void getufromG(double *h, double *G, double u0, double u1, double h0, double h1, double dx , int n, double *u)
{
double idx = 1.0 / dx;
double ithree = 1.0 / 3.0;
double *a = malloc((n-1)*sizeof(double));
double *b = malloc(n*sizeof(double));
double *c = malloc((n-1)*sizeof(double));
int i;
double thx;
for (i =1;i < n-1 ; i++)
{
thx = 0.5*idx*(h[i+1] - h[i-1]);
a[i-1] = -ithree*idx*idx*h[i]*h[i]*h[i] + 0.5*idx*h[i]*h[i]*thx;
b[i] = h[i] + 2.0*ithree*idx*idx*h[i]*h[i]*h[i];
c[i] = -ithree*idx*idx*h[i]*h[i]*h[i] - 0.5*idx*h[i]*h[i]*thx;
}
//Boundaries
i = 0;
thx = 0.5*idx*(h[i+1] - h0);
//a[i-1] = -ithree*idx*idx*h[i]*h[i]*h[i] + 0.5*idx*th*th*thx
b[i] = h[i] + 2.0*ithree*idx*idx*h[i]*h[i]*h[i];
c[i] = -ithree*idx*idx*h[i]*h[i]*h[i] - 0.5*idx*h[i]*h[i]*thx;
double tmpG1 = G[i];
G[i] = tmpG1 - u0*(-ithree*idx*idx*h[i]*h[i]*h[i] + 0.5*idx*h[i]*h[i]*thx);
i = n-1;
thx = 0.5*idx*(h1 - h[i-1]);
a[i-1] = -ithree*idx*idx*h[i]*h[i]*h[i] + 0.5*idx*h[i]*h[i]*thx;
b[i] = h[i] + 2.0*ithree*idx*idx*h[i]*h[i]*h[i];
//c[i] = -ithree*idx*idx*h[i]*h[i]*h[i] - 0.5*idx*h[i]*h[i]*thx;
double tmpG2 = G[i];
G[i] = tmpG2 - u1*(-ithree*idx*idx*h[i]*h[i]*h[i] - 0.5*idx*h[i]*h[i]*thx);
TDMA(a,b,c,G,n,u);
G[0] = tmpG1;
G[n-1] = tmpG2;
free(a);
free(b);
free(c);
}
void simpleCFD::matrix::solve()
{
for (unsigned int i=1; i<=Grid_.nCells(); ++i) {
a_p[i] += a_w[i]+a_e[i];
}
TDMA();
}
void evolveu(double *h, double *u, double *fh, double *ph, double *pu, double g, double dx, double dt, int nBC, int n,double *fu)
{
//modifies nh and nG to give the new values of h and G after a single time step
double idx = 1.0 / dx;
double *a = malloc((n-1)*sizeof(double));
double *b = malloc(n*sizeof(double));
double *c = malloc((n-1)*sizeof(double));
double *f = malloc(n*sizeof(double));
int i,j;
double nu,nh,nux,nuxx,nuxxx,nhx,pux,puxx,F,S;
for (i =1;i < n-1 ; i++)
{
//i for tridiagonals, j for the BC u,h vectors
j = i + nBC;
nhx = 0.5*idx*(h[j+1] - h[j-1]);
a[i-1] = 0.5*idx*h[j]*h[j]*nhx - i3*idx*idx*h[j]*h[j]*h[j];
b[i] = fh[j] + 2*i3*idx*idx*h[j]*h[j]*h[j];
c[i] = -0.5*idx*h[j]*h[j]*nhx - i3*idx*idx*h[j]*h[j]*h[j];
nu = u[j];
nh = h[j];
nux = 0.5*idx*(u[j+1] - u[j-1]);
nuxx = idx*idx*(u[j+1] - 2*u[j] + u[j-1]);
nuxxx = 0.5*idx*idx*idx*(u[j+2] - 2*u[j+1] + 2*u[j-1] - u[j-2]);
pux = 0.5*idx*(pu[j+1] - pu[j-1]);
puxx = idx*idx*(pu[j+1] - 2*pu[j] + pu[j-1]);
F = 2*nu*nh*nux + nu*nu*nhx + g*nh*nhx + nh*nh*nhx*nux*nux + i3*nh*nh*nh*nux*nuxx
- nh*nh*nhx*nu*nuxx -i3*nh*nh*nh*nu*nuxxx;
S = 2*dt*F - pu[j]*ph[j] + nh*nh*nhx*pux + i3*nh*nh*nh*puxx;
f[i] = -S;
}
//Boundaries
i = 0;
j = i + nBC;
//a[i-1] = 0.5*idx*h[j]*h[j] - i3*idx*idx*h[j]*h[j]*h[j];
b[i] = fh[j] + 2*i3*idx*idx*h[j]*h[j]*h[j];
c[i] = -0.5*idx*h[j]*h[j] - i3*idx*idx*h[j]*h[j]*h[j];
nu = u[j];
nh = h[j];
