[suhailepm]

I'm studying the Eulerian multiphase flow modeling. In FLUENT, the Eulerian model for multiphase flow adopts the Phase Coupled SIMPLE (PC-SIMPLE) algorithm. I want to know details for the PC-SIMPLE algorithm. However I have no access to the article S. A. Vasquez and V. A. Ivanov, “A Phase Coupled Method for Solving Multiphase Problem on Unstructured Meshes,” Fluids Engineering Division Summer Meeting, ASME, Boston, 11-15 June 2000. So would you give me a detailed presentation on the algorithm?

[mprinkey]

Phase-coupling is done per velocity component but across all phases. The momentum transport equations are built as normal with SIMPLE...lagging y- and z-components while solving the x-momentum equation, etc. With FLUENT, it is actually the phase mass fluxes at the faces that are lagged, but it is conceptually the same thing. The big difference with PC-SIMPLE is that there are coupling terms among the phases. The most obvious is drag.

To be specific, assume that we have two phases 1 and 2. u1 and u2 are the x-velocity components of each phase.

The momentum equations will be:

(A1-c).u1 + c u2 = b1

(A2-c).u2 +c u1= b2

where A1 and A2 are the normal SIMPLE momentum matrices, b1 and b2 are the normal RHSs, and c is a row vector of drag coefficients. This is a coupled system of equations that FLUENT solves together--in this case, unknown count is 2*Ncells. So, the solution is still SIMPLE--segregated by velocity component--but is coupled by phase.

This same technique can be applied to other transport equations like heat transfer. I'm sorry though, I don't remember the particulars of the pressure correction (if any) that needed to be made.

[suhailepm]

My descretized equation contains n+1 terms (time step) of velocity and void fraction on the LHS of the multiphase momentum equation. Is there any method to calculate the n+1 terms for the void fraction seperately.