On preservation of symmetry in r–z staggered Lagrangian schemes

Abstract

In the focus of this work are symmetry preservation, conservation of energy and volume, and other important properties of staggered Lagrangian hydrodynamic schemes in cylindrical (r–z) geometry. It is well known that on quadrilateral cells in r–z, preservation of spherical symmetry, perfect satisfaction of the Geometrical Conservation Law (GCL), and total energy conservation are incompatible even on conforming grids. This paper suggests a novel staggered grid approach that preserves symmetry, conserves total energy by construction and tries to do its best by diminishing the GCL error to the order of entropy error. In particular, the forces from an existing volume consistent scheme are corrected so that spherical symmetry is preserved. The incorporation of subcell pressure mechanism to reduce spurious grid deformations is described and the relation of the new scheme to popular area-weighted and control volume approaches studied.