Geodesic
Application of explicit schemes to simulation of two-phase filtration process
Matematičeskoe modelirovanie, Tome 23 (2011) no. 7, pp. 52-60.

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In the paper the new model based on the kinetic approach is proposed to describe the process of two-phase slightly compressible fluid filtration. The capillary and gravity forces are taken into account. The obtained hyperbolic continuity equations for phase liquids are approximated by the explicit three-level schemes with the mild enough stability condition. Due to the logical simplicity the computational algorithm can be easily adapted to the hybrid architecture of modern supercomputers. Results of computations on a graphics accelerator are presented for the problem on the contaminant infiltration into the water-saturated soil, the high parallelization efficiency is demonstrated.
Keywords: flow in a porous medium, two-phase fluid, hyperbolic system of equations, three-level explicit scheme, graphics accelerator. 
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D. N. Morozov; M. A. Trapeznikova; B. N. Chetverushkin; N. G. Churbanova. Application of explicit schemes to simulation of two-phase filtration process. Matematičeskoe modelirovanie, Tome 23 (2011) no. 7, pp. 52-60. http://geodesic.mathdoc.fr/item/MM_2011_23_7_a3/

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