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/*
* Copyright (c) Contributors, http://opensimulator.org/
* See CONTRIBUTORS.TXT for a full list of copyright holders.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the OpenSim Project nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE DEVELOPERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE CONTRIBUTORS BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
*/
namespace libTerrain
{
partial class Channel
{
// Navier Stokes Algorithms ported from
// "Real-Time Fluid Dynamics for Games" by Jos Stam.
// presented at GDC 2003.
// Poorly ported from C++. (I gave up making it properly native somewhere after nsSetBnd)
private static int nsIX(int i, int j, int N)
{
return ((i) + (N + 2)*(j));
}
private static void nsSwap(ref double x0, ref double x)
{
double tmp = x0;
x0 = x;
x = tmp;
}
private static void nsSwap(ref double[] x0, ref double[] x)
{
double[] tmp = x0;
x0 = x;
x = tmp;
}
private void nsAddSource(int N, ref double[] x, ref double[] s, double dt)
{
int i;
int size = (N + 2)*(N + 2);
for (i = 0; i < size; i++)
{
x[i] += dt*s[i];
}
}
private void nsSetBnd(int N, int b, ref double[] x)
{
int i;
for (i = 0; i <= N; i++)
{
x[nsIX(0, i, N)] = b == 1 ? -x[nsIX(1, i, N)] : x[nsIX(1, i, N)];
x[nsIX(0, N + 1, N)] = b == 1 ? -x[nsIX(N, i, N)] : x[nsIX(N, i, N)];
x[nsIX(i, 0, N)] = b == 2 ? -x[nsIX(i, 1, N)] : x[nsIX(i, 1, N)];
x[nsIX(i, N + 1, N)] = b == 2 ? -x[nsIX(i, N, N)] : x[nsIX(i, N, N)];
}
x[nsIX(0, 0, N)] = 0.5f*(x[nsIX(1, 0, N)] + x[nsIX(0, 1, N)]);
x[nsIX(0, N + 1, N)] = 0.5f*(x[nsIX(1, N + 1, N)] + x[nsIX(0, N, N)]);
x[nsIX(N + 1, 0, N)] = 0.5f*(x[nsIX(N, 0, N)] + x[nsIX(N + 1, 1, N)]);
x[nsIX(N + 1, N + 1, N)] = 0.5f*(x[nsIX(N, N + 1, N)] + x[nsIX(N + 1, N, N)]);
}
private void nsLinSolve(int N, int b, ref double[] x, ref double[] x0, double a, double c)
{
int i, j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
x[nsIX(i, j, N)] = (x0[nsIX(i, j, N)] + a*
(x[nsIX(i - 1, j, N)] +
x[nsIX(i + 1, j, N)] +
x[nsIX(i, j - 1, N)] + x[nsIX(i, j + 1, N)])
)/c;
}
}
nsSetBnd(N, b, ref x);
}
private void nsDiffuse(int N, int b, ref double[] x, ref double[] x0, double diff, double dt)
{
double a = dt*diff*N*N;
nsLinSolve(N, b, ref x, ref x0, a, 1 + 4*a);
}
private void nsAdvect(int N, int b, ref double[] d, ref double[] d0, ref double[] u, ref double[] v, double dt)
{
int i, j, i0, j0, i1, j1;
double x, y, s0, t0, s1, t1, dt0;
dt0 = dt*N;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
x = i - dt0*u[nsIX(i, j, N)];
y = j - dt0*v[nsIX(i, j, N)];
if (x < 0.5)
x = 0.5;
if (x > N + 0.5)
x = N + 0.5;
i0 = (int) x;
i1 = i0 + 1;
if (y < 0.5)
y = 0.5;
if (y > N + 0.5)
y = N + 0.5;
j0 = (int) y;
j1 = j0 + 1;
s1 = x - i0;
s0 = 1 - s1;
t1 = y - j0;
t0 = 1 - t1;
d[nsIX(i, j, N)] = s0*(t0*d0[nsIX(i0, j0, N)] + t1*d0[nsIX(i0, j1, N)]) +
s1*(t0*d0[nsIX(i1, j0, N)] + t1*d0[nsIX(i1, j1, N)]);
}
}
nsSetBnd(N, b, ref d);
}
public void nsProject(int N, ref double[] u, ref double[] v, ref double[] p, ref double[] div)
{
int i, j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
div[nsIX(i, j, N)] = -0.5*
(u[nsIX(i + 1, j, N)] - u[nsIX(i - 1, j, N)] + v[nsIX(i, j + 1, N)] -
v[nsIX(i, j - 1, N)])/N;
p[nsIX(i, j, N)] = 0;
}
}
nsSetBnd(N, 0, ref div);
nsSetBnd(N, 0, ref p);
nsLinSolve(N, 0, ref p, ref div, 1, 4);
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
u[nsIX(i, j, N)] -= 0.5*N*(p[nsIX(i + 1, j, N)] - p[nsIX(i - 1, j, N)]);
