Justification of Godunov’s scheme in the multidimensional case
| Autor: | Vladimir Fedorovich Tishkin, V. T. Zhukov, E. E. Myshetskaya |
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| Rok vydání: | 2016 |
| Předmět: |
Godunov's theorem
010102 general mathematics Mathematical analysis Godunov's scheme 01 natural sciences Riemann solver 010305 fluids & plasmas Euler method Roe solver Computational Mathematics symbols.namesake Discontinuity (linguistics) Riemann problem Flow (mathematics) Modeling and Simulation 0103 physical sciences symbols 0101 mathematics Mathematics |
| Zdroj: | Mathematical Models and Computer Simulations. 8:548-556 |
| ISSN: | 2070-0490 2070-0482 |
| DOI: | 10.1134/s2070048216050124 |
| Popis: | The classical Godunov scheme for the numerical solution of 3D gas dynamics equations is justified in the multidimensional case. An estimate is obtained for the error induced by replacing the exact solution of the multidimensional discontinuity breakup problem (known as the Riemann problem) with the solution of the 1D problems with the data on the left and right of the interface of each cell without considering the complicated flow in the neighborhood of the cells’ vertices. It is shown that, in the case of plane interfaces, the error has the first order of smallness in the time step and the approximate solution converges to the solution of semidiscrete equations as the time step vanishes. In fact, the time integration of these equations using the explicit Euler method represents the Godunov scheme. |
| Databáze: | OpenAIRE |
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