A finite volume moving mesh method for the simulation of compressible flows

Abstract

A finite volume adaptive mesh redistribution method for efficient and accurate simulation of one and two dimensional compressible Euler equations is developed. The method consists of two coupled steps; evolution of the governing equations using an adaptively redistributed mesh followed by a redistribution of the computational nodes. Mesh redistribution is accomplished through the solution of an elliptic equation which allows for determination of redistributed coordinates corresponding to the physical domain on a simplified computational domain, discretized using a uniform Cartesian grid. The governing hyperbolic compressible Euler equations, originally defined in the physical domain, are first transformed on to the simplified computational domain and then recast in a strong conservative form. These are then solved directly on the computational domain with the primary aim of maximizing accuracy while minimizing the computational overheads associated with the grid redistribution. The method is demonstrated on compressible Rayleigh-Taylor instability in two dimensions.