Cell-centered Lagrangian Lax-Wendroff HLL hybrid scheme in cylindrical geometry - Fridrich, David; Liska, Richard; Wendroff, Burton (Journal of computational physics, 2020)
•A new numerical method for Lagrangian hydrodynamics in cylindrical geometry is proposed.•Conservation laws are approximated by a cell-centered Lax-Wendroff HLL hybrid scheme.•Proposed scheme keeps exact spherical symmetry on equiangular meshes while symmetry for Cartesian grids remains very good.•The geometric conservation law is satisfied by the method. Lagrangian hydrodynamics as described by the Euler equations is treated by an improved version of the basic predictor-corrector Lax-Wendroff method that also has added HLL-type dissipative fluxes, including both artificial viscosity and energy dissipation. The method in Cartesian geometry is enhanced by a different weighting of the conservative variables in the predictor and a new treatment of material interfaces. The basic method is extended to cylindrical r,z geometry, where it satisfies the geometric conservation law and keeps exact spherical symmetry on equiangular polar meshes. The added viscosity does not preserve symmetry, so in order to achieve that we have added a symmetry correction. Numerical hydrodynamic tests, including the Noh, Sedov, spherical Sod, free expansion and Kidder problems show a reasonable performance of the method. In addition, the spherical Noh problem was simulated on an initially rectangular mesh with a very good result regarding its symmetry.