A solution adaptive simulation of compressible multi-fluid flows with general equation of state

Abstract

The unstructured quadrilateral mesh-based solution adaptive method is proposed in this article for simulation of compressible multi-fluid flows with a general form of equation of state (EOS). The five equation model (J. Comput. Phys. 2002; 118:577-616) is employed to describe the compressible multi-fluid flows. To preserve the oscillation-free property of velocity and pressure across the interface, the non-conservative transport equation is discretized in a compatible way of the HLLC scheme for the conservative Euler equations on the unstructured quadrilateral cell-based adaptive mesh. Five numerical examples, including an interface translation problem, a shock tube problem with two fluids, a solid impact problem, a two-dimensional Riemann problem and a bubble explosion under free surface, are used to examine its performance in solving the various compressible multi-fluid flow problems with either the same types of EOS or different types of EOS. The results are compared with those calculated by the following methods: the method with ROE scheme (J. Comput. Phys. 2002; 118:577-616), the seven equation model (J. Comput. Phys. 1999; 150:425-467), Shyue's fluid-mixture model (J. Comput. Phys. 2001; 171:678-707) or the method in Liu et al. (Comp. Fluids 2001; 30:315-337). The comparisons for the test problems show that the proposed method seems to be more accurate than the method in Allaire et al. (J. Comput. Phys. 2002; 118:577-616) or the seven-equation model (J. Comput. Phys. 1999; 150:425-467). They also show that it can adaptively and accurately solve these compressible multi-fluid problems and preserve the oscillation-free property of pressure and velocity across the material interface. © 2010 John Wiley & Sons, Ltd.