The multiscale perturbation method for two-phase reservoir flow problems
Franciane F. Rocha, Het Mankad, Fabricio Simeoni de Sousa, Felipe Pereira · Applied Mathematics and Computation · 2022
In this work we formulate and test a new procedure, the Multiscale Perturbation Method for Two-Phase Flows (MPM-2P), for the fast, accurate and naturally parallelizable numerical solution of two-phase, incompressible, immiscible displacement in porous media approximated by an operator splitting method. The proposed procedure is based on domain decomposition and combines the Multiscale Perturbation Method (MPM) [Ali, et al., Appl. Math. and Comput., 387 (2020) pp. 125023] with the Multiscale Robin Coupled Method (MRCM) [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21]. When an update of the velocity field is called for by the operator splitting algorithm, the MPM-2P may provide, depending on the magnitude of a dimensionless algorithmic parameter, an accurate and computationally inexpensive approximation for the velocity field by reusing previously computed multiscale basis functions. Thus, a full update of all multiscale basis functions required by the MRCM for the construction of a new velocity field is avoided.