A general computational framework for Lagrangian hydrodynamic scheme. I: Unification of staggered-grid and cell-centered methods

Abstract

This paper focuses on a general computational framework to unify both Lagrangian staggered-grid hydrodynamic (SGH) and cell-centered hydrodynamic (CCH) methods. One challenge is that artificial viscosity has contained empirical parameters in the SGH method for seven decades. To address this challenge, a new relationship between pressure and velocity is constructed using specific volume as a medium. Another challenge is that entropy is increasing in isentropic flows for the CCH method. To overcome this second challenge, the forces acting on a target cell are split into linear and quadratic terms in the CCH method. The numerical results of the two methods are almost identical. The scheme is more general than both existing SGH and CCH methods.