  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.
