An energy-splitting high order numerical method for multi-material flows

TL;DR

This paper introduces a novel energy-splitting Godunov-type numerical scheme based on a reduced Baer-Nunziato model, effectively simulating multi-material flows and addressing challenges like stability and positivity in shock interactions.

Contribution

It presents a new reduced BN model and a second-order energy-splitting scheme that improves simulation accuracy and stability for multi-material flow problems.

Findings

Effective simulation of kinetic energy exchange at interfaces

Excellent performance in shock-interface and shock-bubble interactions

Stable and positive volume fraction computations

Abstract

This chapter deals with multi-material flow problems by a kind of effective numerical methods, based on a series of reduced forms of the Baer-Nunziato (BN) model. Numerical simulations often face a host of difficult challenges, typically including the volume fraction positivity and stability of multi-material shocks. To cope with these challenges, we propose a new non-oscillatory {\em energy-splitting} Godunov-type scheme for computing multi-fluid flows in the Eulerian framework. A novel reduced version of the BN model is introduced as the basis for the energy-splitting scheme. In comparison with existing two-material compressible flow models obtained by reducing the BN model in the literature, it is shown that our new reduced model can simulate the kinetic energy exchange around material interfaces very effectively. Then a second-order accurate extension of the energy-splitting Godunov-type scheme is made using the generalized Riemann problem (GRP) solver. Numerical experiments are carried out for the shock-interface interaction, shock-bubble interaction and the Richtmyer-Meshkov instability problems, which demonstrate the excellent performance of this type of schemes.