Application of MFCAV Riemann solver to Maire's cell-centered Lagrangian method

In this paper, we apply arbitrary Riemann solvers, which may not satisfy the Maire's requirement, to the Maire's node-based Lagrangian scheme developed in [P. H. Maire et al, SIAM J. Sci. Comput, 29 (2007), 1781-1824]. In particular, we apply the so-called Multi-Fluid Channel on Averaged Volume (MFCAV) Riemann solver and a Riemann solver that adaptively combines the MFCAV solver with other more dissipative Riemann solvers to the Maire's scheme. It is noted that neither of the two solvers satisfies the Maire's requirement. Numerical experiments are presented to demonstrate that the application of the two Riemann solvers is successful.