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

In this work, we propose a novel model order reduction approach for two-phase flow in porous media by introducing a formulation in which the mo-bility, which realizes the coupling between phase saturations and phase pres-sures, is regarded as a parameter to the pressure equation. Using this for-mulation, we introduce the Localized Reduced Basis Multiscale method to obtain a low-dimensional surrogate of the high-dimensional pressure equa-tion. By applying ideas from model order reduction for parametrized partial differential equations, we are able to split the computational effort for solv-ing the pressure equation into a costly offline step that is performed only once and an inexpensive online step that is carried out in every time step of the two-phase flow simulation, which is thereby largely accelerated. Us-age of elements from numerical multiscale methods allows us to displace the computational intensity between the offline and online step to reach an ideal runtime at acceptable error increase for the two-phase flow simulation.