nux = 0.5*idx*(u[j+1] - u[j-1]);
nuxx = idx*idx*(u[j+1] - 2*u[j] + u[j-1]);
nuxxx = 0.5*idx*idx*idx*(u[j+2] - 2*u[j+1] + 2*u[j-1] - u[j-2]);
nhx = 0.5*idx*(h[j+1] - h[j-1]);
pux = 0.5*idx*(pu[j+1] - pu[j-1]);
puxx = idx*idx*(pu[j+1] - 2*pu[j] + pu[j-1]);
F = 2*nu*nh*nux + nu*nu*nhx + g*nh*nhx + nh*nh*nux*nux + i3*nh*nh*nh*nux*nuxx - nh*nh*nu*nuxx
-i3*nh*nh*nh*nu*nuxxx;
S = 2*dt*F - pu[j]*ph[j] + nh*nh*pux + i3*nh*nh*nh*puxx;
f[i] = -S - u[j-1]*(0.5*idx*h[j]*h[j] - i3*idx*idx*h[j]*h[j]*h[j]);
i = n-1;
j = i + nBC;
a[i-1] = 0.5*idx*h[j]*h[j] - i3*idx*idx*h[j]*h[j]*h[j];
b[i] = fh[j] + 2*i3*idx*idx*h[j]*h[j]*h[j];
//c[i] = -0.5*idx*h[j]*h[j] - i3*idx*idx*h[j]*h[j]*h[j];
nu = u[j];
nh = h[j];
nux = 0.5*idx*(u[j+1] - u[j-1]);
nuxx = idx*idx*(u[j+1] - 2*u[j] + u[j-1]);
nuxxx = 0.5*idx*idx*idx*(u[j+2] - 2*u[j+1] + 2*u[j-1] - u[j-2]);
nhx = 0.5*idx*(h[j+1] - h[j-1]);
pux = 0.5*idx*(pu[j+1] - pu[j-1]);
puxx = idx*idx*(pu[j+1] - 2*pu[j] + pu[j-1]);
F = 2*nu*nh*nux + nu*nu*nhx + g*nh*nhx + nh*nh*nux*nux + i3*nh*nh*nh*nux*nuxx - nh*nh*nu*nuxx
-i3*nh*nh*nh*nu*nuxxx;
S = 2*dt*F - pu[j]*ph[j] + nh*nh*pux + i3*nh*nh*nh*puxx;
f[i] = -S - u[j+1]*(-0.5*idx*h[j]*h[j] - i3*idx*idx*h[j]*h[j]*h[j]);
TDMA(a,b,c,f,n,fu);
free(a);
free(b);
free(c);
free(f);
}
void getufromG(double *h, double *G,double *bed, double u0, double u1, double h0, double h1, double b0, double b1,double dx, int n,double *ublank)
{
double idx = 1.0 / dx;
double *a = malloc((n-1)*sizeof(double));
double *b = malloc(n*sizeof(double));
double *c = malloc((n-1)*sizeof(double));
double th,thx,tbx,tbxx,D,ai,bi,ci;
int i;
for(i = 1; i < n-1; i++)
{
th = h[i];
thx = 0.5*idx*(h[i+1] - h[i-1]);
tbx = 0.5*idx*(bed[i+1] - bed[i-1]);
tbxx = idx*idx*(bed[i+1] -2*bed[i]+ bed[i-1]);
D = th + th*th*tbx + 0.5*th*th*tbxx + th*tbx*tbx;
ai = -i3*idx*idx*th*th*th + 0.5*idx*th*th*thx;
bi = D + 2.0*i3*idx*idx*th*th*th;
ci = -i3*idx*idx*th*th*th - 0.5*idx*th*th*thx;
a[i-1] = ai;
b[i] = bi;
c[i] = ci;
}
//Boundary
//i = 0
i = 0;
th = h[i];
thx = 0.5*idx*(h[i+1] - h0);
tbx = 0.5*idx*(bed[i+1] - b0);
tbxx = idx*idx*(bed[i+1] -2*bed[i]+ b0);
D = th + th*th*tbx + 0.5*th*th*tbxx + th*tbx*tbx;
ai = -i3*idx*idx*th*th*th + 0.5*idx*th*th*thx;
bi = D + 2.0*i3*idx*idx*th*th*th;
ci = -i3*idx*idx*th*th*th - 0.5*idx*th*th*thx;
b[i] = bi;
c[i] = ci;
double tmpG1 = G[i];
G[i] = tmpG1 - u0*ai;
i = n-1;
th = h[i];
thx = 0.5*idx*(h1- h[i-1]);
tbx = 0.5*idx*(b1 - bed[i-1]);
tbxx = idx*idx*(b1 -2*bed[i]+ bed[i-1]);
D = th + th*th*tbx + 0.5*th*th*tbxx + th*tbx*tbx;
ai = -i3*idx*idx*th*th*th + 0.5*idx*th*th*thx;
bi = D + 2.0*i3*idx*idx*th*th*th;
ci = -i3*idx*idx*th*th*th - 0.5*idx*th*th*thx;
a[i-1] = ai;
b[i] = bi;
double tmpG2 = G[i];
G[i] = tmpG2 - u1*ci;
TDMA(a,b,c,G,n,ublank);
G[0] = tmpG1;
G[n-1] = tmpG2;
free(a);
free(b);
free(c);
}
