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Regular version of the site

Article

Verification of an Entropy Dissipative QGD-Scheme for the 1D Gas Dynamics Equations

Mathematical Modelling and Analysis. 2019. Vol. 24. No. 2. P. 179-194.
Zlotnik Alexander, Lomonosov T.

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 $L^1$-norm are computed. We also analyze the practical relevance in the nonlinear statement as the Mach number grows of recently derived necessary conditions for $L^2$-dissipativity of the Cauchy problem for a linearized QGD-scheme.