16.5.12 Solution Method in ANSYS FLUENT

For Eulerian multiphase calculations, ANSYS FLUENT can solve the phase momentum equations, the shared pressure, and phasic volume fraction equations in a coupled and segregated fashion. The coupled solution for multiphase flows is discussed in detail in this section in the separate User's Guide. When solving the equations in a segregated manner, ANSYS FLUENT uses the phase coupled SIMPLE (PC-SIMPLE) algorithm [ 354] for the pressure-velocity coupling. PC-SIMPLE is an extension of the SIMPLE algorithm [ 264] to multiphase flows. The velocities are solved coupled by phases, but in a segregated fashion. The block algebraic multigrid scheme used by the density-based solver described in [ 371] is used to solve a vector equation formed by the velocity components of all phases simultaneously. Then, a pressure correction equation is built based on total volume continuity rather than mass continuity. Pressure and velocities are then corrected so as to satisfy the continuity constraint.

The Pressure-Correction Equation

For incompressible multiphase flow, the pressure-correction equation takes the form

where $\rho_{\rm rk}$ is the phase reference density for the $k^{\rm th}$ phase (defined as the total volume average density of phase $k$), $\vec{v}_{k}'$ is the velocity correction for the $k^{\rm th}$ phase, and $\vec{v}_{k}^*$ is the value of $\vec{v}_{k}$ at the current iteration. The velocity corrections are themselves expressed as functions of the pressure corrections.

Volume Fractions

The volume fractions are obtained from the phase continuity equations. In discretized form, the equation of the $k^{\rm th}$ volume fraction is

In order to satisfy the condition that all the volume fractions sum to one,