The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas-gas and gas-water cases

A technique to simulate the flow field near a moving material interface is developed for multi-material compressible flow, in particular, for compressible gas-water flow. This technique can be conveniently applied with a well-established conservative scheme to solve for the regions away from the interface. Material interfaces are captured using the level set technique with minimum or no smearing. To treat wave interaction with the interface, an implicit characteristic method is developed. In this paper, the method is described in detail and tested extensively for several one-dimensional gas-gas and gas-water cases. Application to multi-dimensional shock-free surface interaction and shock-gas bubble interaction are presented in Part II [Liu TG, Khoo BC, Yeo KS. The simulation of compressible multi-medium flow. Part II: Applications to 2D underwater shock refraction. Comp. and Fluids 2000;30:315-37].