The localized reduced basis multiscale method for two‐phase flows in porous media

Abstract

SummaryIn this work, we propose a novel model order reduction approach for two‐phase flow in porous media by introducing a global pressure formulation in which the total mobility, which realizes the coupling between saturation and pressure, is regarded as a parameter to the pressure equation. In our approach, the mobility itself is an optimal fit of mobility profiles that are precomputed using the time‐of‐flight for the initial saturation. Using this formulation and the localized reduced basis multiscale method, we obtain a low‐dimensional surrogate of the high‐dimensional pressure equation. By applying ideas from model order reduction for parametrized partial differential equations, we are able to split the computational effort for solving 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. Usage of elements from numerical multiscale methods allows us to displace the computational intensity between the offline and online steps to reach an ideal runtime at acceptable error increase for the two‐phase flow simulation. This is achieved by constructing reduced‐dimensional local spaces that lead to a non‐conforming global approximation space. As one example for a coupling on the global space, we introduce a discontinuous Galerkin scheme. Copyright © 2014 John Wiley & Sons, Ltd.