Cell-Centred Lagrangian Lax–Wendroff HLL Hybrid Schemes in Cylindrical Geometry

Abstract

Lagrangian hydrodynamics described by Euler equations is treated by the Lax–Wendroff method with the dissipative fluxes in the HLL form, including both artificial viscosity and artificial energy flux. In cylindrical geometry, the velocity is discretized using source terms. The proposed method works reasonably well on Noh, Sedov and spherical Sod tests. The scheme preserves exact symmetry of results on initially polar meshes while the symmetry on initially rectangular meshes remains very good.