v[nsIX(i, j, N)] -= 0.5*N*(p[nsIX(i, j + 1, N)] - p[nsIX(i, j - 1, N)]);
}
}
nsSetBnd(N, 1, ref u);
nsSetBnd(N, 2, ref v);
}
private void nsDensStep(int N, ref double[] x, ref double[] x0, ref double[] u, ref double[] v, double diff,
double dt)
{
nsAddSource(N, ref x, ref x0, dt);
nsSwap(ref x0, ref x);
nsDiffuse(N, 0, ref x, ref x0, diff, dt);
nsSwap(ref x0, ref x);
nsAdvect(N, 0, ref x, ref x0, ref u, ref v, dt);
}
private void nsVelStep(int N, ref double[] u, ref double[] v, ref double[] u0, ref double[] v0, double visc,
double dt)
{
nsAddSource(N, ref u, ref u0, dt);
nsAddSource(N, ref v, ref v0, dt);
nsSwap(ref u0, ref u);
nsDiffuse(N, 1, ref u, ref u0, visc, dt);
nsSwap(ref v0, ref v);
nsDiffuse(N, 2, ref v, ref v0, visc, dt);
nsProject(N, ref u, ref v, ref u0, ref v0);
nsSwap(ref u0, ref u);
nsSwap(ref v0, ref v);
nsAdvect(N, 1, ref u, ref u0, ref u0, ref v0, dt);
nsAdvect(N, 2, ref v, ref v0, ref u0, ref v0, dt);
nsProject(N, ref u, ref v, ref u0, ref v0);
}
private void nsBufferToDoubles(ref double[] dens, int N, ref double[,] doubles)
{
int i;
int j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
doubles[i - 1, j - 1] = dens[nsIX(i, j, N)];
}
}
}
private void nsDoublesToBuffer(double[,] doubles, int N, ref double[] dens)
{
int i;
int j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
dens[nsIX(i, j, N)] = doubles[i - 1, j - 1];
}
}
}
private void nsSimulate(int N, int rounds, double dt, double diff, double visc)
{
int size = (N*2)*(N*2);
double[] u = new double[size]; // Force, X axis
double[] v = new double[size]; // Force, Y axis
double[] u_prev = new double[size];
double[] v_prev = new double[size];
double[] dens = new double[size];
double[] dens_prev = new double[size];
nsDoublesToBuffer(map, N, ref dens);
nsDoublesToBuffer(map, N, ref dens_prev);
for (int i = 0; i < rounds; i++)
{
u_prev = u;
v_prev = v;
dens_prev = dens;
nsVelStep(N, ref u, ref v, ref u_prev, ref v_prev, visc, dt);
nsDensStep(N, ref dens, ref dens_prev, ref u, ref v, diff, dt);
}
nsBufferToDoubles(ref dens, N, ref map);
}
/// <summary>
/// Performs computational fluid dynamics on a channel
/// </summary>
/// <param name="rounds">The number of steps to perform (Recommended: 20)</param>
/// <param name="dt">Delta Time - The time between steps (Recommended: 0.1)</param>
/// <param name="diff">Fluid diffusion rate (Recommended: 0.0)</param>
/// <param name="visc">Fluid viscosity (Recommended: 0.0)</param>
public void navierStokes(int rounds, double dt, double diff, double visc)
{
nsSimulate(h, rounds, dt, diff, visc);
}
public void navierStokes(int rounds, double dt, double diff, double visc, ref double[,] uret, ref double[,] vret)
{
int N = h;
int size = (N*2)*(N*2);
double[] u = new double[size]; // Force, X axis
double[] v = new double[size]; // Force, Y axis
double[] u_prev = new double[size];
double[] v_prev = new double[size];
double[] dens = new double[size];
double[] dens_prev = new double[size];
nsDoublesToBuffer(map, N, ref dens);
nsDoublesToBuffer(map, N, ref dens_prev);
for (int i = 0; i < rounds; i++)
{
u_prev = u;
v_prev = v;
dens_prev = dens;
nsVelStep(N, ref u, ref v, ref u_prev, ref v_prev, visc, dt);
nsDensStep(N, ref dens, ref dens_prev, ref u, ref v, diff, dt);
}
nsBufferToDoubles(ref u, N, ref uret);
nsBufferToDoubles(ref v, N, ref vret);
nsBufferToDoubles(ref dens, N, ref map);
}
}
}
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