General mechanisms for stabilizing weakly compressible multiphase models and their applications

Abstract

The present paper analyzes three representative weakly compressible multiphase models. It is found that these models contain some identical numerical dissipation terms, pressure diffusion, and bulk viscosity terms. Numerical investigations show that these identical numerical dissipation terms interpret general mechanisms for stabilizing computations. The generality of mechanisms is reflected in (a) they are likely to present in many weakly compressible multiphase models and (b) they represent interpretable physical mechanisms. Based on those general mechanisms, many weakly compressible multiphase models can be incorporated into a general theoretical framework. And a general weakly compressible solver for multiphase flows (GWCS-MF) is proposed. It is derived from standard governing equations and can easily be applied to nonuniform meshes. Detailed numerical tests demonstrate that it can achieve good numerical stability and accuracy for challenging conditions (inviscid fluids, large density ratios, high Weber numbers, and high Reynolds numbers) and can simulate complex interface evolution well. These good performances exhibit the advantages of GWCS-MF and further validate those general mechanisms.