A decoupled algorithm for fluid-fluid interaction at small viscosity

Abstract

In this paper, a decoupled finite element algorithm is proposed for solving the fluid-fluid interaction at small viscosity. The basic idea of the presented algorithm is to first solve an artificial viscosity elliptic problem with explicit treatment for nonlinear interface conditions, and then solve an artificial viscosity Stokes problem to correct the previous solution. The unconditional stability is established and the efficiency is illustrated by some numerical tests.