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.
Highlights
Vast literature is devoted to methods for numerical solving gas dynamics equations, see, in particular, [1, 10, 11, 16]
Those methods that are in addition entropy dissipative attract much attention, see, in particular, [1, Ch. 18, 19], [6, 8, 13, 14, 15, 17]
The explicit finite-difference scheme with this discretization is verified in the 1D case on several versions of the Riemann problem on the disintegration of a discontinuity, both well-known in the literature [12, 15] and new
Summary
Vast literature is devoted to methods for numerical solving gas dynamics equations, see, in particular, [1, 10, 11, 16]. Entropy dissipative spatial QGD-discretizations were first constructed and verified in the 1D case in [7, 19].
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