opensim/trunk/OpenSim/Region/Terrain.BasicTerrain/libTerrainBSD/Channel/Manipulators/NavierStokes.cs

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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);
        }
    }
}