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ThD-RK-Euler_order.cpp
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ThD-RK-Euler_order.cpp
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#include <math.h>
#include <iostream>
#include <ctime>
#include <cstring>
#include <string>
#include <fstream>
#include <iterator>
#include <valarray>
using namespace std;
// example:Euler 3-4-L-W 增加CFL数输出误差， 不特征分裂 Exp3 差分格式不为守恒性
class cfda
{
private:
int w;
public:
double PI = 3.141592653589793;
// double PI = 3.1415926535897932385;
int n; // 网格结点数（有限差分）
int nb; // 边界网格结点数（有限差分）
double t, tt, CFL; // 计算总时 间t,实际计算时间tt;
int nt, kt, ij, ijj, onet_out = 2; // 计算时间步长;
double nx_begin, nx_end; // 网格长度;
int n1, ii1, m; // 总的网格结点数（有限差分）
double *Ltt_n0, *x, *Ltt_n1, *Lttx_n1; // 声明变长数组
double *L_n0, *L_n1, *L_n2; // f=L
double *Lt_n0, *Lt_n1, *Lt_n2; // L_t
double *Ltx_n0, *Ltx_n1, *Ltx_n2; // L_t
double *u_n0, *u_n1, *u_n2, *u_n3, *u_n4, *u_n5, *u_n6, *u_n7; // 推进步中间时刻
double *f_n0, *f_n1, *f_n2, *f_n3, *f_n4, *f_n5, *f_n6, *f_n7; // 推进步中间时刻
double *u_nn, *f_nn, *Lttx_n0; // 下一时刻（n+1)
double *TL_n0, *TLt_n0, *TL_n1, *TLt_n1, *TL_n2, *TLt_n2, *Tu1, *Tu2;
double *flux; // j+1/2处的通量
double *df, *u_excat, *uc_max; // du[513 + 6 * 2],df[513 + 6 * 2],
////-----------------------------------------
double dx;
double dt;
double *dd; // ss
double A1, A2, A3, A4, A5, B0, B1, B2, C0, C1, C2, D0, D1, D2, D3, maxuu, TVmax;
double a21, a31, a32, aa12, aa21, aa31, aa32, aaa31, aaa32, w11, w22, v1, v2, v3, vv1, vv2, vv3, ww1, ww2, b1, b2, b3, bb1, bb2, bb3, bbb1, bbb2, bbb3;
double put_obj[10000]; // //onet_out = 10;
double put_one_n[10000];
// Euler参数——————————————————————————————————————————————————
double *u, *c, *p, *a; // 原始变量 u速度，c声速，p压强，a密度
double *fz, *ff; // 守恒通量
double fza[61], ffa[61]; // 特征变换守恒通量
double y = 1.4; // 热力系数
////-----------------------------------------
void pc_to_uu(double *uuu)
{
for (int i = 0; i < n1; i++) // Sod激波管
{
uuu[i] = a[i], uuu[n1 + i] = a[i] * u[i], uuu[2 * n1 + i] = p[i] / (y - 1.0) + a[i] * u[i] * u[i] / 2.0;
}
}
void pc_to_ff(double *fff)
{
for (int i = 0; i < n1; i++) // Sod激波管
{
fff[i] = a[i] * u[i], fff[n1 + i] = a[i] * u[i] * u[i] + p[i];
fff[2 * n1 + i] = (p[i] / (y - 1.0) + a[i] * u[i] * u[i] / 2.0 + p[i]) * u[i];
}
}
void uu_to_ff(double *uuu, double *fff)
{
for (int i = 0; i < n1; i++) // Sod激波管
{
fff[i] = uuu[i] * u[i], fff[n1 + i] = uuu[i] * u[i] + p[i];
fff[2 * n1 + i] = (uuu[i] + p[i]) * u[i];
}
}
void uu_to_pc(double *uuu)
{
for (int i = 0; i < n1; i++) // Sod激波管
{
a[i] = uuu[i], u[i] = uuu[n1 + i] / a[i];
p[i] = (y - 1.0) * (uuu[n1 * 2 + i] - 0.5 * uuu[n1 + i] * u[i]);
c[i] = sqrt(y * p[i] / a[i]);
}
}
void intc()
{
double p1, a1, u1, c1, p2, a2, u2, c2, ssss;
dx = (nx_end - nx_begin) / (1.0 * (n - 1));
u1 = 0.00, a1 = 1.0, p1 = 1.0;
u2 = 0.00, a2 = 0.125, p2 = 0.1;
c1 = sqrt(y * p1 / a1), c2 = sqrt(y * p2 / a2);
ssss = sqrt(2.0);
