On the total mass conservation and the volume preservation in the diffuse interface method

Abstract In this paper a diffuse interface method which can conserve the total mass and preserve the volume of each phase is proposed for simulating the incompressible two-phase flows. The basic idea of this method is that a source term with two free parameters is introduced into the Cahn-Hilliard equation. The two free parameters are determined by the mass conservation law and the volume preservation property. In the numerical implementation, the multiple-relaxation-time lattice Boltzmann scheme is used to solve the modified Cahn-Hilliard equation and the velocity-based Navier-Stokes equations. To verify the proposed method, several numerical examples are simulated. The numerical results show that the present method can preserve the total mass and the volume of each phase at the same time. The numerical results are also in good agreement with the analytical solutions and the previous results.