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L^2-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations

Applied Mathematics Letters. 2020. Vol. 103.

We study an explicit in time and symmetric in space finite-difference scheme with a kinetic regularization for the 2D and 3D gas dynamics system of equations linearized at a constant solution (with any velocity). We derive both necessary and sufficient conditions for $L^2$-dissipativity of the Cauchy problem for the scheme by the spectral method. The Courant number is uniformly bounded with respect to the Mach number in them.