internalwacesAMR.c

Internal waves using an adaptive grid

Internal waves using an adaptive grid

Similar to the succesful simulation using the multigrid we now want to use adaptive mesh refinement for the simulation of internal waves.

Numerical set-up

The set-up is very similar to the multigrid simulation. This run is altered so that it uses an adaptive quadtree grid.

#include "navier-stokes/centered.h"
#include "tracer.h"
#include "view.h"  //For cells()
#include "navier-stokes/perfs.h"

scalar b[], * tracers = {b};
face vector av[];
double sqN = 1, omega;

b[top]    = neumann (sqN);
b[bottom] = neumann (-sqN);

int main() {
  omega = sqrt(1./2.);
  a = av;
  L0 = 30;
  X0 = Y0 = -L0/2;
  TOLERANCE = 1e-4;
  DT = 0.2/omega;
  p.prolongation = p.refine = refine_linear; //3rd-order interpolation (vertical)
  N = 256;
  run();
}

event init (t = 0) {
  foreach()
    b[] = sqN*y;
  boundary ({b});
}

event acceleration (i++) {
  coord del = {0, 1};
  foreach_face()
    av.x[] = del.x*((b[] + b[-1])/2 +
		   0.1*(sin(omega*t)*((sq(x) + sq(y)) < 1)));
}

event output (t += 0.5; t <= 75) {
  scalar grb[];
  foreach() {
    grb[] = 0;
    foreach_dimension()
      grb[] += sq((b[1] - b[-1])/(2*Delta));
    grb[] = sqrt(grb[]);
  }
  boundary ({grb});
  squares ("grb", linear = true);
  cells();
  save ("mov.mp4");
}

Adaptivity

Inspired by the equations of motion, we decide to refine upon the discrete representation for the byoyancy and velocity-component fields.

event adapt (i++)
  adapt_wavelet ({b, u}, (double[]){0.01, 0.01, 0.01}, 8, 4);

Results

Waves and grid

set xlabel 'iteration'
set ylabel 'mgp.i / mgp.nrelax'
plot 'perfs' u 3, '' u 4