// for (int i = 0; i < n1; i++) //Sod激波管
// {
// x[i] = nx_begin + (i - nb) * dx;
// if (x[i] < (nx_end - nx_begin) / 2.0)
// {
// u[i] = u1, c[i] = c1, p[i] = p1, a[i] = a1;
// u_n0[i] = a[i], u_n0[n1 + i] = a[i] * u[i], u_n0[2 * n1 + i] = p[i] / (y - 1.0) + a[i] * u[i] * u[i] / 2.0;
// }
// else
// {
// u[i] = u2, c[i] = c2, p[i] = p2, a[i] = a2;
// u_n0[i] = a[i], u_n0[n1 + i] = a[i] * u[i], u_n0[2 * n1 + i] = p[i] / (y - 1.0) + a[i] * u[i] * u[i] / 2.0;
// }
// }
for (int i = 0; i < n1; i++) // Sin 测精度
{
x[i] = nx_begin + (i - nb) * dx;
u[i] = 1.0, p[i] = 1.0, a[i] = 2.0 + sin(PI * x[i]); // a[i] = 1.0 + 0.5 * sin(PI * x[i]); //
c[i] = sqrt(y * p[i] / a[i]);
u_n0[i] = a[i], u_n0[n1 + i] = a[i] * u[i], u_n0[2 * n1 + i] = p[i] / (y - 1.0) + a[i] * u[i] * u[i] / 2.0;
}
// Store_obj(put_obj, u, a, p);
// Write_obj(0); //初始值
}
double intc_fun(double xxf)
{
double yyf;
// yyf = (sin(2 * PI * xxf) / 2.0 + 0.5) * 1.0; // / PIbergure
// yyf = sin(PI * xxf) / 2.0 + 0.25;//bergure
yyf = sin(PI * xxf); // line
return yyf;
}
double dmax1(double a, double b, double c)
{
if (b > a)
{
a = b;
}
if (c > a)
{
a = c;
}
return a;
}
// //-----------------------------------------
void border()
{
borderfun(u_n0), borderfun(u_n1), borderfun(u_n2), borderfun(u_nn);
borderfun(f_n0), borderfun(f_n1), borderfun(f_n2), borderfun(f_nn);
borderfun(L_n0), borderfun(L_n1), borderfun(L_n2), borderfun(Lt_n0);
borderfun(Lt_n1), borderfun(Lt_n2), borderfun(Ltt_n0);
borderfun(Ltx_n0), borderfun(Lttx_n0), borderfun(u_n3);
borderfun(Ltx_n1), borderfun(Ltx_n2), borderfun(f_n3);
}
void borderfun(double *ffbc)
{
for (int i = 0; i < nb; i++)
{
*(ffbc + i) = *(ffbc + n1 - 2 * nb + i - 1); // 周期边条
*(ffbc + n1 - nb + i) = *(ffbc + nb + i + 1); // 周期边条
// *(ffbc + i) = 0;
//*(ffbc + n1 - nb + i) = 0;
// f_n0[i] = f_n0[nb]; //恒定边条
// f_n0[n1 - 1 - i] = f_n0[n1 - 1 - nb]; //恒定边条
// *(ffbc + i) = *(ffbc + nb); //恒定边条
// *(ffbc + n1 - 1 - i) = *(ffbc + n1 - 1 - nb); //恒定边条
// *(ffbc + i) = 0.0; //恒定边条
// *(ffbc + n1 - 1 - i) = 0.0; //恒定边条
// ffbc++;
}
}
void borderfun3(double *ffbc)
{
for (int i = 0; i < nb; i++)
{
*(ffbc + i) = *(ffbc + n1 - 2 * nb + i - 1); // 周期边条
*(ffbc + n1 - nb + i) = *(ffbc + nb + i + 1); // 周期边条
*(ffbc + i + n1) = *(ffbc + n1 + n1 - 2 * nb + i - 1); // 周期边条
*(ffbc + n1 + n1 - nb + i) = *(ffbc + n1 + nb + i + 1); // 周期边条
*(ffbc + i + n1 + n1) = *(ffbc + n1 + n1 + n1 - 2 * nb + i - 1); // 周期边条
*(ffbc + n1 + n1 + n1 - nb + i) = *(ffbc + n1 + n1 + nb + i + 1); // 周期边条
// *(ffbc + i) = 0;
//*(ffbc + n1 - nb + i) = 0;
// f_n0[i] = f_n0[nb]; //恒定边条
// f_n0[n1 - 1 - i] = f_n0[n1 - 1 - nb]; //恒定边条
// *(ffbc + i) = *(ffbc + nb); //恒定边条
// *(ffbc + n1 - 1 - i) = *(ffbc + n1 - 1 - nb); //恒定边条
// *(ffbc + i + n1) = *(ffbc + nb + n1); //恒定边条
// *(ffbc + n1 - 1 - i + n1) = *(ffbc + n1 - 1 - nb + n1); //恒定边条
// *(ffbc + i + n1 + n1) = *(ffbc + nb + n1 + n1); //恒定边条
// *(ffbc + n1 - 1 - i + n1 + n1) = *(ffbc + n1 - 1 - nb + n1 + n1); //恒定边条
