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Some recent finite volume schemes to compute Euler equations using real gas EOS. (English) Zbl 1053.76044

Summary: This paper deals with the solution by finite volume methods of Euler equations in one space dimension, with real gas state laws (namely, perfect gas EOS, Tammann EOS and van der Waals EOS). All tests are of unsteady shock tube type, in order to examine a wide class of solutions, involving Sod shock-tube, stationary shock wave, simple contact discontinuity, occurrence of vacuum by double rarefaction wave, propagation of a one-rarefaction wave over vacuum,…Most of the methods computed herein are approximate Godunov solvers: VFRoe, VFFC, VFRoe \(ncv(\tau,u,p)\) and PVRS. The energy relaxation method with VFRoe \(ncv(\tau,u,p)\) and Rusanov scheme have been investigated, too. Qualitative results are presented or commented for all test cases, and numerical rates of convergence in some test cases have been measured for first- and second-order (Runge-Kutta 2 with MUSCL reconstruction) approximations. Note that the rates are measured for solutions involving discontinuities, in order to estimate the loss of accuracy due to these discontinuities.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
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References:

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