TY - JOUR
T1 - Conservative multirate multiscale simulation of multiphase flow in heterogeneous porous media
AU - Delpopolo Carciopolo, Ludovica
AU - Formaggia, Luca
AU - Scotti, Anna
AU - Hajibeygi, Hadi
PY - 2020
Y1 - 2020
N2 - Accurate and efficient simulation of multiphase flow in heterogeneous porous media motivates the development of space-time multiscale strategies for the coupled nonlinear flow (pressure) and saturation transport equations. The flow equation entails heterogeneous high-resolution (fine-scale) coefficients and is global (elliptic or parabolic). The time-dependent saturation profile, on the other hand, may exhibit sharp local gradients or discontinuities (fronts) where the solution accuracy is highly sensitive to the time-step size. Therefore, accurate flow solvers need to address the multiscale spatial scales, while advanced transport solvers need to also tackle multiple time scales. This paper presents the first multirate multiscale method for space-time conservative multiscale simulation of sequentially coupled flow and transport equations. The method computes the pressure equation at the coarse spatial scale with a multiscale finite volume technique, while the transport equation is solved by taking variable time-step sizes at different locations of the domain. At each coarse time step, the developed local time-stepping technique employs an adaptive recursive time step refinement to capture the fronts accurately. The applicability (accuracy and efficiency) of the method is investigated for a wide range of two-phase flow simulations in heterogeneous porous media. For the studied cases, the proposed method is found to provide 3 to 4 times faster simulations. Therefore, it provides a promising strategy to minimize the tradeoff between accuracy and efficiency for field-scale applications.
AB - Accurate and efficient simulation of multiphase flow in heterogeneous porous media motivates the development of space-time multiscale strategies for the coupled nonlinear flow (pressure) and saturation transport equations. The flow equation entails heterogeneous high-resolution (fine-scale) coefficients and is global (elliptic or parabolic). The time-dependent saturation profile, on the other hand, may exhibit sharp local gradients or discontinuities (fronts) where the solution accuracy is highly sensitive to the time-step size. Therefore, accurate flow solvers need to address the multiscale spatial scales, while advanced transport solvers need to also tackle multiple time scales. This paper presents the first multirate multiscale method for space-time conservative multiscale simulation of sequentially coupled flow and transport equations. The method computes the pressure equation at the coarse spatial scale with a multiscale finite volume technique, while the transport equation is solved by taking variable time-step sizes at different locations of the domain. At each coarse time step, the developed local time-stepping technique employs an adaptive recursive time step refinement to capture the fronts accurately. The applicability (accuracy and efficiency) of the method is investigated for a wide range of two-phase flow simulations in heterogeneous porous media. For the studied cases, the proposed method is found to provide 3 to 4 times faster simulations. Therefore, it provides a promising strategy to minimize the tradeoff between accuracy and efficiency for field-scale applications.
KW - Conservative multirate methods
KW - Iterative multiscale methods
KW - Multiphase flow
KW - Multiscale finite-volume method
KW - Porous media
UR - http://www.scopus.com/inward/record.url?scp=85076630845&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2019.109134
DO - 10.1016/j.jcp.2019.109134
M3 - Article
AN - SCOPUS:85076630845
SN - 0021-9991
VL - 404
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 109134
ER -