An efficient matrix factorization within the projection framework for ameliorating the surface tension time step constraint in interfacial flows

Abstract

An efficient matrix factorization approach is proposed for simulation of interfacial flows involving surface tension forces within the projection framework. The level set method is used to capture the interface of different phases and a projection based fluid solver is used for solving the variable density problem on a staggered grid. The governing equations for the two-phase flow, together with the convection equation for the interface, are organized into a matrix representation. Instead of explicitly partitioning the system or adopting non-linear iterative strategy, the system is factorized into separate equations using nested approximate LU decomposition with resort to the projection approach. Second-order temporal accuracy and implicit property are maintained throughout the decomposition. Numerical tests showed that the current scheme is second-order accurate in time, and can maintain numerical stability even when the time step is 80 times of the capillary time step constraint.