Geodesic
On justification of the Godunov scheme in multidimensional case
Matematičeskoe modelirovanie, Tome 28 (2016) no. 2, pp. 86-96

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Classical Godunov scheme for numerical solution of 3D gasdynamics equations is justified for multidimensional case. It is istimated an error introduced by replacing the exact solution of the multidimensional Riemann problem at solving one-dimensional problems with the data on the left and right of the interface of each cell without taking account of complicated flow in the vicinity of the vertices of the cell. It is shown that in the case of plane interfaces the error is the first order with respect to time step and approximate solution converges to solution of semidiscrete equations. The Euler explicit time integration metod for these equations represents the Godunov scheme.
Keywords: computational fluid dynamics, Godunov scheme, multidimensional Riemann solvers. 
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     author = {V. F. Tishkin and V. T. Zhukov and E. E. Myshetskaya},
     title = {On justification of the {Godunov} scheme in multidimensional case},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {86--96},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_2_a7/}
}
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V. F. Tishkin; V. T. Zhukov; E. E. Myshetskaya. On justification of the Godunov scheme in multidimensional case. Matematičeskoe modelirovanie, Tome 28 (2016) no. 2, pp. 86-96. http://geodesic.mathdoc.fr/item/MM_2016_28_2_a7/