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An arbitrary Lagrangian–Eulerian method based on the adaptive Riemann solvers for general equations of state
Author(s) -
Tian Baolin,
Shen Weidong,
Jiang Song,
Wang Shuanghu,
Liu Yan
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1871
Subject(s) - riemann solver , riemann problem , godunov's scheme , classification of discontinuities , riemann hypothesis , shock wave , mathematics , eulerian path , shallow water equations , numerical analysis , mathematical analysis , lagrangian , physics , mechanics , finite volume method
Approximate or exact Riemann solvers play a key role in Godunov‐type methods. In this paper, three approximate Riemann solvers, the MFCAV, DKWZ and weak wave approximation method schemes, are investigated through numerical experiments, and their numerical features, such as the resolution for shock and contact waves, are analyzed and compared. Based on the analysis, two new adaptive Riemann solvers for general equations of state are proposed, which can resolve both shock and contact waves well. As a result, an ALE method based on the adaptive Riemann solvers is formulated. A number of numerical experiments show good performance of the adaptive solvers in resolving both shock waves and contact discontinuities. Copyright © 2008 John Wiley & Sons, Ltd.