Abstract:The most time-consuming part of modern reservoir simulation is solving a sequence of large scale and ill-conditioned Jacobian systems. In this work, we develop a new effective preconditioner for solving these Jacobian systems. According to the different properties of the equations in the black oil model, the new preconditioning technique chooses appropriate auxiliary spaces for different parts of the Jacobian systems and designs effective solvers for each part. By combining the new preconditioner with Krylov subspace methods, we construct an efficient and robust solver, which can be easily generalized to more complicated models for enhanced oil recovery. Numerical experiments including preliminary parallel implementation demonstrate the effectiveness and robustness of the solver.