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An exact Riemann solver for one‐dimensional multimaterial elastic‐plastic flows with Mie‐Grüneisen equation of state without vacuum
Author(s) -
Liu Li,
Cheng JunBo,
Shen Yongxing
Publication year - 2021
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.4917
Subject(s) - riemann solver , riemann problem , riemann hypothesis , solver , mathematics , jacobian matrix and determinant , mathematical analysis , roe solver , physics , mechanics , mathematical optimization , finite volume method
In this article, we present exact Riemann solvers for the Riemann problem and the half Riemann problem, respectively, for one‐dimensional multimaterial elastic‐plastic flows with the Mie‐Grüneisen equation of state (EOS), hypoelastic constitutive model, and the von Mises' yielding condition. We first analyze the Jacobian matrices in the elastic and plastic states, and then build the relations of different variables across different type of waves. Based on these formulations, an exact Riemann solver is constructed with totally 36 possible cases of wave structures. A large number of tests prove the rightness of the new exact Riemann solver. Moreover, an exact Riemann solver is also deduced for the half Riemann problem and its validity is tested by two examples.