Verification of an entropy dissipative QGD-scheme for the 1D gas dynamics equations

    Alexander Zlotnik Affiliation
    ; Timofey Lomonosov Affiliation


An entropy dissipative spatial discretization has recently been constructed for the multidimensional gas dynamics equations based on their preliminary parabolic quasi-gasdynamic (QGD) regularization. In this paper, an explicit finite-difference scheme with such a discretization is verified on several versions of the 1D Riemann problem, both well-known in the literature and new. The scheme is compared with the previously constructed QGD-schemes and its merits are noticed. Practical convergence rates in the mesh L1-norm are computed. We also analyze the practical relevance in the nonlinear statement as the Mach number grows of recently derived necessary conditions for L2-dissipativity of the Cauchy problem for a linearized QGD-scheme.

Keyword : 1D gas dynamics equations, entropy dissipative spatial discretization, explicit finite-difference scheme, verification on the Riemann problem, practical stability analysis

How to Cite
Zlotnik, A., & Lomonosov, T. (2019). Verification of an entropy dissipative QGD-scheme for the 1D gas dynamics equations. Mathematical Modelling and Analysis, 24(2), 179-194.
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Feb 5, 2019
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