# Two-phase interfacial flows

This file helps setup simulations for flows of two fluids separated by an interface (i.e. immiscible fluids). It is typically used in combination with a Navier–Stokes solver.

The interface between the fluids is tracked with a Volume-Of-Fluid method. The volume fraction in fluid 1 is $f=1$ and $f=0$ in fluid 2. The densities and dynamic viscosities for fluid 1 and 2 are rho1, mu1, rho2, mu2, respectively.

``````#include "vof.h"

scalar f[], * interfaces = {f};
double rho1 = 1., mu1 = 0., rho2 = 1., mu2 = 0.;``````

Auxilliary fields are necessary to define the (variable) specific volume $\alpha =1/\rho$ as well as the cell-centered density.

``````face vector alphav[];
scalar rhov[];

event defaults (i = 0) {
α = alphav;
ρ = rhov;``````

If the viscosity is non-zero, we need to allocate the face-centered viscosity field.

``````  if (mu1 || mu2)
μ = new face vector;
}``````

The density and viscosity are defined using arithmetic averages by default. The user can overload these definitions to use other types of averages (i.e. harmonic).

``````#ifndef ρ
# define rho(f) (clamp(f,0.,1.)*(rho1 - rho2) + rho2)
#endif
#ifndef μ
# define mu(f)  (clamp(f,0.,1.)*(mu1 - mu2) + mu2)
#endif``````

We have the option of using some “smearing” of the density/viscosity jump.

``````#ifdef FILTERED
scalar sf[];
#else
# define sf f
#endif

event properties (i++) {``````

When using smearing of the density jump, we initialise sf with the vertex-average of f.

``````#ifndef sf
#if dimension <= 2
foreach()
sf[] = (4.*f[] +
2.*(f[0,1] + f[0,-1] + f[1,0] + f[-1,0]) +
f[-1,-1] + f[1,-1] + f[1,1] + f[-1,1])/16.;
#else // dimension == 3
foreach()
sf[] = (8.*f[] +
4.*(f[-1] + f[1] + f[0,1] + f[0,-1] + f[0,0,1] + f[0,0,-1]) +
2.*(f[-1,1] + f[-1,0,1] + f[-1,0,-1] + f[-1,-1] +
f[0,1,1] + f[0,1,-1] + f[0,-1,1] + f[0,-1,-1] +
f[1,1] + f[1,0,1] + f[1,-1] + f[1,0,-1]) +
f[1,-1,1] + f[-1,1,1] + f[-1,1,-1] + f[1,1,1] +
f[1,1,-1] + f[-1,-1,-1] + f[1,-1,-1] + f[-1,-1,1])/64.;
#endif
#endif

#if TREE
sf.prolongation = refine_bilinear;
boundary ({sf});
#endif

foreach_face() {
double ff = (sf[] + sf[-1])/2.;
alphav.x[] = fm.x[]/ρ(ff);
if (mu1 || mu2) {
face vector muv = μ;
muv.x[] = fm.x[]*μ(ff);
}
}
foreach()
rhov[] = cm[]*ρ(sf[]);

#if TREE
sf.prolongation = fraction_refine;
boundary ({sf});
#endif
}``````