The present paper analyzes the stability of Godunov's scheme for Euler equations, accounting for the nonlinear behavior of solutions in the zones of large gradients (shock waves, contact breakages). The development of perturbations is assessed, including the contribution of nonlinear terms of the exact solution of the breakage decomposition problem, demonstrating instability of the original Godunov's scheme and explaining the development mechanism of the so-called «carbuncle phenomenon?. A possibility of introducing corrections for providing the stability without changing the approximation of the original scheme or of its second- order accuracy modification is shown. The results of numerical modeling demonstrating the efficiency of the obtained corrections are presented.
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