Yu V Tunik
In this paper are developed modifications of the Godunov scheme, based on Kolgan's scheme of the second order of accuracy in the spatial variables for smooth solutions. It is constructed schemes of the first and the variable order of approximation, which exceed the Godunov scheme in accuracy. Referencing to the system of differential equations for propagation of flat sound waves in a gas at rest, the Kolgan scheme and the first-order schemes obtained are investigated onto the ability to ensure the non decrease of entropy, that is, to product of physically justified numerical solutions. The test problems of nonlinear gas dynamics on the decay of a discontinuity in a pipe and the transformation of a non uniformity in a plane-parallel flow are solved. Cylindrical explosion task is considered as the main one. The stability of a contact discontinuity behind a blast wave is investigated numerically in the Cartesian and polar coordinate systems. Analysis of obtained and published solutions does not confirm the instability of the contact discontinuity which initially has the circular shape. Change of the shape of initially perturbed break is largely caused by the instability of Taylor, not Richtmyer-Meshkov. Calculations are partially fulfilled using supercomputer “Lomonosov” of Moscow state university.
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