An ALE/embedded boundary method for two-material flow simulations

Abstract

We present a computational framework that combines an embedded boundary method and an arbitrary Lagrangian–Eulerian (ALE) method for multi-material flow computations of compressible fluids. The methodology is presented for two-material flows and one-material flow with moving boundaries, whereas the concept extends easily to multiple immiscible fluids. The proposed method is capable of handling geometrically complex material interfaces on moving grids and is suitable for multi-material flow computations in the context of ALE shock hydrodynamics. Furthermore, it can serve as the underlying framework for multi-fluid/structure interaction, where a portion of the boundary of a computational domain for a fluid mixture deforms according to the solid domain motion. Specifically, we use a variational multiscale stabilized finite element method to update the fluid state of each material, and define ghost values to enforce the transmission condition at the embedded material interface, which is captured using a level-set approach. Two different strategies to populate ghost values are considered and compared in extensive benchmark numerical tests: simple constant extrapolation and a multi-material Riemann solver, respectively.