A coupled solver approach for multiphase flow calculations on collocated grids

Paper in proceeding, 2006

Because of increasing computer speed and memory, the numerical solution of the incompressible Navier-Stokes equations by a fully coupled approach is an attractive and emerging trend in computational fluid dynamics (CFD) calculations. The main advantage of this approach is an increased robustness due to the implicit treatment of the pressure velocity coupling Although the equations describing multiphase flows appear similar to single-phase flow equations, their nature is often much more difficult due to the presence of volume fractions, large source terms, and gradients of these as well as density. This makes the requirement for a robust solving approach even more desirable. Almost all multiphase CFD solvers today are based upon standard decoupled approaches (SIMPLE, SIMPLER, PISO, fractional step, and other pressure projection methods) and most often employ a staggered variable arrangement. In this paper, momentum weighted interpolation is used to determine analytical expressions for the cell face velocities which are employed in the multiphase continuity equation in a collocated variable arrangement. A special approach is adopted for the momentum weighted interpolation to handle large source terms, volume fractions, and gradients of these. The resulting linearized equations are solved in a fully coupled manner. The fully coupled method is demonstrated on two practical multiphase cases. Firstly, the method is demonstrated simulating volume of fluid (VOF) computations of a gas-liquid flow case. Secondly, the method is demonstrated on solving the continuous part of an Euler-Lagrange gas-solid flow problem. The difficulties in the first case are large source terms and gradients of density, and in the second case the presence of volume fraction and gradients hereof, as well as source terms. The results are in accordance with results from the staggered segregated approach. Moreover, due to the collocated variable arrangement, complex geometries can be easily handeled. Both robustness and computational efficiency of this fully coupled approach are shown.