Verification of an entropy dissipative QGD-scheme for the 1D gas dynamics equations
Abstract
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.
Keywords:
1D gas dynamics equations, entropy dissipative spatial discretization, explicit finite-difference scheme, verification on the Riemann problem, practical stability analysisHow to Cite
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Copyright (c) 2019 The Author(s). Published by Vilnius Gediminas Technical University.
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A.A. Zlotnik and T.A. Lomonosov. Conditions for L2-dissipativity of linearized explicit finite-difference schemes with regularization for the equations of 1D barotropic gas dynamics. Comput. Math. Math. Phys., 59, 2019. (accepted).
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Copyright (c) 2019 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.