# sandbox/bugs/bug_karman_rho.c

I am using Ubuntu 20.04LTS and I updated Basilisk before this.

I tried manually setting the density to 1 (which I think is the default value) in examples/karman.c and including it in the expression for the viscosity, but I experinced a problem.

I added to the top of the file:

const double rho_value = 1.;

const scalar rhoc[] = rho_value;

and to main():

rho = rhoc;

In “event properties”, when I added rhoc[] to the expression for the viscosity:

muv.x[] = fm.x[]*rhoc[]*0.125/Reynolds;

I think I did not notice any difference. But, when I added rho[]:

muv.x[] = fm.x[]*rho[]*0.125/Reynolds;

I think that the difference is obvious.

According to this, “rho” is not equal to “rhoc” and hence is not equal to 1? Also, the value for the density that I manually set is different than the default one?

I also added a movie for “rho”. I also saw artefacts similar to the ones I previously reported in:

http://basilisk.fr/sandbox/bugs/bug_karman.c

so maybe the artefacts in “omega” are caused by artefacts in “rho”.

Did I make a mistake or did I encounter a bug? Based on this and on the previous report about setting the viscosity:

http://basilisk.fr/sandbox/bugs/porous3D_mu.c

results obtained with Basilisk could be questionable. It looks to me that both the density and the viscosity cannot be set to desired values.

# Bénard–von Kármán Vortex Street for flow around a cylinder at Re=160

An example of 2D viscous flow around a simple solid boundary. Fluid is injected to the left of a channel bounded by solid walls with a slip boundary condition. A passive tracer is injected in the bottom half of the inlet.

We use the centered Navier-Stokes solver, with embedded boundaries and advect the passive tracer *f*.

```
#include "embed.h"
#include "navier-stokes/centered.h"
// #include "navier-stokes/perfs.h"
#include "tracer.h"
scalar f[];
scalar * tracers = {f};
double Reynolds = 160.;
int maxlevel = 9;
face vector muv[];
const double rho_value = 1.; //ADDED///////////////////////////////////////////////////////////////
const scalar rhoc[] = rho_value; //ADDED///////////////////////////////////////////////////////////
```

The domain is eight units long, centered vertically.

```
int main() {
L0 = 8.;
origin (-0.5, -L0/2.);
N = 512;
mu = muv;
rho = rhoc; //ADDED//////////////////////////////////////////////////////////////////////////////
```

When using bview we can interactively control the Reynolds number and maximum level of refinement.

```
display_control (Reynolds, 10, 1000);
display_control (maxlevel, 6, 12);
run();
}
```

We set a constant viscosity corresponding to a Reynolds number of 160, based on the cylinder diameter (0.125) and the inflow velocity (1).

```
event properties (i++)
{
foreach_face()
// muv.x[] = fm.x[]*0.125/Reynolds; //DEFAULT///////////////////////////////////////////////////
// muv.x[] = fm.x[]*rhoc[]*0.125/Reynolds; //OPTION_1///////////////////////////////////////////
muv.x[] = fm.x[]*rho[]*0.125/Reynolds; //OPTION_2////////////////////////////////////////////
}
```

The fluid is injected on the left boundary with a unit velocity. The tracer is injected in the lower-half of the left boundary. An outflow condition is used on the right boundary.

```
u.n[left] = dirichlet(1.);
p[left] = neumann(0.);
pf[left] = neumann(0.);
f[left] = dirichlet(y < 0);
u.n[right] = neumann(0.);
p[right] = dirichlet(0.);
pf[right] = dirichlet(0.);
```

The top and bottom walls are free-slip and the cylinder is no-slip.

```
u.n[embed] = fabs(y) > 0.25 ? neumann(0.) : dirichlet(0.);
u.t[embed] = fabs(y) > 0.25 ? neumann(0.) : dirichlet(0.);
event init (t = 0)
{
```

The domain is the intersection of a channel of width unity and a circle of diameter 0.125.

```
solid (cs, fs, intersection (intersection (0.5 - y, 0.5 + y),
sq(x) + sq(y) - sq(0.125/2.)));
```

We set the initial velocity field.

```
foreach()
u.x[] = cs[] ? 1. : 0.;
}
```

We check the number of iterations of the Poisson and viscous problems.

```
event logfile (i++)
fprintf (stderr, "%d %g %d %d\n", i, t, mgp.i, mgu.i);
```

We produce animations of the vorticity and tracer fields…

```
event movies (i += 4; t <= 15.)
{
scalar omega[], m[];
vorticity (u, omega);
foreach()
m[] = cs[] - 0.5;
output_ppm (omega, file = "vort.mp4", box = {{-0.5,-0.5},{7.5,0.5}},
min = -10, max = 10, linear = true, mask = m);
output_ppm (f, file = "f.mp4", box = {{-0.5,-0.5},{7.5,0.5}},
linear = false, min = 0, max = 1, mask = m);
output_ppm (rho, file = "rho.mp4", box = {{-0.5,-0.5},{7.5,0.5}}, //ADDED////////////////////////
min = 0, max = 2, linear = true, mask = m); //ADDED//////////////////////////////////
}
```

We adapt according to the error on the embedded geometry, velocity and tracer fields.

```
event adapt (i++) {
adapt_wavelet ({cs,u,f}, (double[]){1e-2,3e-2,3e-2,3e-2}, maxlevel, 4);
}
```