static dErr JakoSIAVelocity(VHTCase scase,dReal b,dReal h,dReal dh[2],dReal z,dScalar u[3])
{
struct VHTRheology *rheo = &scase->rheo;
const dReal
p = rheo->pe,
n = 1 ? 1 : 1./(p-1),
B = rheo->B0 * pow(2*rheo->gamma0,(n-1)/(2*n)), // reduce to Stress = B |Du|^{1/n}
A = pow(B,-n);
const dScalar
slope = dSqrt(dSqr(dh[0]) + dSqr(dh[1])),
sliding = 0,
hmz = z > h ? 0 : (z < b ? h-b : h-z),
// The strain rate is: Du = A tau^n
// where: tau = rho*grav*(h-z)*dh
int_bz = -1. / (n+1) * (pow(hmz,n+1) - pow(h-b,n+1)), // \int_b^z (h-z)^n
//bstress = rheo->rhoi * dAbs(rheo->gravity[2]) * (h-b) * slope, // diagnostic
//rstress = dUnitNonDimensionalizeSI(scase->utable.Pressure,1e5),
siaspeed = sliding + A * pow(rheo->rhoi * dAbs(rheo->gravity[2]) * slope, n) * int_bz, // Integrate strain rate from the bottom
speed = siaspeed * (5 + 0 * (1 + tanh((z-b)/100))/2);
u[0] = -speed / slope * dh[0];
u[1] = -speed / slope * dh[1];
u[2] = 0; // Would need another derivative to evaluate this and it should not be a big deal for this stationary computation
//printf("u0 %g u1 %g rho %g grav %g stress %g 1bar %g dh[2] %g %g A %g B %g;\n",u[0],u[1],rheo->rhoi,rheo->gravity[2],bstress,rstress,dh[0],dh[1],A,B);
return 0;
}
// Advection model
static dErr VHTCaseSolution_Wind(VHTCase scase,const dReal x[3],dScalar rhou[],dScalar drhou[],dScalar *p,dScalar dp[],dScalar *E,dScalar dE[])
{ /* Defines inhomogeneous Dirichlet boundary conditions */
const dReal L[3] = {0.5*(scase->bbox[0][1] - scase->bbox[0][0]),
0.5*(scase->bbox[1][1] - scase->bbox[1][0]),
0.5*(scase->bbox[2][1] - scase->bbox[2][0])}; // Each var is in [-L,L]
const dReal X[3] = {x[0]/L[0],x[1]/L[1],x[2]/L[2]};
dReal z = (1 + X[2])/2; // in range [0,1]
dReal depth = 1-z;
rhou[0] = (1 - dSqr(X[1])) * (1 - pow(depth,2));
rhou[1] = 0;
rhou[2] = 0;
for (dInt i=0; i<9; i++) drhou[i] = 0;
*p = 0;
for (dInt i=0; i<3; i++) dp[i] = 0;
*E = -X[0] * (1 - dSqr(X[1]));
for (dInt i=0; i<3; i++) dE[i] = 0;
return 0;
}
static dErr JakoInternalEnergy_Smooth(VHTCase scase,dReal b,dReal h,const dReal x[],dScalar *e)
{
struct VHTRheology *rheo = &scase->rheo;
dReal z,t,T;
dFunctionBegin;
z = (x[2] - b) / (h-b); // Normalize to [0,1] plus possible fuzz
z = dMax(0,dMin(1,z)); // Clip to [0,1]
t = 90*dSqr(z)*exp(-5*z); // hump with maximum value close to 2
T = rheo->T3 - (rheo->T3 - rheo->T0)*t; // Maximum value is at the bed and equal to T3, extends past T0
*e = rheo->c_i * (T - rheo->T0); // energy/mass
dFunctionReturn(0);
}
int main(){
double lightspeed, Newton_G, mass;
double R_sch;
double xp[STEPS], yp[STEPS][NVAR], Ene[STEPS];
double apo, per, Va, Vp, E, AngMom, Vc, ecc, mjAxis;
double rIni, vIni, T;
int i, j, k, loop;
double y1[NVAR], y[NVAR], Ene1, x1, x2, xbin, xend, delX;
double eps, h0, hmax;
inData data;
void *custom_data = &data;
