Vasilev E.I., Vasileva T.A., Kolybelkin D.I., Krasovitov B. The Third-Order Approximation Godunov Method for the Equations of Gas Dynamics

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https://doi.org/10.15688/mpcm.jvolsu.2019.1.6

Eugene Ivanovich Vasilev
Doctor of Physical and Mathematical Sciences, Professor,
Department of Fundamental Informatics and Optimal Control,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Tatiana Anatolievna Vasileva
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Fundamental Informatics and Optimal Control,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Dmitriy Igorevich Kolybelkin
Student, Department of Fundamental Informatics and Optimal Control,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Boris Krasovitov
Ph.D., Senior Researcher, Department of Mechanical Engineering,
the Pearlstone Center for Aeronautical Engineering Studies,
Ben-Gurion University of the Negev
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P. O. Box 653, 84105 Beer-Sheva, Israel

Abstract. The paper suggests a new modification of Godunov difference method with the 3rd order approximation in space and time for hyperbolic systems of conservation laws. The diёerence scheme uses the simultaneous discretization of the equations in space and time without of Runge — Kutta stages. An exact or approximate solution of Riemann problem is applied to calculate numerical fluxes between cells. Before the time step, corrections to the arguments of the Riemann problem providing third-order approximations for linear systems are calculated. After the time step, the numerical solution correction procedure is applied to eliminate the second-order error arising from the nonlinearity of the equations. The paper presents the results of experimental numerical verification of the method approximation order on the exact smooth solution inside the fan of the expansion wave. The test results completely confirm the third order of the presented method. The proposed approach of constructing third-order difference schemes can be used for inhomogeneous and two-dimensional hyperbolic systems of nonlinear equations.

Key words: nonlinear hyperbolic systems, Godunov method, third order, approximation, construction of difference schemes.

The Third-Order Approximation Godunov Method for the Equations of Gas Dynamics by Vasilev E.I., Vasileva T.A., Kolybelkin D.I., Krasovitov B. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 22 No. 1 2019, pp. 71-83

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