Transport Coordinate (TC) Method for the Dynamics of Multiple Materials

Abstract

In this paper, we propose a new idea of tracking material interface. Since the regions filled with different materials at the initial time are merely transported by the velocity field, the material type at present is determined by its original location. We introduce the advection equation of the base coordinates to specify the material type, and solve this equation in the Euler framework. Thanks to the initial linear distribution, this method is free of numerical diffusion for the problems with a constant or a rigid body rotation velocity field and can produce accurate results for the general case. Moreover, it is applicable to the advection function of arbitrary distribution, for example, problems with more than two types of fluids. The new method is incorporated into a newly developed flow solver employing the semi-Lagrangian model to successfully solve the flow problems with multiple types of fluids. [S0098-2202(00)02001-0]