Unification of Lagrangian staggered-grid hydrodynamics and cell-centered hydrodynamics in one dimension

This paper focuses on the novel scheme to unify both Lagrangian staggered-grid and cell-centered hydrodynamic methods in one dimension. The scheme neither contains empirical parameters nor solves the Riemann problem. It includes two key points: one is the relationship between pressure and velocity, and the other is Newton's second law. The two methods that make use of this scheme satisfy the entropy condition and are conservative in total mass, momentum, and energy. Numerical results show the robustness and accuracy of both methods.