写一个三维硬球碰撞模型计算粒子碰撞后速度的udf

以下是一个简单的三维硬球碰撞模型的 UDF。这个 UDF 模拟了两个球体的弹性碰撞，并计算了它们之间的相对速度和碰撞后的速度。

#include "udf.h"

DEFINE_CG_MOTION(ball_motion, dt, vel, omega, time, dtime)
{
    real x[3], v[3], r, m, Ekin;

    /* Get the position and velocity of the ball */
    x[0] = RP_ORIGIN_X(rp);
    x[1] = RP_ORIGIN_Y(rp);
    x[2] = RP_ORIGIN_Z(rp);

    v[0] = vel[0];
    v[1] = vel[1];
    v[2] = vel[2];

    /* Get the mass and radius of the ball */
    m = RP_MASS(rp);
    r = RP_RADIUS(rp);

    /* Calculate the kinetic energy of the ball */
    Ekin = 0.5 * m * (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);

    /* Check for collisions with other balls */
    Thread *t = RP_THREAD(rp);
    cell_t c = RP_CELL(rp);
    int i, j, id;
    real x2[3], v2[3], r2, m2, Ekin2, R, Vrel, Vrel_n, Vrel_t, vn[3], vt[3], v2f[3];
    Thread *t2;
    cell_t c2;

    /* Loop over all cells in the domain */
    for (i = 0; i < N_CELLS; i++)
    {
        /* Get the cell id */
        id = cell_zone_id[i];

        /* Loop over all particles in the cell */
        begin_c_loop(c, t)
        {
            /* Get the position and velocity of the ball */
            x[0] = RP_ORIGIN_X(rp);
            x[1] = RP_ORIGIN_Y(rp);
            x[2] = RP_ORIGIN_Z(rp);

            v[0] = vel[0];
            v[1] = vel[1];
            v[2] = vel[2];

            /* Get the mass and radius of the ball */
            m = RP_MASS(rp);
            r = RP_RADIUS(rp);

            /* Calculate the kinetic energy of the ball */
            Ekin = 0.5 * m * (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);

            /* Loop over all particles in the cell */
            begin_c_loop(c2, t2)
            {
                /* Check if the particle is not the same as the current one */
                if (i != j)
                {
                    /* Get the position and velocity of the other ball */
                    x2[0] = RP_ORIGIN_X(rp);
                    x2[1] = RP_ORIGIN_Y(rp);
                    x2[2] = RP_ORIGIN_Z(rp);

                    v2[0] = vel[0];
                    v2[1] = vel[1];
                    v2[2] = vel[2];

                    /* Get the mass and radius of the other ball */
                    m2 = RP_MASS(rp);
                    r2 = RP_RADIUS(rp);

                    /* Calculate the kinetic energy of the other ball */
                    Ekin2 = 0.5 * m2 * (v2[0]*v2[0] + v2[1]*v2[1] + v2[2]*v2[2]);

                    /* Calculate the distance between the balls */
                    R = sqrt(pow(x[0]-x2[0],2) + pow(x[1]-x2[1],2) + pow(x[2]-x2[2],2));

                    /* Check if the balls are colliding */
                    if (R < r+r2)
                    {
                        /* Calculate the relative velocity between the balls */
                        Vrel = sqrt(pow(v[0]-v2[0],2) + pow(v[1]-v2[1],2) + pow(v[2]-v2[2],2));

                        /* Calculate the normal and tangential components of Vrel */
                        vn[0] = (v2[0]-v[0])*(x2[0]-x[0])/R;
                        vn[1] = (v2[1]-v[1])*(x2[1]-x[1])/R;
                        vn[2] = (v2[2]-v[2])*(x2[2]-x[2])/R;

                        vt[0] = v[0] - vn[0];
                        vt[1] = v[1] - vn[1];
                        vt[2] = v[2] - vn[2];

                        /* Calculate the magnitude of the normal component of Vrel */
                        Vrel_n = sqrt(pow(vn[0],2) + pow(vn[1],2) + pow(vn[2],2));

                        /* Calculate the magnitude of the tangential component of Vrel */
                        Vrel_t = sqrt(pow(vt[0],2) + pow(vt[1],2) + pow(vt[2],2));

                        /* Calculate the new velocity of the ball */
                        v2f[0] = (v[0] - vn[0]) + (v2[0] - vn[0]);
                        v2f[1] = (v[1] - vn[1]) + (v2[1] - vn[1]);
                        v2f[2] = (v[2] - vn[2]) + (v2[2] - vn[2]);

                        /* Update the velocity of the ball */
                        vel[0] = v2f[0];
                        vel[1] = v2f[1];
                        vel[2] = v2f[2];
                    }
                }
            }
        }
    }
}

注意，这个 UDF 只是一个简单的模型，只考虑了两个球体之间的碰撞，并没有考虑其他因素，如摩擦、空气阻力等。在实际应用中，需要根据具体情况进行修改和优化。