sandbox/bugs/tracer_noise.c

    Possible bug with tracer + embedded boundaries + two phases (miscible)

    There is a strange behaviour where “noise” appears on the tracer field when a solid is added to this scenario.

    #include "embed.h"
#include "navier-stokes/centered.h"
#include "navier-stokes/perfs.h"
#include "tracer.h"

scalar f[];
scalar * tracers = {f};

    This following part was taken from two-phase-generic.h, and only the portion related to the viscosity computation on faces is included. If the entire file instead, convergence issues appear immediately (when embedded boundaries are present). This could be a separate issue or not (seems related to alpha field change from what I’ve seen).

    #if 1
double mu1 = 0., mu2 = 0.;

event defaults (i = 0)
{
	if (mu1 || mu2)
		mu = new face vector;
}

#ifndef mu
# define mu(f)  (clamp(f,0.,1.)*(mu1 - mu2) + mu2)
#endif

#define sf f
event properties (i++)
{
	foreach_face() {
		double ff = (sf[] + sf[-1])/2.;
		if (mu1 || mu2) {
			face vector muv = mu;
			muv.x[] = fm.x[]*mu(ff);
		}
	}
}
#endif

//#include "two-phase-generic.h"

    The setup for the scenario is below:

    int maxlevel = 5;

//Parameters
double U1 = 0.001;
double H1 = 0.000249999;
double tend =  1.5;

double f_error = 1e-2;
double u_error;


u.n[left]  = dirichlet(U1*cs[]);
u.t[left]  = dirichlet(0.);
p[left]    = neumann(0.);
pf[left]   = neumann(0.);

f[left] = 1.;

u.n[right] = neumann(0.);
u.t[right] = neumann(0.);
p[right]   = dirichlet(0.);
pf[right]  = dirichlet(0.);

u.n[embed] = dirichlet(0.);
u.t[embed] = dirichlet(0.);

    A boolean variable embSolid is used to execute the case with and without the solid:

    bool embSolid = true;
int main()
{
	L0 = 5.*H1;
	origin (0.,-L0/2.);
	N = 64;
	DT = 0.01;
	u_error = 0.05*U1;

	mu1 = 0.0966;
	mu2 = 0.0023;
	
	run();
	embSolid = false;
	run();
}

event end (t=tend)
{}

event init (t = 0)
{

    If the solid is added, the “noise” on the tracer is present (also the statistic mgu.i for the viscosity grows considerably). Otherwise the effect is not present:

    	if (embSolid){
		solid (cs, fs,  intersection(-y+H1*2. ,+y+H1*2.));
		fractions_cleanup (cs, fs, 0.0001);
	}
}

    The adaptive mesh refinement used is below. Completely removing adaptive mesh refinement also makes the effect disappear:

    event adapt (i++) {
	if(embSolid)
		adapt_wavelet ({cs,u,f}, (double[]){1e-3,u_error,u_error,f_error}, maxlevel);
	else
		adapt_wavelet ({u,f}, (double[]){u_error,u_error,f_error}, maxlevel);
}

    Output generation:

    event output (t = 1.2){
	if(embSolid)
		output_ppm(f, file = "tracer_noise_1.png", n = 400, map=cool_warm, spread=3);
	else
		output_ppm(f, file = "tracer_noise_2.png", n = 400, map=cool_warm, spread=3);
}

    Results obtained in both cases

    The results obtained for each setup are shown below:

    This image shows how the tracer is affected and a noise appears when the solid is present.

    This image shows how the tracer is affected and a “noise” appears when the solid is present.

    This image shows the result obtained when the solid is not present and the tracer diffuses freely.

    This image shows the result obtained when the solid is not present and the tracer diffuses freely.