Abstract <p>The work is devoted to solving the problem of multiphase nonisothermal fluid flow in heavy oil reservoirs with a large number of wells. The problem of steam-assisted gravity drainage is considered taking into account the implementation of the nonlinear filtration law in areas with small pressure gradients. Methods for solving the problem on grids with fine grid segments based on decomposition methods are proposed. The systems of equations are independently solved for each fine grid segments, and then matched with the solution on a coarse grid. The superiority of the proposed methods is shown in comparison with the known decomposition methods. Calculations are performed on heterogeneous computing systems.</p>