A coupled solver approach for multiphase flow problems

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 validated with the lid driven cavity data of Ghia (1982), and 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.

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