A central compact scheme for numerical solution of two-phase incompressible flow using Allen–Cahn phase field model

Abstract

This article presents a numerical method for the Allen–Cahn phase field model coupled with the incompressible Navier–Stokes equations for simulating two-phase incompressible flow. The numerical method is based on the artificial compressibility method with dual-time stepping technique applied to the governing equations written in conservative form. The convective terms are approximated by using an eighth-order central compact scheme with filtering while the viscous terms are approximated by a sixth-order central compact scheme. Approximate factorization-based alternating direction implicit algorithm is used to solve the discretized linear system. The effectiveness of the method is demonstrated by computing several benchmark two-phase incompressible flow problems.