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Verification of an entropy dissipative QGD-scheme for the 1D gas dynamics equations. (English) Zbl 1473.65132

Summary: 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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76N99 Compressible fluids and gas dynamics

Software:

QGDFoam; QHDFoam
PDFBibTeX XMLCite
Full Text: DOI

References:

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