Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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)
Kudryashova, T., Karamzin, Y., Podryga, V., Polyakov, S.: Two-scale computation of N2–H2 jet flow based on QGD and MMD on heterogeneous multi-core hardware. Adv. Eng. Softw. 120, 79–87 (2018)
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)
Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press, Cambridge (1999)
Osher, S.J., Fedkiw, R.P.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2002)
Chetverushkin, B.N.: Kinetic Schemes and Quasi-Gasdynamic System of Equations. CIMNE, Barcelona (2008)
Elizarova, T.G.: Quasi-Gas Dynamic Equations. Springer, Berlin (2009)
Zlotnik, A.A.: Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations. Comput. Math. Math. Phys. 57(4), 706–725 (2017)
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)
Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker Inc., New York (2001)
Polyakov, S.V., Karamzin, Y.N., Kudryashova, T.A., Tsybulin, I.V.: Exponential difference schemes for solving boundary-value problems for Diffusion-Convection-type equations. Math. Models Comput. Simul. 9(1), 71–82 (2017)
Kudryashova, T.A., Polyakov, S.V., Sverdlin, A.A.: Calculation of gas flow parameters around a reentry vehicle. Math. Models Comput. Simul. 1(4), 445–452 (2009)
Acknowledgment
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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Karamzin, Y.N., Kudryashova, T.A., Polyakov, S.V., Podryga, V.O. (2019). Finite Difference Schemes on Locally Refined Cartesian Grids for the Solution of Gas Dynamic Problems on the Basis of Quasigasdynamics Equations. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_36
Download citation
DOI: https://doi.org/10.1007/978-3-030-11539-5_36
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11538-8
Online ISBN: 978-3-030-11539-5
eBook Packages: Computer ScienceComputer Science (R0)