// *(ffbc + i) = 0.0; //恒定边条
// *(ffbc + n1 - 1 - i) = 0.0; //恒定边条
// ffbc++;
}
}
// //-----------------------------------------
void carr(double *p1, double *p2, int i)
{
while (i-- > 0)
{
*p1++ = *p2++;
}
}
// //-----------------------------------------
void Splitting(double *uuu) //_gobal
{
double lmax = 0.0, lmax0;
for (int i = 0; i < n1; i++) // comput L(n0)
{
lmax0 = dmax1(abs(u[i]), abs(u[i] - c[i]), abs(u[i] + c[i])); // 当地最大特征值
if (lmax0 > lmax)
{
lmax = lmax0;
}
}
lmax = lmax * 1.0;
for (int i = 0; i < n1; i++) // comput L(n0)
{
fz[i] = 0.5 * (a[i] * u[i] + lmax * uuu[i]); // 正通量
fz[n1 + i] = 0.5 * (a[i] * u[i] * u[i] + p[i] + lmax * uuu[n1 + i]);
fz[n1 + n1 + i] = 0.5 * ((uuu[n1 + n1 + i] + p[i]) * u[i] + lmax * uuu[n1 + n1 + i]);
ff[i] = 0.5 * (a[i] * u[i] - lmax * uuu[i]); // 负通量
ff[n1 + i] = 0.5 * (a[i] * u[i] * u[i] + p[i] - lmax * uuu[n1 + i]);
ff[n1 + n1 + i] = 0.5 * ((uuu[n1 + n1 + i] + p[i]) * u[i] - lmax * uuu[n1 + n1 + i]);
}
borderfun3(ff);
borderfun3(fz);
}
void Splitting_local(double *uuu) //
{
double lmax = 0.0, lmax0;
for (int i = 0; i < n1; i++) // comput L(n0)
{
lmax = dmax1(abs(u[i]), abs(u[i] - c[i]), abs(u[i] + c[i])); // 当地最大特征值
fz[i] = 0.5 * (a[i] * u[i] + lmax * uuu[i]); // 正通量
fz[n1 + i] = 0.5 * (a[i] * u[i] * u[i] + p[i] + lmax * uuu[n1 + i]);
fz[n1 + n1 + i] = 0.5 * ((uuu[n1 + n1 + i] + p[i]) * u[i] + lmax * uuu[n1 + n1 + i]);
ff[i] = 0.5 * (a[i] * u[i] - lmax * uuu[i]); // 负通量
ff[n1 + i] = 0.5 * (a[i] * u[i] * u[i] + p[i] - lmax * uuu[n1 + i]);
ff[n1 + n1 + i] = 0.5 * ((uuu[n1 + n1 + i] + p[i]) * u[i] - lmax * uuu[n1 + n1 + i]);
}
borderfun3(ff);
borderfun3(fz);
}
void Splitting_char(double *uuu)
{
double gamma = 1.4, fa0[3];
double a1, u1, H1, a2, u2, H2, r1, r2, r0, u0, H0, c0, t1, s11, s12, s13, s21, s22, s23, s31, s32, s33;
double t2, D11, D12, D13, D21, D22, D23, D31, D32, D33;
int k1, mm;
int j = 0, i, k;
i = n1 - nb * 2;
// border();
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
flux[nb + j + k * n1] = df_dx_char(fz, ff, nb + j + k * n1);
}
j++;
}
borderfun3(flux);
}
//------------------------------------------------
void Store_obj(double *ss, double *us, double *as, double *ps)
{
for (int ik = 0; ik < n1; ik++) //
{
ss[ik] = us[ik], ss[n1 + ik] = as[ik], ss[n1 * 2 + ik] = ps[ik];
}
}
void Write_obj(int j)
{
if (j < -0.9)
{
// string title = "result_t_burgers_excat"; //+ to_string(t);
string title = to_string(n);
string Title = title + ".plt";
ofstream ofs;
ofs.open(Title, ios::out);
ofs << " VARIABLES=x,u,a,p " << endl;
for (int i = nb; i < n1 - nb; i++)
{
ofs.precision(10);
ofs << x[i];
for (int j = 0; j < 3; j++)
{
ofs << " ";
ofs.precision(18);
ofs << put_obj[j * n1 + i];
}
ofs << endl;
}
ofs.close();
}
if (j < 0.5 && j > -0.8)
{
string Title = "int.plt";
ofstream ofs;
ofs.open(Title, ios::out);
ofs << " VARIABLES=x,u,a,p " << endl;
for (int i = nb; i < n1 - nb; i++)
{
ofs.precision(10);
ofs << x[i];
for (int j = 0; j < 3; j++)
