public static System.Double SolveDouble(long timesteps, DataDouble data)
{
//Convenience indices
R RN = R.El(data.N); //Same as [n]
R RN1 = R.El(data.N + 1); //Same as [n+1]
System.Double g = 9.8f; // gravitational constant
System.Double dt = 0.02f; // hardwired timestep
System.Double dx = 1.0f;
System.Double dy = 1.0f;
long droploc = data.N / 4;
var H = data.H;
var U = data.U;
var V = data.V;
var Hx = data.Hx;
var Ux = data.Ux;
var Vx = data.Vx;
var Hy = data.Hy;
var Uy = data.Uy;
var Vy = data.Vy;
//Splash!!!
H[droploc, droploc] += 5.0f;
for (int i = 0; i < timesteps; i++)
{
H.Flush();
// Reflecting boundary conditions
H[ALL, FIRST] = H[ALL, SECOND];
U[ALL, FIRST] = U[ALL, SECOND];
V[ALL, FIRST] = -V[ALL, SECOND];
H[ALL, RN1] = H[ALL, RN];
U[ALL, RN1] = U[ALL, RN];
V[ALL, RN1] = -V[ALL, RN];
H[FIRST, ALL] = H[SECOND, ALL];
U[FIRST, ALL] = -U[SECOND, ALL];
V[FIRST, ALL] = V[SECOND, ALL];
H[RN1, ALL] = H[RN, ALL];
U[RN1, ALL] = -U[RN, ALL];
V[RN1, ALL] = V[RN, ALL];
//First half-step
//Height
Hx[ALL, R.Slice(0, -1)] = (H[SKIP1, INNER] + H[ZM1, INNER]) / 2 -
dt / (2 * dx) * (U[SKIP1, INNER] - U[ZM1, INNER]);
//x momentum
Ux[ALL, R.Slice(0, -1)] = (U[SKIP1, INNER] + U[ZM1, INNER]) / 2 -
dt / (2 * dx) * ((U[SKIP1, INNER].Pow(2) / H[SKIP1, INNER] +
g / 2 * H[SKIP1, INNER].Pow(2)) -
(U[ZM1, INNER].Pow(2) / H[ZM1, INNER] +
g / 2 * H[ZM1, INNER].Pow(2)));
// y momentum
Vx[ALL, ZM1] = (V[SKIP1, INNER] + V[ZM1, INNER]) / 2 -
dt / (2 * dx) * ((U[SKIP1, INNER] *
V[SKIP1, INNER] / H[SKIP1, INNER]) -
(U[ZM1, INNER] *
V[ZM1, INNER] / H[ZM1, INNER]));
// height
Hy[ZM1, ALL] = (H[INNER, SKIP1] + H[INNER, ZM1]) / 2 -
dt / (2 * dy) * (V[INNER, SKIP1] - V[INNER, ZM1]);
// x momentum
Uy[ZM1, ALL] = (U[INNER, SKIP1] + U[INNER, ZM1]) / 2 -
dt / (2 * dy) * ((V[INNER, SKIP1] *
U[INNER, SKIP1] / H[INNER, SKIP1]) -
(V[INNER, ZM1] *
U[INNER, ZM1] / H[INNER, ZM1]));
// y momentum
Vy[ZM1, ALL] = (V[INNER, SKIP1] + V[INNER, ZM1]) / 2 -
dt / (2 * dy) * ((V[INNER, SKIP1].Pow(2) / H[INNER, SKIP1] +
g / 2 * H[INNER, SKIP1].Pow(2)) -
(V[INNER, ZM1].Pow(2) / H[INNER, ZM1] +
g / 2 * H[INNER, ZM1].Pow(2)));
// Second half step
// height
H[INNER, INNER] = H[INNER, INNER] -
(dt / dx) * (Ux[SKIP1, ZM1] - Ux[ZM1, ZM1]) -
(dt / dy) * (Vy[ZM1, SKIP1] - Vy[ZM1, ZM1]);
// x momentum
U[INNER, INNER] = U[INNER, INNER] -
(dt / dx) * ((Ux[SKIP1, ZM1].Pow(2) / Hx[SKIP1, ZM1] +
g / 2 * Hx[SKIP1, ZM1].Pow(2)) -
(Ux[ZM1, ZM1].Pow(2) / Hx[ZM1, ZM1] +
g / 2 * Hx[ZM1, ZM1].Pow(2))) -
(dt / dy) * ((Vy[ZM1, SKIP1] *
Uy[ZM1, SKIP1] / Hy[ZM1, SKIP1]) -
(Vy[ZM1, ZM1] *
Uy[ZM1, ZM1] / Hy[ZM1, ZM1]));
// y momentum
V[R.Slice(1, -1), R.Slice(1, -1)] = V[R.Slice(1, -1), R.Slice(1, -1)] -
(dt / dx) * ((Ux[SKIP1, ZM1] *
Vx[SKIP1, ZM1] / Hx[SKIP1, ZM1]) -
(Ux[ZM1, ZM1] * Vx[ZM1, ZM1] / Hx[ZM1, ZM1])) -
(dt / dy) * ((Vy[ZM1, SKIP1].Pow(2) / Hy[ZM1, SKIP1] +
g / 2 * Hy[ZM1, SKIP1].Pow(2)) -
(Vy[ZM1, ZM1].Pow(2) / Hy[ZM1, ZM1] +
g / 2 * Hy[ZM1, ZM1].Pow(2)));
}
//Make sure we have the actual data and use it as a checksum
return(NumCIL.Double.Add.Reduce(NumCIL.Double.Add.Reduce(H / data.N)).Value[0]);
}
public static T Solve(long n, long timesteps)
{
//Convenience indices
R RN = R.El(n); //Same as [n]
R RN1 = R.El(n + 1); //Same as [n+1]
T g = 9.8f; // gravitational constant
T dt = 0.02f; // hardwired timestep
T dx = 1.0f;
T dy = 1.0f;
long droploc = n / 4;
var H = Generate.Ones(n + 2, n + 2);
var U = Generate.Ones(n + 2, n + 2);
var V = Generate.Ones(n + 2, n + 2);
var Hx = Generate.Ones(n + 1, n + 1);
var Ux = Generate.Ones(n + 1, n + 1);
var Vx = Generate.Ones(n + 1, n + 1);
var Hy = Generate.Ones(n + 1, n + 1);
var Uy = Generate.Ones(n + 1, n + 1);
var Vy = Generate.Ones(n + 1, n + 1);
//Splash!!!
