/**
# Momentum-conserving formulation for two-phase interfacial flows
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 "all-mach.h"
#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 $\alpha=1/\rho$ and average viscosity $\mu$ (on faces) as well
as the cell-centered density. */
face vector alphav[], muv[];
scalar rhov[];
event defaults (i = 0) {
alpha = alphav;
rho = rhov;
mu = muv;
}
/**
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 rho
# define rho(f) (clamp(f,0,1)*(rho1 - rho2) + rho2)
#endif
#ifndef mu
# define mu(f) (clamp(f,0,1)*(mu1 - mu2) + mu2)
#endif
event properties (i++) {
// fixme: metric
foreach()
rhov[] = rho(f[]);
boundary ({rhov});
foreach_face () {
alphav.x[] = 2./(rhov[] + rhov[-1]);
double ff = (f[] + f[-1])/2.;
muv.x[] = fm.x[]*mu(ff);
}
boundary ((scalar *){muv});
}
/**
We overload the *vof()* event to transport consistently the volume
fraction and the momentum of each phase. */
static scalar * interfaces1 = NULL;
event vof (i++) {
/**
We split the total momentum $q$ into its two components $q1$ and
$q2$ associated with $f$ and $1 - f$ respectively. */
vector q1 = q, q2[];
foreach()
foreach_dimension() {
double u = q.x[]/rho(f[]);
q1.x[] = f[]*rho1*u;
q2.x[] = (1. - f[])*rho2*u;
}
boundary ((scalar *){q1,q2});
/**
Momentum $q2$ is associated with $1 - f$, so we set the *inverse*
attribute to *true*. We use (strict) minmod slope limiting for all
components. */
theta = 1.;
foreach_dimension() {
q2.x.inverse = true;
q1.x.gradient = q2.x.gradient = minmod2;
}
/**
We associate the transport of $q1$ and $q2$ with $f$ and transport
all fields consistently using the VOF scheme. */
scalar * tracers = f.tracers;
f.tracers = list_concat (tracers, (scalar *){q1, q2});
vof_advection ({f}, i);
free (f.tracers);
f.tracers = tracers;
/**
We recover the total momentum. */
foreach()
foreach_dimension()
q.x[] = q1.x[] + q2.x[];
boundary ((scalar *){q});
/**
We set the list of interfaces to NULL so that the default *vof()*
event does nothing (otherwise we would transport $f$ twice). */
interfaces1 = interfaces, interfaces = NULL;
}
/**
We set the list of interfaces back to its default value. */
event tracer_advection (i++) {
interfaces = interfaces1;
}
/**
## See also
* [Two-phase interfacial flows](two-phase.h)
*/