int flag, nvar;
fluxfn fn;
fluxEn En;
FILE *fp;
char *str;
char str1[] = "result_NT";
char str2[] = "result_WG";
char str3[] = "result_SG";
char str4[] = "result_GN";
// Integration-----------------------------------------------------------
lightspeed = 10;
Newton_G = 1;
mass = 1e6;
R_sch = 2 * Newton_G * mass / dSqr(lightspeed);
per = 5.0 * R_sch;
ecc = 0.998;
apo = (1 + ecc) / (1 - ecc) * per;
mjAxis = (per + apo) / 2.0;
E = -0.5 * Newton_G * mass / mjAxis;
Va = pow(2 * (E + (Newton_G * mass / apo)), 0.5);
Vp = pow(2 * (E + (Newton_G * mass / per)), 0.5);
rIni = apo;
vIni = Va;
// rIni = per;
// vIni = Vp;
AngMom = rIni * vIni;
T = 2.0 * PI * pow(mjAxis, 1.5) * pow((Newton_G * mass), -0.5);
Vc = pow((Newton_G * mass / rIni), 0.5);
/* rIni = 10000.0;
vIni = 4;
E = 0.5 * vIni*vIni - (Newton_G * mass / rIni);
AngMom = rIni * vIni;
mjAxis = -1.0 * Newton_G * mass / (2 * E);
ecc = pow((1.0 - dSqr(AngMom) / (Newton_G * mass * mjAxis)), 0.5);
apo = mjAxis * (1.0 + ecc);
per = mjAxis * (1.0 - ecc);
T = 2.0 * PI * pow(mjAxis, 1.5) * pow((Newton_G * mass), -0.5);
Vc = pow((Newton_G * mass / rIni), 0.5);
*/
for(loop = 1; loop <= 4; loop++){
switch (loop){
case 1:
fn = F_NT;
En = E_NT;
str = &str1[0];
break;
case 2:
fn = F_WG;
En = E_WG;
str = &str2[0];
break;
case 3:
fn = F_SG;
En = E_SG;
str = &str3[0];
break;
case 4:
fn = F_GN;
En = E_GN;
str = &str4[0];
break;
}
printf("%s\n", str);
x1 = 0;
x2 = 6.0 * T;
delX = (x2 - x1) / STEPS;
eps = 1e-13;
hmax = delX / HACCU;
h0 = 1e-10;
nvar = NVAR;
data.mass = mass;
data.lightspeed = lightspeed;
data.Newton_G = Newton_G;
for(i = 0; i < NVAR; i++){
y1[i] = 0;
}
y1[1] = -1.0 * rIni;
y1[2] = vIni;
for(i = 0; i < NVAR; i++){
y[i] = y1[i];
}
Ene1 = En(nvar, y, custom_data);
// Run--------------------------------------------------------------
for(i = 0; i < STEPS; i++){
xbin = x1 + delX * i;
xend = x1 + delX * (i + 1);
flag = dopri8(fn, nvar, xbin, y, xend, eps, hmax, &h0, NULL, NULL, custom_data);
if(flag == 0) printf("!!%d\n", i);
Ene[i] = En(nvar, y, custom_data);
for(j = 0; j < NVAR; j++) yp[i][j] = y[j];
xp[i] = xend;
}
fp = fopen(str,"w+");
if(fp == NULL)
printf("Cannot open the file!\n");
fprintf(fp, "%10.6f \t", x1);
for(j = 0; j < NVAR; j++){
fprintf(fp, "%20.15f \t", y1[j]);
}
fprintf(fp, "%20.15f \n", Ene1);
for(i = 0; i < STEPS; i++){
fprintf(fp, "%10.6f \t", xp[i]);
for(j = 0; j < NVAR; j++){
fprintf(fp, "%20.15f \t", yp[i][j]);
}
fprintf(fp, "%20.15f \n", Ene[i]);
}
fclose(fp);
}
printf("END-----------------------------------\n");
printf("R_sch = %e, Vc = %e\n", R_sch, Vc);
printf("apo = %e, per = %e, ecc = %e, mjAxis = %e\n", apo, per, ecc, mjAxis);
printf("Va = %e, Vp = %e\n", Va, Vp);
printf("Initial quantities:\n");
printf("rIni = %e, vIni = %e, T = %e\n", rIni, vIni, T);
printf("E = %e, apo = %e\n", E, apo);
}
