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Oil modeling in sedimentary basins commonly involves a great variety of complex physics, which leads to a fully coupled nonlinear set of partial differential equations. The most classical sequential time stepping is the fully implicit method, which computes pressure and oil saturation simultaneously. Although this method provides accurate solutions, it turns out to be computationally expensive. The aim of this chapter is to propose a new time-stepping strategy that allows computational cost to be minimized while preserving the accuracy of the numerical solution. The new approach is based on separating pressure from oil saturation and using a local time-step...

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