Symmetry Preservation by a Compatible Staggered Lagrangian Scheme Using the Control-Volume Discretization Method in $r–z$ Coordinate

Abstract

This paper aims at developing a control volume staggered Lagrangian scheme in $r–z$ coordinate that preserves symmetry property. To achieve this goal, the support operator method is first utilized to derive the compatible discretization that satisfies the Geometrical Conservation Law (GCL) and momentum and total energy conservation property. We further introduce a method of source term treatment to recover the spherical symmetry of the current scheme. It is shown that the developed scheme has the benefit of maintaining the momentum and total energy conservation. The equi-angular grid, randomly distorted polar grid, and Cartesian grid are considered for one-dimensional spherical flow simulations. Also, an extension to the non-spherical flow is presented. The results confirm the good performance of the developed scheme.