Two-dimensional compressible multimaterial flow calculations in a unified coordinate system

Abstract

We extend the unified coordinate system method introduced in [J Comput Phys 153 (1999) 596, Comput Fluid Dyn J 8 (2000) 495] for single-fluid computations to multimaterial fluid computations by incorporating a γ-model scheme [P.L. Roe, A new approach to computing discontinuous flow of several ideal gases, Technical Report, (Cranfield Institute of Technology) 1984, J Comput Phys 169 (2001) 594], and propose therefore a γ-model unified coordinate system method, in which interfaces of multifluids are described by contact discontinuities of a conservation equation, i.e., the γ-model that is added into the Euler equations, forming the extended Euler equations (of a single fluid). The Godunov/MUSCL method is then used to solve the extended Euler equations numerically. Numerical examples validate the scheme in avoiding disadvantages of excessive numerical diffusion across interfaces in the Eulerian description and of severe mesh deformation in the Lagrangian description which may result in numerical inaccuracy and even break down computations.