H[droploc, droploc] += 5.0f;
for (int i = 0; i < timesteps; i++)
{
H.Flush();
// Reflecting boundary conditions
H[ALL, FIRST] = H[ALL, SECOND];
U[ALL, FIRST] = U[ALL, SECOND];
V[ALL, FIRST] = -V[ALL, SECOND];
H[ALL, RN1] = H[ALL, RN];
U[ALL, RN1] = U[ALL, RN];
V[ALL, RN1] = -V[ALL, RN];
H[FIRST, ALL] = H[SECOND, ALL];
U[FIRST, ALL] = -U[SECOND, ALL];
V[FIRST, ALL] = V[SECOND, ALL];
H[RN1, ALL] = H[RN, ALL];
U[RN1, ALL] = -U[RN, ALL];
V[RN1, ALL] = V[RN, ALL];
//First half-step
//Height
Hx[ALL, R.Slice(0, -1)] = (H[SKIP1, INNER] + H[ZM1, INNER]) / 2 -
dt / (2 * dx) * (U[SKIP1, INNER] - U[ZM1, INNER]);
//x momentum
Ux[ALL, R.Slice(0, -1)] = (U[SKIP1, INNER] + U[ZM1, INNER]) / 2 -
dt / (2 * dx) * ((U[SKIP1, INNER].Pow(2) / H[SKIP1, INNER] +
g / 2 * H[SKIP1, INNER].Pow(2)) -
(U[ZM1, INNER].Pow(2) / H[ZM1, INNER] +
g / 2 * H[ZM1, INNER].Pow(2)));
// y momentum
Vx[ALL, ZM1] = (V[SKIP1, INNER] + V[ZM1, INNER]) / 2 -
dt / (2 * dx) * ((U[SKIP1, INNER] *
V[SKIP1, INNER] / H[SKIP1, INNER]) -
(U[ZM1, INNER] *
V[ZM1, INNER] / H[ZM1, INNER]));
// height
Hy[ZM1, ALL] = (H[INNER, SKIP1] + H[INNER, ZM1]) / 2 -
dt / (2 * dy) * (V[INNER, SKIP1] - V[INNER, ZM1]);
// x momentum
Uy[ZM1, ALL] = (U[INNER, SKIP1] + U[INNER, ZM1]) / 2 -
dt / (2 * dy) * ((V[INNER, SKIP1] *
U[INNER, SKIP1] / H[INNER, SKIP1]) -
(V[INNER, ZM1] *
U[INNER, ZM1] / H[INNER, ZM1]));
// y momentum
Vy[ZM1, ALL] = (V[INNER, SKIP1] + V[INNER, ZM1]) / 2 -
dt / (2 * dy) * ((V[INNER, SKIP1].Pow(2) / H[INNER, SKIP1] +
g / 2 * H[INNER, SKIP1].Pow(2)) -
(V[INNER, ZM1].Pow(2) / H[INNER, ZM1] +
g / 2 * H[INNER, ZM1].Pow(2)));
// Second half step
// height
H[INNER, INNER] = H[INNER, INNER] -
(dt / dx) * (Ux[SKIP1, ZM1] - Ux[ZM1, ZM1]) -
(dt / dy) * (Vy[ZM1, SKIP1] - Vy[ZM1, ZM1]);
// x momentum
U[INNER, INNER] = U[INNER, INNER] -
(dt / dx) * ((Ux[SKIP1, ZM1].Pow(2) / Hx[SKIP1, ZM1] +
g / 2 * Hx[SKIP1, ZM1].Pow(2)) -
(Ux[ZM1, ZM1].Pow(2) / Hx[ZM1, ZM1] +
g / 2 * Hx[ZM1, ZM1].Pow(2))) -
(dt / dy) * ((Vy[ZM1, SKIP1] *
Uy[ZM1, SKIP1] / Hy[ZM1, SKIP1]) -
(Vy[ZM1, ZM1] *
Uy[ZM1, ZM1] / Hy[ZM1, ZM1]));
// y momentum
V[R.Slice(1, -1), R.Slice(1, -1)] = V[R.Slice(1, -1), R.Slice(1, -1)] -
(dt / dx) * ((Ux[SKIP1, ZM1] *
Vx[SKIP1, ZM1] / Hx[SKIP1, ZM1]) -
(Ux[ZM1, ZM1] * Vx[ZM1, ZM1] / Hx[ZM1, ZM1])) -
(dt / dy) * ((Vy[ZM1, SKIP1].Pow(2) / Hy[ZM1, SKIP1] +
g / 2 * Hy[ZM1, SKIP1].Pow(2)) -
(Vy[ZM1, ZM1].Pow(2) / Hy[ZM1, ZM1] +
g / 2 * Hy[ZM1, ZM1].Pow(2)));
}
//Make sure we have the actual data and use it as a checksum
return(Add.Reduce(Add.Reduce(H / n)).Value[0]);
}