Symmetry Preservation and Volume Consistency in an R-z Staggered Scheme

Abstract. This work is focused on the issue of symmetry preservation, energy and volume conservation and other important properties of staggered Lagrangian hydrodynamic schemes in cylindrical geometry. Typical advantages and drawbacks of existing areaweighted (AW) and genuinely r-z schemes will be pointed out. With quadrilateral cells it is known that, in r-z, spherical symmetry preservation, perfect satisfaction of GCL, and total energy conservation are incompatible [9]. Being aware of this, we propose a staggered approach that conserves energy by construction and tries to do its best by diminishing the GCL error to the order of entropy error. In particular, we correct the volume consistent forces from [5] so that spherical symmetry is preserved. This idea is similar to the approach from [8], where we suggested a new r-z artificial viscosity that preserves symmetry and is (unlike typical AW viscosities) strictly dissipative. A practical implementation our symmetrization term will be presented. Its comparison to the existing methods from [1] and [5] will be demonstrated on a convergence study of the adiabatic Coggeshall test, and the effect of the symmetrization term on accuracy will be assessed using the Sedov blast wave test.