void FormPreconditioner()
{
const float mic_parameter = 0.99f;
float d;
preconditioner.Reset(0);
var preconditionernx = this.preconditioner.DataSize.x;
var preconditionerny = this.preconditioner.DataSize.y;
for (int j = 1; j < preconditionerny - 1; ++j)
{
for (int i = 1; i < preconditionernx - 1; ++i)
{
if (marker[i, j] == FLUID)
{
d = poisson[i, j].x - sqr(poisson[i - 1, j].y * preconditioner[i - 1, j])
- sqr(poisson[i, j - 1].z * preconditioner[i, j - 1])
- mic_parameter * (poisson[i - 1, j].y * poisson[i - 1, j].z * sqr(preconditioner[i - 1, j])
+ poisson[i, j - 1].z * poisson[i, j - 1].y * sqr(preconditioner[i, j - 1]));
preconditioner[i, j] = 1 / Mathf.Sqrt(d + 1e-6f);
}
}
}
}
void FindDivergence()
{
r.Reset(0);
this.r.ForEachData((ref float value, int[] list) =>
{
var i = list[0];
var j = list[1];
if (this.marker[i, j] == FLUID)
{
this.r[i, j] = (this.velocity[MACGrid2DData.DataType.U, i + 1, j] - this.velocity[MACGrid2DData.DataType.U, i, j])
+ (this.velocity[MACGrid2DData.DataType.V, i, j + 1] - this.velocity[MACGrid2DData.DataType.V, i, j]);
//this.r[i, j] = 0.5f * (this.velocity[MACGrid2DData.DataType.U, i + 1, j] - this.velocity[MACGrid2DData.DataType.U, i-1, j])
// + 0.5f * (this.velocity[MACGrid2DData.DataType.V, i, j + 1] - this.velocity[MACGrid2DData.DataType.V, i, j-1]);
//this.r[i, j] = this.velocity.GetDivergenceFromIndex(i, j);
}
});
}
void ApplyPoisson(CellCenteredScalarGrid2D x, CellCenteredScalarGrid2D y)
{
y.Reset(0);
var poissonnx = this.poisson.DataSize.x;
var poissonny = this.poisson.DataSize.y;
for (int j = 1; j < poissonny - 1; ++j)
{
for (int i = 1; i < poissonnx - 1; ++i)
{
if (this.marker.GetDataFromIndex(i, j) == FLUID)
{
var value = poisson.GetDataFromIndex(i, j).x *x.GetDataFromIndex(i, j)
+ poisson.GetDataFromIndex(i - 1, j).y *x.GetDataFromIndex(i - 1, j)
+ poisson.GetDataFromIndex(i, j).y *x.GetDataFromIndex(i + 1, j)
+ poisson.GetDataFromIndex(i, j - 1).z *x.GetDataFromIndex(i, j - 1)
+ poisson.GetDataFromIndex(i, j).z *x.GetDataFromIndex(i, j + 1);
y.SetDataToIndex(value, i, j);
}
}
}
}
void SolvePressure(int maxits, float tolerance)
{
int its;
float rNorm = FluidHelper.Infnorm(this.r);
float tol = tolerance * rNorm;
pressure.Reset();
if (rNorm == 0)
{
return;
}
ApplyPreconditioner(r, z, mField);
z.CopyTo(s);
float rho = FluidHelper.Dot(z, r);
if (rho == 0)
{
return;
}
for (its = 0; its < maxits; ++its)
{
ApplyPoisson(s, z);
float alpha = rho / FluidHelper.Dot(s, z);
FluidHelper.Increment(pressure, s, alpha);
FluidHelper.Increment(r, z, -alpha);
if (FluidHelper.Infnorm(this.r) <= tol)
{
Debug.LogFormat("pressure converged to {0} in {1} iterations\n", FluidHelper.Infnorm(this.r), its);
return;
}
ApplyPreconditioner(r, z, mField);
float rhonew = FluidHelper.Dot(z, r);
float beta = rhonew / rho;
FluidHelper.ScaleAndIncrement(s, z, beta);
rho = rhonew;
}
Debug.LogFormat("Didn't converge in pressure solve (its={0}, tol={1}, |r|={2})\n", its, tol, FluidHelper.Infnorm(this.r));
}
void ApplyPreconditioner(CellCenteredScalarGrid2D x, CellCenteredScalarGrid2D y, CellCenteredScalarGrid2D m)
{
//Maybe Incomplete Cholesky??
int i, j;
float d;
var xnx = x.DataSize.x;
var xny = x.DataSize.y;
m.Reset();
// solve L*m=x
for (j = 1; j < xny - 1; ++j)
{
for (i = 1; i < xnx - 1; ++i)
{
if (marker[i, j] == FLUID)
{
d = x[i, j] - poisson[i - 1, j].y * preconditioner[i - 1, j] * m[i - 1, j]
- poisson[i, j - 1].z * preconditioner[i, j - 1] * m[i, j - 1];
m[i, j] = preconditioner[i, j] * d;
}
}
}
// solve L'*y=m
y.Reset();
for (j = xny - 2; j > 0; --j)
{
for (i = xnx - 2; i > 0; --i)
{
if (marker[i, j] == FLUID)
{
d = m[i, j] - poisson[i, j].y * preconditioner[i, j] * y[i + 1, j]
- poisson[i, j].z * preconditioner[i, j] * y[i, j + 1];
y[i, j] = preconditioner[i, j] * d;
}
}
}
}