Overstability in Saturn Rings (C)

A narrow box of Saturn’s rings is simulated to study the viscous overstability. Collisions are resolved using the plane-sweep method.

It takes about 30 orbits for the overstability to occur. You can speed up the calculation by turning off the visualization. Just press d while the simulation is running. Press d again to turn it back on.

You can change the viewing angle of the camera with your mouse or by pressing the r key.

#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <math.h>
#include "rebound.h"

extern double OMEGA;
extern double OMEGAZ;

double coefficient_of_restitution(const struct reb_simulation*r, double v){
    return 0.5;
}

int main(int argc, char* argv[]){
    struct reb_simulation* r = reb_create_simulation();
    // Setup constants
    r->ri_sei.OMEGA         = 1.;
    r->ri_sei.OMEGAZ         = 3.6;
    r->dt                = 2e-3*2.*M_PI;
    double particle_r         = 1;
    double tau            = 1.64;
    r->coefficient_of_restitution     = coefficient_of_restitution;
    r->integrator            = REB_INTEGRATOR_SEI;
    r->collision            = REB_COLLISION_TREE;
    r->collision_resolve = reb_collision_resolve_hardsphere;
    r->gravity            = REB_GRAVITY_NONE;
    r->boundary            = REB_BOUNDARY_SHEAR;

    reb_configure_box(r,1.,200,5,20);
    r->nghostx = 1;     r->nghosty = 1;     r->nghostz = 0;

    // Initial conditions
    double _N = tau * r->boxsize.x * r->boxsize.y/(M_PI*particle_r *particle_r);
    while (r->N<_N){
        struct reb_particle p;
        p.x     = ((double)rand()/(double)RAND_MAX-0.5)*r->boxsize.x;
        p.y     = ((double)rand()/(double)RAND_MAX-0.5)*r->boxsize.y;
        p.z     = 10.0*((double)rand()/(double)RAND_MAX-0.5)*particle_r;
        p.vx     = 0;
        p.vy     = -1.5*p.x; // shear
        p.vz     = 0;
        p.ax     = 0; p.ay     = 0; p.az     = 0;
        p.m     = 1.;
        p.r     = particle_r;
        reb_add(r, p);
    }
    reb_integrate(r,INFINITY);
}

void heartbeat(struct reb_simulation* r){
    if (reb_output_check(r,2.*M_PI)){
        reb_output_timing(r,0);
    }
}

This example is located in the directory examples/overstability