An ALE‐based finite element strategy for modeling compressible two‐phase flows

Abstract

AbstractIn this work, we develop a numerical strategy for solving two‐phase immiscible compressible fluid flows in a general arbitrary Lagrangian–Eulerian framework. The interpolation functions for the field variables are chosen so as to produce a stable numerical formulation. We model one of the fluids in a Lagrangian setting and use a conforming mesh moving with it which circumvents the need of solving an additional diffusion equation to track or construct the interface. The discontinuity in the pressure field across the interface is accurately modeled using the dummy‐node technique. This technique yields a sharp and accurate representation of the interface and in turn a correct computation of the surface tension forces. We present a variational form of the governing equations including the surface tension effect and their exact linearization. Various benchmark examples are presented to illustrate the good performance and good coarse‐mesh accuracy of the proposed scheme.