Most of commercial simulators for multiphase flow in porous media use implicit or adaptively implicit discretization schemes which allow for rather large time steps. It is important that in the iterative process the equations being approximated may change, e.g. in cases of well target change, counterflow. To increase stability of nonlinear iterations convergence, we propose a method relying on the control of residual norm decreasing and taking into account the features of the problem under consideration. Final correction of recurrent solution increment is carried out after direct calculation of the residual with corresponding approximation before and after the point where equations change. Correction of the increment which tries to retain form of equations being approximated (e.g. well mode) makes convergence more stable and additionally allows avoiding convergence to nonphysical solution. In the paper a number of possibilities for safeguard retaining of approximation type from the previous iteration is pointed out for situations (e.g. for low filtration rate) where it has to be changed by algorithm in the strict sense, given constraints being controlled to obtain “physical” solution. Several simulation results are presented, demonstrating the robustness and effectiveness of the proposed method for challenging problems.


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