Justification of Godunov’s scheme in the multidimensional case
- Authors: Tishkin V.F.1, Zhukov V.T.1, Myshetskaya E.E.1
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Affiliations:
- Keldysh Institute of Applied Mathematics
- Issue: Vol 8, No 5 (2016)
- Pages: 548-556
- Section: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/201201
- DOI: https://doi.org/10.1134/S2070048216050124
- ID: 201201
Cite item
Abstract
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.
About the authors
V. F. Tishkin
Keldysh Institute of Applied Mathematics
Author for correspondence.
Email: v.f.tishkin@mail.ru
Russian Federation, Moscow
V. T. Zhukov
Keldysh Institute of Applied Mathematics
Email: v.f.tishkin@mail.ru
Russian Federation, Moscow
E. E. Myshetskaya
Keldysh Institute of Applied Mathematics
Email: v.f.tishkin@mail.ru
Russian Federation, Moscow
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