{
ofs << " ";
ofs.precision(18);
ofs << put_obj[j * n1 + i];
}
ofs << endl;
}
ofs.close();
}
if (j > 1.5)
{
string title = "result_one_t_burgers_every-" + to_string(j);
string Title = title + ".plt";
ofstream ofs;
ofs.open(Title, ios::out);
ofs << "Title=" << title << endl;
for (int i = nb; i < n1 - nb; i++)
{
ofs.precision(10);
ofs << x[i];
for (j = 0; j < onet_out; j++)
{
ofs << " ";
ofs.precision(18);
ofs << put_one_n[i];
}
ofs << endl;
}
ofs.close();
}
}
////-----------------------------------------
void RK33_compt()
{
int j, i, k, rr;
uu_to_pc(u_n0);
Splitting(u_n0);
// Splitting_char(u_n0);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
u_n1[rr] = u_n0[rr] + dt * df[rr];
}
j++;
}
borderfun3(u_n1);
uu_to_pc(u_n1);
Splitting(u_n1);
// Splitting_char(u_n1);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1; // df[rr] = -df_dx(fz, ff, rr);
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
u_n2[rr] = 0.75 * u_n0[rr] + 0.25 * (u_n1[rr] + dt * df[rr]);
}
j++;
}
borderfun3(u_n2);
uu_to_pc(u_n2);
Splitting(u_n2);
// Splitting_char(u_n2);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1; // df[rr] = -df_dx(fz, ff, rr);
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
u_nn[rr] = 1.0 / 3.0 * u_n0[rr] + 2.0 / 3.0 * (u_n2[rr] + dt * df[rr]);
}
j++;
}
borderfun3(u_nn);
}
void SSPRK54_compt_Shu() // Strong stability preserving Runge-Kutta and multistep time discretizations P23
{
int j, i, k, rr;
uu_to_pc(u_n0);
Splitting(u_n0);
// Splitting_char(u_n0);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
u_n1[rr] = u_n0[rr] + 0.391752226571890 * dt * df[rr];
}
j++;
}
borderfun3(u_n1);
uu_to_pc(u_n1);
Splitting(u_n1);
// Splitting_char(u_n1);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
u_n2[rr] = 0.444370493651235 * u_n0[rr] + 0.555629506348765 * u_n1[rr] + 0.368410593050371 * dt * df[rr];
}
j++;
}
borderfun3(u_n2);
uu_to_pc(u_n2);
Splitting(u_n2);
// Splitting_char(u_n2);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
u_n3[rr] = 0.620101851488403 * u_n0[rr] + 0.379898148511597 * u_n2[rr] + 0.251891774271694 * dt * df[rr];
}
j++;
}
borderfun3(u_n3);
uu_to_pc(u_n3);
Splitting(u_n3);
// Splitting_char(u_n3);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// L_n0[rr] = -(flux[rr] - flux[rr - 1]) / dx;
L_n0[rr] = -df_dx(fz, ff, rr);
u_n4[rr] = 0.178079954393132 * u_n0[rr] + 0.821920045606868 * u_n3[rr] + 0.544974750228521 * dt * L_n0[rr];
}
j++;
}
borderfun3(u_n4);
uu_to_pc(u_n4);
Splitting(u_n4);
// Splitting_char(u_n4);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
// u_nn[rr] = 0.00683325884039 * u_n0[rr] + 0.51723167208978 * u_n2[rr] + 0.12759831133288 * u_n3[rr] +
// 0.34833675773694 * u_n4[rr] + 0.08460416338212 * dt * L_n0[rr] + 0.22600748319395 * dt * df[rr];
u_nn[rr] = 0.517231671970585 * u_n2[rr] + 0.096059710526147 * u_n3[rr] + 0.063692468666290 * dt * L_n0[rr] +
0.386708617503269 * u_n4[rr] + 0.226007483236906 * dt * df[rr];
}
j++;
}
