Maire´s New Cell-Centered Lagrangian Method Based on Arbitrary Riemann Solver

In this paper, we develop an approach to stably apply the Riemann solvers without an acoustic form to the Maire´s node-based Lagrangian scheme developed in (P. H. Maire, R. Abgrall, J. Breil, et al, A cell-centered lagrangian scheme for multidimensional compressible ow problems, SIAM J. Sci. Comput, 2007, 29, 1781-1824). We apply the Dukowicz [2], HLLC Riemann solver with complex wave speed estimate and exact Riemann solver to the Maire´s scheme by this approach. Numerical examples are presented to validate the Maire´s scheme using these three Riemann solvers.