
For Eulerian multiphase calculations, FLUENT uses the phase coupled SIMPLE (PCSIMPLE) algorithm [ 380] for the pressurevelocity coupling. PCSIMPLE is an extension of the SIMPLE algorithm [ 277] to multiphase flows. The velocities are solved coupled by phases, but in a segregated fashion. The block algebraic multigrid scheme used by the densitybased solver described in [ 395] 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 PressureCorrection Equation
For incompressible multiphase flow, the pressurecorrection equation takes the form
(23.5130) 
where is the phase reference density for the phase (defined as the total volume average density of phase ), is the velocity correction for the phase, and is the value of 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 volume fraction is
In order to satisfy the condition that all the volume fractions sum to one,