borderfun3(u_nn);
}
void LSRK65_compt2() // Numerical Methods for Ordinary Differential Equations
{
int j = 0, i, k, rr;
uu_to_pc(u_n0);
Splitting(u_n0);
// Splitting_char(u_n0);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// L_n0[rr] = -(flux[rr] - flux[rr - 1]) / dx;
L_n0[rr] = -df_dx(fz, ff, rr);
u_n1[rr] = u_n0[rr] + 1. / 4. * dt * L_n0[rr];
}
j++;
}
borderfun3(u_n1);
uu_to_pc(u_n1);
Splitting(u_n1);
// Splitting_char(u_n1);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// L_n1[rr] = -(flux[rr] - flux[rr - 1]) / dx;
L_n1[rr] = -df_dx(fz, ff, rr);
u_n2[rr] = u_n0[rr] + 1. / 8. * dt * L_n0[rr] + 1. / 8. * dt * L_n1[rr];
// u_n2[rr] = 0.75 * u_n0[rr] + 0.25 * (u_n1[rr] + dt * L_n1[rr]);
}
j++;
}
borderfun3(u_n2);
uu_to_pc(u_n2);
Splitting(u_n2);
// Splitting_char(u_n2);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// L_n2[rr] = -(flux[rr] - flux[rr - 1]) / dx;
L_n2[rr] = -df_dx(fz, ff, rr);
u_n3[rr] = u_n0[rr] + 0. * dt * L_n0[rr] + 0. * dt * L_n1[rr] +
0.5 * dt * L_n2[rr];
}
j++;
}
borderfun3(u_n3);
uu_to_pc(u_n3);
Splitting(u_n3);
// Splitting_char(u_n3);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// Lt_n0[rr] = -(flux[rr] - flux[rr - 1]) / dx;
Lt_n0[rr] = -df_dx(fz, ff, rr);
u_n4[rr] = u_n0[rr] + 3. / 16. * dt * L_n0[rr] - 3. / 8. * dt * L_n1[rr] +
3. / 8. * dt * L_n2[rr] + 9. / 16. * dt * Lt_n0[rr];
}
j++;
}
borderfun3(u_n4);
uu_to_pc(u_n4);
Splitting(u_n4);
// Splitting_char(u_n4);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// Lt_n1[rr] = -(flux[rr] - flux[rr - 1]) / dx;
Lt_n1[rr] = -df_dx(fz, ff, rr);
u_n5[rr] = u_n0[rr] - 3. / 7. * dt * L_n0[rr] + 8. / 7. * dt * L_n1[rr] + 6. / 7. * dt * L_n2[rr] -
12. / 7. * dt * Lt_n0[rr] + 8. / 7. * dt * Lt_n1[rr];
}
j++;
}
borderfun3(u_n5);
uu_to_pc(u_n5);
Splitting(u_n5);
// Splitting_char(u_n5);
j = nb, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
rr = j + k * n1;
// df[rr] = -(flux[rr] - flux[rr - 1]) / dx;
df[rr] = -df_dx(fz, ff, rr);
u_nn[rr] = u_n0[rr] + 7. / 90. * dt * L_n0[rr] + 0. * dt * L_n1[rr] +
16. / 45. * dt * L_n2[rr] + 2. / 15. * dt * Lt_n0[rr] +
16. / 45. * dt * Lt_n1[rr] + 7. / 90. * dt * df[rr];
// u_nn[rr] = 1.0 / 3.0 * u_n0[rr] + 2.0 / 3.0 * (u_n2[rr] + dt * L_n2[rr]);
}
j++;
}
borderfun3(u_nn);
}
// -----------
void comput_LWqt0(double *fqtt, double *qt, double *uuu)
{
int j, k;
double fq[4][4];
for (int i = 0; i < n1; i++) // comput L(n0)
{
fq[1][1] = 0.0, fq[1][2] = 1.0, fq[1][3] = 0.0;
fq[2][1] = (y - 3.0) * uuu[n1 + i] * uuu[n1 + i] / 2.0 / uuu[i] / uuu[i];
fq[2][2] = (3.0 - y) * uuu[n1 + i] / uuu[i];
fq[2][3] = y - 1.0;
fq[3][1] = ((y - 1.0) * uuu[n1 + i] * uuu[n1 + i] * uuu[n1 + i] - y * uuu[i] * uuu[n1 + i] * uuu[n1 + n1 + i]);
fq[3][1] = fq[3][1] / uuu[i] / uuu[i] / uuu[i];
fq[3][2] = (3 * (1.0 - y) * uuu[n1 + i] * uuu[n1 + i] + 2 * y * uuu[i] * uuu[n1 + n1 + i]) / uuu[i] / uuu[i] / 2.0;
fq[3][3] = y * uuu[n1 + i] / uuu[i];
