On the computation of multi-material flows using ALE formulation

Computation of compressible multi-fluid flows with a general equation of state using interface tracking and moving grid approach is discussed in this paper. The AUSM+, HLLC, and Godunov methods are presented and implemented in the context of arbitrary Lagrangian–Eulerian formulation for solving the unsteady compressible Euler equations. The developed methods are fully conservative, and used to compute a variety of multi-component flow problems, where the equations of state can be drastically different and stiff. Numerical results indicate that both ALE HLLC and Godunov schemes demonstrate their simplicity and robustness for solving such multi-phase flow problems, and yet ALE AUSM+ scheme exhibits strong oscillations around material interfaces even using a first order monotone scheme and therefore is not suitable for this class of problems.