 |
Center for Nonlinear Studies |
Modeling multiphase flow in porous media is important for many applications, such as groundwater storage, oil and gas extraction, contaminant transport, and CO2 sequestration. At the same time, it is computationally expensive and numerically challenging especially when phase change needs to be taken into account. The system of equations describing multiphase flow consists of difficult nonlinear conservation laws, constitutive laws (e.g., Darcy’s law), and algebraic constraints (saturation, molar fractions, etc.). Usually, one can use the constraints to eliminate some of the unknowns to get a reduced set of primary variables. For example, using the constraint that the gas and liquid saturations sum to 1, we can eliminate the gas saturation and choose the liquid saturation as a primary variable. However, if the liquid phase disappears, this reduced set of equations is not well defined. The traditional approach is to use primary variable switching (PVS). The primary variables may be switched depending on the conditions of the phases. One drawback of PVS is that its solver, relied on a serial algorithm, may not perform well on emerging architecture, especially at exascale. A scalable solver such as multigrid, however, cannot be applied directly, and needs extensive customization for PVS. Recently, a new approach based on complementary constraints has been developed. This makes use of a set of complementary equations and a reformulation of the balance equations, which are subsequently solved using a semi-smooth Newton method. I will present this approach as well as some numerical examples and test cases.