A sub-cell force-based framework to derive cell-centered Lagrangian schemes on two-dimensional polygonal grids

Abstract

We present a general sub-cell force-based formalism to derive cell-centered schemes for two-dimensional Lagrangian hydrodynamics on unstructured grids. For a general polygonal grid, the discrete equations that govern the time rate of change of volume, momentum and total energy are obtained by means of a control volume formulation of the gas dynamics equations written using a cell-centered placement of the physical variables. Numerical fluxes are expressed in terms of sub-cell forces. Nodal velocity and sub-cell forces are computed consistently with the cell volume variation through the use of a node-centered approximate Riemann solver. These cell-centered Lagrangian schemes are conservative for momentum and total energy and satisfy a local semi-discrete entropy inequality.