Geodesic
A method for shock calculation
Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 60-70

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The mass, momentum and energy conservation laws allow shock and rarefaction waves to be present in the solution of continuum mechanics problems. When these problems are solved with homogeneous difference techniques, the strong shock surface is represented by a layer of a finite width within which the quantities vary continuously from a state before the shock front to a state behind it. These states are related by the strong shock conditions. Since they lie on the Hugoniot, there must exist a mechanism which maintains energy dissipation in the shock layer. One of these mechanisms is a method by Kuropatenko which uses the difference equations applicable for strong shocks. The method can be implemented in different difference schemes. The paper presents one of them, describes its basic properties, and provides results of some calculations.
Keywords: conservation laws, energy dissipation, difference scheme, shock, rarefaction. 
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     author = {V. F. Kuropatenko and M. N. Yakimova},
     title = {A method for shock calculation},
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V. F. Kuropatenko; M. N. Yakimova. A method for shock calculation. Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 60-70. http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a5/