J. Comp. Math., 33 (2015), pp. 128-145.

Application of MFCAV Riemann Solver to Maire's Cell-Centered Lagrangian Method

Yan Liu 1, Weidong Shen 1, Baolin Tian 1, Shuanghu Wang 1, Song Jiang 1, Dekang Mao 2

1 Institute of Applied Physics and Computational Mathematics, Beijing 100094, P. R. China
2 Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

Received 2013-7-15 Accepted 2014-9-28
Available online 2015-3-13


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.

Key words: Maire's node-based Lagrangian scheme, Riemann solvers, Riemann invariants, weighted least squares procedure.

AMS subject classifications: 65N06, 65B99.

Email: yan_liu_zh@163.com, dkmao@staff.shu.edu.cn

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