16.5 MultiFluid

The multiFluid implementation of the equation of state is meant to complement the volume-of-fluid (VOF) hydrodynamics solver for capturing material interfaces described in sec:vof. The EoS operates as previously described for any cells that are purely a single fluid. In mixed cells the EoS is called separately on each of the components, here labelled by $\alpha$ , for the state $(f^\alpha \rho^\alpha,f^\alpha E^\alpha,P^\alpha)$ . After a call to the EoS it is possible that $P^\alpha\neq P^\beta$ . In order to maintain the mechanical equilibrium assumed in VOF the volume fractions, $f^\alpha$ need to be relaxed until the two pressures equilibriate. First an average pressure is computed,

$\displaystyle P = \frac{\sum_\alpha f^\alpha/\gamma^\alpha}{\sum_\alpha \frac{f^\alpha}{P^\alpha \gamma^\alpha}},$

(16.27)

and the component fluid states are adjusted as

$\displaystyle \Delta f^\alpha$	$\displaystyle = \frac{f^\alpha}{\gamma^\alpha}(1 - \frac{P}{P^\alpha})$	(16.28)
$\displaystyle f^\alpha$	$\displaystyle \leftarrow f^\alpha + \Delta f^\alpha$	(16.29)
$\displaystyle \rho^\alpha$	$\displaystyle \leftarrow \frac{f^\alpha \rho^\alpha}{f^\alpha + \Delta f^\alpha}$	(16.30)
$\displaystyle f^\alpha\rho^\alpha E^\alpha$	$\displaystyle \leftarrow f^\alpha\rho^\alpha E^\alpha - P\Delta f^\alpha.$	(16.31)

In the above $\gamma^\alpha$ is the adiabatic index for fluid $\alpha$ as in other EoS implementations,

$\displaystyle \gamma^\alpha \equiv \frac{\rho^\alpha c^2_\alpha}{P^\alpha}.$

(16.32)

An equivalent single fluid state may also be parameterized in mixed cells as

$\displaystyle \rho$	$\displaystyle = \sum f^\alpha \rho^\alpha$	(16.33)
$\displaystyle E$	$\displaystyle = \sum f^\alpha \rho^\alpha E^\alpha$	(16.34)
$\displaystyle \gamma$	$\displaystyle = \left( \sum \frac{f^\alpha}{\gamma^\alpha} \right)^{-1}.$	(16.35)