The work is devoted to the methods of solving two-phase fluid flow problems in the reservoirs. It is assumed that in domain with high velocities Darcy's law is violated and a nonlinear filtration law is used. To determine the temperature use the law of conservation of energy (first law of thermodynamics). The temperature of the fluid and of the skeleton are considered the same. The fluid viscosities are taken by the temperature functions. The methods for solving two-phase flow problems in porous medium with a nonlinear filtration law based on the decomposition methods are proposed. The proposed methods are implemented on the heterogeneous computing systems.
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