fqtt[i] = -1.0 * (fq[1][1] * qt[i] + fq[1][2] * qt[n1 + i] + fq[1][3] * qt[n1 + n1 + i]);
fqtt[n1 + i] = -1.0 * (fq[2][1] * qt[i] + fq[2][2] * qt[n1 + i] + fq[2][3] * qt[n1 + n1 + i]);
fqtt[n1 + n1 + i] = -1.0 * (fq[3][1] * qt[i] + fq[3][2] * qt[n1 + i] + fq[3][3] * qt[n1 + n1 + i]);
}
borderfun3(fqtt);
}
// comput_LWqtt0(Lttx_n0, Lt_n0, L_n0, u_n0); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
// void comput_LWqtt0(double *qttt, double *qtt, double *qt, double *uuu)
// {
// int j, k;
// double q1, q2, q3, qt1, qt2, qt3, qtt1, qtt2, qtt3;
// for (int i = 0; i < n1; i++) // comput L(n0)
// {
// q1 = uuu[i], q2 = uuu[n1 + i], q3 = uuu[n1 + n1 + i];
// qt1 = qt[i], qt2 = qt[n1 + i], qt3 = qt[n1 + n1 + i];
// qtt1 = qtt[i], qtt2 = qtt[n1 + i], qtt3 = qtt[n1 + n1 + i];
// qttt[i] = -qtt2;
// qttt[n1 + i] = (2. * pow(q1, 2) * (pow(qt2, 2) * (y - 3.) - q1 * qtt3 * (y - 1.)) +
// pow(q2, 2) * (2. * pow(qt1, 2) - q1 * qtt1) * (y - 3.) +
// 2. * q1 * q2 * (-2. * qt1 * qt2 + q1 * qtt2) * (y - 3.)) /
// (2. * pow(q1, 3));
// qttt[n1 + n1 + i] = (2. * pow(q2, 3) * (3. * pow(qt1, 2) - q1 * qtt1) * (y - 1) +
// 3 * q1 * pow(q2, 2) * (-4. * qt1 * qt2 + q1 * qtt2) * (y - 1) -
// 2. * pow(q1, 2) * (-2. * q3 * qt1 * qt2 + 2. * q1 * qt2 * qt3 + q1 * q3 * qtt2) * y +
// 2. * q1 * q2 * (3. * q1 * pow(qt2, 2) * (y - 1) - 2. * q3 * pow(qt1, 2) * y + q1 * (2. * qt1 * qt3 + q3 * qtt1 - q1 * qtt3) * y)) /
// (2. * pow(q1, 4));
// }
// borderfun3(qttt);
// }
void comput_LWqtt0(double *qttt, double *qtt, double *qt, double *uuu)
{
int j, k;
double q1, q2, q3, qt1, qt2, qt3, qtt1, qtt2, qtt3, mq1e2, mq2e2, mqt1e2, mqt2e2, qt1qt2, xxx1, y3, y1;
for (int i = 0; i < n1; i++) // comput L(n0)
{
q1 = uuu[i], q2 = uuu[n1 + i], q3 = uuu[n1 + n1 + i];
qt1 = qt[i], qt2 = qt[n1 + i], qt3 = qt[n1 + n1 + i];
qtt1 = qtt[i], qtt2 = qtt[n1 + i], qtt3 = qtt[n1 + n1 + i];
qttt[i] = -qtt2;
mq1e2 = 2. * q1 * q1, mq2e2 = q2 * q2, mqt1e2 = 2. * qt1 * qt1, mqt2e2 = qt2 * qt2;
qt1qt2 = -2. * qt1 * qt2, xxx1 = qt1qt2 + q1 * qtt2, y3 = y - 3., y1 = y - 1.;
qttt[n1 + i] = (mq1e2 * (mqt2e2 * y3 - q1 * qtt3 * y1) + (mq2e2 * (mqt1e2 - q1 * qtt1) + 2. * q1 * q2 * xxx1) * y3) /
(mq1e2 * q1);
qttt[n1 + n1 + i] = ((2. * q2 * (1.5 * mqt1e2 - q1 * qtt1) + 3 * q1 * (xxx1 + qt1qt2)) * y1 * mq2e2 -
mq1e2 * (q3 * qt1qt2 + 2. * q1 * qt2 * qt3 + q1 * q3 * qtt2) * y +
2. * q1 * q2 * (3. * q1 * mqt2e2 * y1 + (-q3 * mqt1e2 + q1 * (2. * qt1 * qt3 + q3 * qtt1 - q1 * qtt3)) * y)) /
(0.5 * mq1e2 * mq1e2);
}
borderfun3(qttt);
}
void compt_ThD13()
{
int j = 0, i, k, ii;
uu_to_pc(u_n0);
Splitting(u_n0);
// Splitting_char(u_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
// L_n0[ii] = -(flux[ii] - flux[ii - 1]) / dx;
L_n0[ii] = -df_dx(fz, ff, ii);
}
j++;
}
comput_LWqt0(Ltx_n0, L_n0, u_n0); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
borderfun3(Ltx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Lt_n0[ii] = dfdxcent(Ltx_n0, ii);
// u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 / 2.0 * dt * dt * Lt_n0[ii];
