Geodesic
Application of the TVD scheme for the two-phase flow calculations at different component velocities and pressures
Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 29-47.

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The finite difference scheme of TVD type and the method of “coarse particles” are studied and developed to solve the problems of the heterogeneous media mechanics at different component velocities and pressures. The calculation results on TVD scheme and modified method of “coarse particles” for two types of shock-wave configurations are compared with the exact solution. It is shown that the TVD schemes are more efficient for calculation of the specified class of the problems of the heterogeneous media mechanics on the following criteria: the calculation time and the grid step. The schemes are applied to calculation of the problem of the shock wave reflection from the wall in mixture characterized by inhomogeneous distribution of the component concentrations. 
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A. A. Zhilin; A. V. Fedorov. Application of the TVD scheme for the two-phase flow calculations at different component velocities and pressures. Matematičeskoe modelirovanie, Tome 20 (2008) no. 1, pp. 29-47. http://geodesic.mathdoc.fr/item/MM_2008_20_1_a2/

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