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Conditions for L² -dissipativity of an explicit symmetric finite-difference scheme for linearized 2D and 3D gas dynamics equations with a regularization

Discrete and Continuous Dynamical Systems - Series B. 2023. Vol. 28. No. 3. P. 1571–1589.
Zlotnik A.

We study an explicit two-level in time and symmetric in space finite-difference scheme for a linearized 2D and 3D gas dynamic system of equations with a kinetic-type regularization. For an initial-boundary value problem on any nonuniform rectangular mesh, sufficient Courant-type conditions for the $L^2$-dissipativity are derived for the first time by the energy method. For the Cauchy problem on the uniform mesh, recent both necessary conditions and sufficient conditions for the $L^2$-dissipativity in the spectral method are improved. A new form for the relaxation parameter is suggested which guarantees that the Courant-type number is uniformly bounded from above and below with respect to the mesh and the Mach number.

Research target: Mathematics
Language: English
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Keywords: linearizationregularizationdissipativitygas dynamics equationsexplicit symmetric finite-difference scheme
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