}
j++;
}
comput_LWqtt0(Lttx_n0, Lt_n0, L_n0, u_n0); // (double *qttt, double *qtt, double *qt, double *uuu)
borderfun3(Lttx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Ltt_n0[ii] = dfdxcent(Lttx_n0, ii);
u_nn[ii] = u_n0[ii] + dt * L_n0[ii] + dt * dt / 2. * Lt_n0[ii] + dt * dt * dt / 6. * Ltt_n0[ii];
}
j++;
}
borderfun3(u_nn);
}
void compt_ThD23()
{
int j = 0, i, k, ii;
a21 = 0.500;
b2 = 0.5;
bb2 = 0.125;
bbb1 = 0.020833333333333;
bbb2 = 1. / 6. * (1. - 3. * a21 * (a21 * b2 + 2. * bb2) - 6. * bbb1);
b1 = 1. - b2;
bb1 = 1. / 2. - a21 * b2 - bb2;
uu_to_pc(u_n0);
Splitting(u_n0);
// Splitting_char(u_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
// L_n0[ii] = -(flux[ii] - flux[ii - 1]) / dx;
L_n0[ii] = -df_dx(fz, ff, ii);
}
j++;
}
comput_LWqt0(Ltx_n0, L_n0, u_n0); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
borderfun3(Ltx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Lt_n0[ii] = dfdxcent(Ltx_n0, ii);
// u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 / 2.0 * dt * dt * Lt_n0[ii];
}
j++;
}
comput_LWqtt0(Lttx_n0, Lt_n0, L_n0, u_n0); // (double *qttt, double *qtt, double *qt, double *uuu)
borderfun3(Lttx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Ltt_n0[ii] = dfdxcent(Lttx_n0, ii);
u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 * dt * dt / 2. * Lt_n0[ii] + a21 * a21 * a21 * dt * dt * dt / 6. * Ltt_n0[ii];
}
j++;
}
borderfun3(u_n1);
uu_to_pc(u_n1);
Splitting(u_n1);
// Splitting_char(u_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
// L_n1[ii] = -(flux[ii] - flux[ii - 1]) / dx;
L_n1[ii] = -df_dx(fz, ff, ii);
}
j++;
}
comput_LWqt0(Ltx_n1, L_n1, u_n1); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
borderfun3(Ltx_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Lt_n1[ii] = dfdxcent(Ltx_n1, ii);
// u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 / 2.0 * dt * dt * Lt_n0[ii];
}
j++;
}
comput_LWqtt0(Lttx_n1, Lt_n1, L_n1, u_n1); // (double *qttt, double *qtt, double *qt, double *uuu)
borderfun3(Lttx_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Ltt_n1[ii] = dfdxcent(Lttx_n1, ii);
u_nn[ii] = u_n0[ii] + b1 * dt * L_n0[ii] + bb1 * dt * dt * Lt_n0[ii] + bbb1 * dt * dt * dt * Ltt_n0[ii] +
b2 * dt * L_n1[ii] + bb2 * dt * dt * Lt_n1[ii] + bbb2 * dt * dt * dt * Ltt_n1[ii];
}
j++;
}
borderfun3(u_nn);
}
void compt_ThD24()
{
int j = 0, i, k, ii;
a21 = 0.614824, b2 = 0.40239, bb2 = 0.082792, b1 = 1 - b2;
bb1 = 1. / 2. - a21 * b2 - bb2;
bbb1 = 1. / 24. * (4. - 1. / a21 - 8. * a21 * a21 * b2 - 12. * a21 * bb2);
bbb2 = 1. / (24. * a21) - 1. / 6. * a21 * (a21 * b2 + 3. * bb2);
uu_to_pc(u_n0);
Splitting(u_n0);
// Splitting_char(u_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
// L_n0[ii] = -(flux[ii] - flux[ii - 1]) / dx;
L_n0[ii] = -df_dx(fz, ff, ii);
}
j++;
}
comput_LWqt0(Ltx_n0, L_n0, u_n0); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
