Geodesic
A method for studying the dissipative properties of difference schemes in Euler coordinates
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 108-116

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At present, numerical methods for calculating shock-wave flows of liquid and gas in Eulerian coordinates have become widespread; therefore, the study of their characteristics is an urgent task. The paper presents an approach to assessing the dissipative properties of such difference schemes on strong discontinuities. The idea of the method is to construct the entropy production equation, the approximation error of which can be expressed by a combination of the approximation errors of the equations that make up the difference scheme. The equation of entropy production on a weak shock wave is used as a criterion for the dissipativity of the difference scheme. The paper evaluates the dissipative properties of the large particle method using the proposed method.
Keywords: difference schemes, Euler coordinates, dissipativity, entropy production. 
@article{VYURU_2021_14_2_a11,
     author = {E. S. Shestakovskaya and Ya. E. Starikov and N. L. Klinacheva},
     title = {A method for studying the dissipative properties of difference schemes in {Euler} coordinates},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {108--116},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a11/}
}
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E. S. Shestakovskaya; Ya. E. Starikov; N. L. Klinacheva. A method for studying the dissipative properties of difference schemes in Euler coordinates. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 108-116. http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a11/