An efficient numerical model for multi-phase fluid dynamics

Abstract

This work presents some newly developed efficient numerical schemes and techniques for the dynamics of multi-phase flows. In the first part of this paper a semi-Lagrangian method for an advection equation, as an important part of our numerical model, is introduced. The scheme is constructed from a rational function and proved to be convexity preserving. It has third-order accuracy in the smooth region and possesses an oscillation suppressing property near discontinuities or steep gradients. There is no need to calculate the slope limiter to eliminate numerical oscillation as other high resolution schemes do. The paper also discusses in the second part some numerical algorithms that prove important to the establishment of an efficient and robust code for simulating the dynamics of multi-material flows, such as the calculation of a moving boundary, the unified procedure for evaluating pressure over different materials and the equivalent volume force formulations for different types of forces.