borderfun3(Ltx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Lt_n0[ii] = dfdxcent(Ltx_n0, ii);
// u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 / 2.0 * dt * dt * Lt_n0[ii];
}
j++;
}
comput_LWqtt0(Lttx_n0, Lt_n0, L_n0, u_n0); // (double *qttt, double *qtt, double *qt, double *uuu)
borderfun3(Lttx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Ltt_n0[ii] = dfdxcent(Lttx_n0, ii);
u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 * dt * dt / 2. * Lt_n0[ii] + a21 * a21 * a21 * dt * dt * dt / 6. * Ltt_n0[ii];
}
j++;
}
borderfun3(u_n1);
uu_to_pc(u_n1);
Splitting(u_n1);
// Splitting_char(u_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
// L_n1[ii] = -(flux[ii] - flux[ii - 1]) / dx;
L_n1[ii] = -df_dx(fz, ff, ii);
}
j++;
}
comput_LWqt0(Ltx_n1, L_n1, u_n1); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
borderfun3(Ltx_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Lt_n1[ii] = dfdxcent(Ltx_n1, ii);
// u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 / 2.0 * dt * dt * Lt_n0[ii];
}
j++;
}
comput_LWqtt0(Lttx_n1, Lt_n1, L_n1, u_n1); // (double *qttt, double *qtt, double *qt, double *uuu)
borderfun3(Lttx_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Ltt_n1[ii] = dfdxcent(Lttx_n1, ii);
u_nn[ii] = u_n0[ii] + b1 * dt * L_n0[ii] + bb1 * dt * dt * Lt_n0[ii] + bbb1 * dt * dt * dt * Ltt_n0[ii] +
b2 * dt * L_n1[ii] + bb2 * dt * dt * Lt_n1[ii] + bbb2 * dt * dt * dt * Ltt_n1[ii];
}
j++;
}
borderfun3(u_nn);
}
void compt_ThD25()
{
int j = 0, i, k, ii;
a21 = 0.6;
b1 = 1., b2 = 0., bb1 = (2. - 5. * a21 + 10. * pow(a21, 3)) / (20. * pow(a21, 3));
bb2 = (-2. + 5. * a21) / (20. * pow(a21, 3));
bbb1 = (3. + 10. * (-1. + a21) * a21) / (60. * pow(a21, 2));
bbb2 = (3. - 5. * a21) / (60. * pow(a21, 2));
uu_to_pc(u_n0);
Splitting(u_n0);
// Splitting_char(u_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
// L_n0[ii] = -(flux[ii] - flux[ii - 1]) / dx;
L_n0[ii] = -df_dx(fz, ff, ii);
}
j++;
}
comput_LWqt0(Ltx_n0, L_n0, u_n0); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
borderfun3(Ltx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Lt_n0[ii] = dfdxcent(Ltx_n0, ii);
// u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 / 2.0 * dt * dt * Lt_n0[ii];
}
j++;
}
comput_LWqtt0(Lttx_n0, Lt_n0, L_n0, u_n0); // (double *qttt, double *qtt, double *qt, double *uuu)
borderfun3(Lttx_n0);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
Ltt_n0[ii] = dfdxcent(Lttx_n0, ii);
u_n1[ii] = u_n0[ii] + a21 * dt * L_n0[ii] + a21 * a21 * dt * dt / 2. * Lt_n0[ii] + a21 * a21 * a21 * dt * dt * dt / 6. * Ltt_n0[ii];
}
j++;
}
borderfun3(u_n1);
uu_to_pc(u_n1);
Splitting(u_n1);
// Splitting_char(u_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{
ii = nb + j + k * n1;
// L_n1[ii] = -(flux[ii] - flux[ii - 1]) / dx;
L_n1[ii] = -df_dx(fz, ff, ii);
}
j++;
}
comput_LWqt0(Ltx_n1, L_n1, u_n1); // Ltx_n0[j] = -L_n0[j] * u_n0[j];
borderfun3(Ltx_n1);
j = 0, i = n1 - nb * 2;
while (i-- > 0)
{
for (int k = 0; k < 3; k++)
{