Geodesic
On methods for increasing the accuracy of shock wave calculations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 6 (2014) no. 3, pp. 5-13

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The paper presents a non-homogeneous difference method for shock wave simulation in Lagrangian coordinates. The method explicitly determines shocks as discontinuities of the first kind. The ways of increasing the accuracy of calculated shocks within the scope of the proposed method are suggested. In particular, the author suggests using the difference approach together with some elements of the method of characteristics to determine quantities before the shock front. The algorithm of the modified method is described. A number of methodical calculations are provided. On their basis it’s shown that the new method improves the monotonicity and accuracy of shock calculations.
Keywords: shock wave; strong discontinuity; non-homogeneous difference method. 
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     title = {On methods for increasing the accuracy of shock wave calculations},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2014_6_3_a0/}
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D. A. Farfolomeyev; K. I. Kazin; V. F. Kuropatenko. On methods for increasing the accuracy of shock wave calculations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 6 (2014) no. 3, pp. 5-13. http://geodesic.mathdoc.fr/item/VYURM_2014_6_3_a0/