A thermodynamically consistent model for two-phase incompressible flows with different densities. Derivation and efficient energy-stable numerical schemes

Abstract

In this work we use phase field ideas to derive a new thermodynamically consistent model to represent two-phase flows with different densities using an energetic variational approach. Moreover, we introduce three linear numerical schemes that decouple the computation of the system in several sub-steps in an energy-stable way. Additionally, we present several numerical results in order to show the validity of the model and the well behavior of the proposed schemes.