Finite Difference Schemes on Locally Refined Cartesian Grids for the Solution of Gas Dynamic Problems on the Basis of Quasigasdynamics Equations
The paper is devoted to the numerical solution of gas dynamic problems on the basis of a system of quasigasdynamic equations in domains of complex shape. One possible grid approach to solving this class of problems is used. An approach is applying to the locally refined Cartesian (LRC) grids, consisting of rectangles (parallelepipeds) of various sizes. In this paper some variants of the construction of finite difference schemes in the two-dimensional case are considered. Their order of approximation is investigated. The analysis of the schemes is carried out numerically on the example of two-dimensional problem of gas flow under conditions of the real equation of state.
KeywordsInitial boundary value problems for quasigasdynamic equation system Finite difference schemes Locally refined Cartesian grids
The work was supported by the Russian Foundation for Basic Research (projects No. 18-07-01292-a, 18-51-18004-bolg-a, 16-29-15095-ofi_m).
- 1.Podryga, V.O., Karamzin, Y.N., Kudryashova, T.A., Polyakov, S.V.: Multiscale simulation of three-dimensional unsteady gas flows in microchannels of technical systems. In: Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), Crete Island, Greece, 5–10 June 2016, vol. 2, pp. 2331–2345 (2016)Google Scholar
- 3.Kudryashova, T., Podryga, V., Polyakov, S.: HPC-simulation of gasdynamic flows on macroscopic and molecular levels. In: Uvarova, L.A., Nadykto, A.B., Latyshev, A.V. (eds.) Nonlinearity. Problems, Solutions and Applications, vol. I, chap. 26, pp. 543–556. Nova Science Publishers, New York (2017)Google Scholar
- 6.Chetverushkin, B.N.: Kinetic Schemes and Quasi-Gasdynamic System of Equations. CIMNE, Barcelona (2008)Google Scholar
- 9.Eymard, R., Gallouet, T.R., Herbin, R.: The finite volume method. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. 7, pp. 713–1020. North Holland, Amsterdam (2000)Google Scholar