  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 mobility, which
realizes the coupling between phase saturations and phase pressures, is
regarded as a parameter to the pressure equation. Using this formulation, we
introduce the Localized Reduced Basis Multiscale method to 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 step to reach an ideal runtime at acceptable
error increase for the two-phase flow simulation.
