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In this work, we propose a novel model order reduction approach for two-phaseflow in porous media by introducing a formulation in which the mobility, whichrealizes the coupling between phase saturations and phase pressures, isregarded as a parameter to the pressure equation. Using this formulation, weintroduce the Localized Reduced Basis Multiscale method to obtain alow-dimensional surrogate of the high-dimensional pressure equation. Byapplying ideas from model order reduction for parametrized partial differentialequations, we are able to split the computational effort for solving thepressure equation into a costly offline step that is performed only once and aninexpensive online step that is carried out in every time step of the two-phaseflow simulation, which is thereby largely accelerated. Usage of elements fromnumerical multiscale methods allows us to displace the computational intensitybetween the offline and online step to reach an ideal runtime at acceptableerror increase for the two-phase flow simulation.

The Localized Reduced Basis Multiscale method for two-phase flows in porous media