A remapping-free, efficient Riemann-solvers based, ALE method for multi-material fluids with general EOS

Abstract

Based on an efficient Riemann solver, a remapping-free ALE method (RALE) for multi-material fluids with general equations of state is proposed. The basic idea of constructing the RALE is to couple the Lagrangian method with a remapping-free ALE-type method. In order to keep the sharpness of a material interface, the Lagrangian formulation is employed for tracking the material interface, where the Lagrangian velocity of nodes and Lagrangian fluxes are designed. In single material regions, the numerical fluxes are constructed on moving meshes which move nodes to the regions with large gradients to increase the numerical accuracy, and the explicit remapping stage is avoided because of the new discrete scheme. The inverse Hermite interpolation argument is employed in solving the Riemann problem with general EOS, consequently, reducing iteration steps greatly and resulting in an efficient and robust Riemann solver. A number of numerical examples are presented.