax += -(FFJ1[I_ - 1][j + 1][k][1] * dSoln[Iu - 1][j + 1][1]) / dX;
Ax += -(FFJ1[I_ - 1][j + 1][k][2] * dSoln[Iu - 1][j + 1][2]) / dX;
I_ = i + 1;
int J = j + 2;
int Ju = j + 1;
By = (GFJ1[I_][J][k][0] * dSoln[I_][Ju][0] - GFJ2[I_][J - 1][k][0] * dSoln[I_][Ju][0]) / dY;
By += (GFJ1[I_][J][k][1] * dSoln[I_][Ju][1] - GFJ2[I_][J - 1][k][1] * dSoln[I_][Ju][1]) / dY;
By += (GFJ1[I_][J][k][2] * dSoln[I_][Ju][2] - GFJ2[I_][J - 1][k][2] * dSoln[I_][Ju][2]) / dY;
Cy = (GFJ2[I_][J][k][0] * dSoln[I_][Ju + 1][0]) / dY;
Cy += (GFJ2[I_][J][k][1] * dSoln[I_][Ju + 1][1]) / dY;
Cy += (GFJ2[I_][J][k][2] * dSoln[I_][Ju + 1][2]) / dY;
Ay = -(GFJ1[I_][J - 1][k][0] * dSoln[I_][Ju - 1][0]) / dY;
Ay += -(GFJ1[I_][J - 1][k][1] * dSoln[I_][Ju - 1][1]) / dY;
Ay += -(GFJ1[I_][J - 1][k][2] * dSoln[I_][Ju - 1][2]) / dY;
RHS[i][j][k] = Bx + By + Cx + Ax + Cy + Ay;
}
}
}
mem_dealloc_fluxJacobian(&FFJ1, &FFJ2, &GFJ1, &GFJ2);
}
/* calculating flux integral with the given solution changes for testing */
void calc_exact_LHS(double*** FI_old, double*** FI_new, double*** LHS) {
for (int i = 0; i < IMAX; i++) {
for (int j = 0; j < JMAX; j++) {
LHS[i][j][0] = FI_new[i][j][0] - FI_old[i][j][0];
LHS[i][j][1] = FI_new[i][j][1] - FI_old[i][j][1];
LHS[i][j][2] = FI_new[i][j][2] - FI_old[i][j][2];
}
}
}
void soln_advance(double*** Soln, double*** dSoln) {
for (int i = 0; i < IMAX + 2; i++) {
for (int j = 0; j < JMAX + 2; j++) {
Soln[i][j][0] += dSoln[i][j][0];
Soln[i][j][1] += dSoln[i][j][1];
Soln[i][j][2] += dSoln[i][j][2];
}
}
}