Abstract
This paper continues investigations initiated previously by the authors on theoretical foundation of the methods for localization of shock waves by shock-capturing results of computation of gas dynamics problems in Eulerian variables. The results obtained are as follows. (1) Within the framework of the first differential approximation (f.d.a.) theory it is shown that the point of the scheme viscosity maximum defined by f.d.a. moves at a speed of the true discontinuity when using certain class of first-order difference schemes, (2) Inapplicability of the mathematical means of progressive wave type solutions of the f.d.a. equation for the description of numerical solution properties in the smeared steady shock wave of weak intensity is shown which takes place in virtue of the purely unsteady character of the numerical solution.
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