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

TL;DR

This paper introduces a new reduced basis multiscale method for two-phase flows in porous media, significantly accelerating simulations by splitting computations into offline and online steps with controlled accuracy.

Contribution

It presents a novel formulation treating mobility as a parameter and applies localized reduced basis techniques to efficiently simulate two-phase flows in porous media.

Findings

Achieved significant speed-up in two-phase flow simulations.

Maintained acceptable accuracy with reduced computational effort.

Demonstrated effectiveness of the multiscale reduced basis approach.

Abstract

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.