A Conservative Diffuse-interface Model-based Advection Equation for Numerical Simulation of Multiphase Flows

Abstract

For efficiently simulating multiphase flows with three or more phases, a conservative Allen-Cahn (AC)-type advection equation for interface is proposed on the basis of multi-phase-field model (MPFM). Based on the free-energy theory, an interface is autonomously formed as a finite volumetric zone between coexisting phases across which physical properties vary steeply but continuously. The MPFM-based AC advection equation with second-order differential diffusion term is numerically solved with use of a lattice Boltzmann method up to second order accuracy in both space and time. From a numerical benchmark test result of linear translation of three-phase interfaces in two dimensions, it is confirmed that the proposed AC equation has a potential to calculate multiphase interface advection more efficiently than the Cahn-Hilliard-type equation with fourth-order differential diffusion term.