In the paper, the new model based on the kinetic approach is proposed to describe the pro cess 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 a sufficiently mild stability condition. Due to its logical simplicity, the computational algorithm can be easily adapted to the hybrid architecture of modern supercomput ers. The results of computations on a graphics accelerator are presented for the problem on contami nant infiltration into water saturated soil and 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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