An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media

Lee, Chak Shing; Hamon, François P.; Castelletto, Nicola; Vassilevski, Panayot S.; White, Joshua A.

doi:10.1016/j.camwa.2022.03.026

An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media

Journal Article · Thu Mar 24 00:00:00 EDT 2022 · Computers and Mathematics with Applications (Oxford)

DOI:https://doi.org/10.1016/j.camwa.2022.03.026· OSTI ID:1860844

^[1]; Hamon, François P. ^[2]; Castelletto, Nicola ^[3]; Vassilevski, Panayot S. ^[4]; ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
TotalEnergies E&P Research and Technology, Houston, TX (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Portland State Univ., OR (United States)

A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our previous work on nonlinear multigrid for heterogeneous diffusion problems. The coarse spaces in the multigrid hierarchy are constructed by first aggregating degrees of freedom, and then solving some local flow problems. The mixed formulation and the choice of coarse spaces allow us to assemble the coarse problems without visiting finer levels during the solving phase, which is crucial for the scalability of multigrid methods. Specifically, a natural generalization of the upwind flux can be evaluated directly on coarse levels using the precomputed coarse flux basis vectors. We find that the resulting solver is applicable to problems discretized on general unstructured grids. The performance of the proposed nonlinear multigrid solver in comparison with the standard single level Newton's method is demonstrated through challenging numerical examples. It is observed that the proposed solver is robust for highly nonlinear problems and clearly outperforms Newton's method in the case of high Courant-Friedrichs-Lewy (CFL) numbers.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1860844

Report Number(s):: LLNL-JRNL-826461; 1041112

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Journal Issue: na Vol. 113; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (32)

The egg model - a geological ensemble for reservoir simulation Jansen, J. D.; Fonseca, R. M.; Kahrobaei, S. Geoscience Data Journal, Vol. 1, Issue 2 https://doi.org/10.1002/gdj3.21	journal	November 2014
Decoupling preconditioners in the implicit parallel accurate reservoir simulator (IPARS) Lacroix, S�bastien; Vassilevski, Yuri V.; Wheeler, Mary F. Numerical Linear Algebra with Applications, Vol. 8, Issue 8 https://doi.org/10.1002/nla.264	journal	January 2001
Analysis of a linearization scheme for an interior penalty discontinuous Galerkin method for two-phase flow in porous media with dynamic capillarity effects: ANALYSIS OF A LINEARIZATION SCHEME FOR AN INTERIOR PENALTY DG METHOD Karpinski, Stefan; Pop, Iuliu Sorin; Radu, Florin Adrian International Journal for Numerical Methods in Engineering, Vol. 112, Issue 6 https://doi.org/10.1002/nme.5526	journal	May 2017
Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity Lee, S. H.; Wolfsteiner, C.; Tchelepi, H. A. Computational Geosciences, Vol. 12, Issue 3 https://doi.org/10.1007/s10596-007-9069-3	journal	January 2008
A comparison of multiscale methods for elliptic problems in porous media flow Kippe, Vegard; Aarnes, Jørg E.; Lie, Knut-Andreas Computational Geosciences, Vol. 12, Issue 3 https://doi.org/10.1007/s10596-007-9074-6	journal	February 2008
Ordering-based nonlinear solver for fully-implicit simulation of three-phase flow Hamon, François P.; Tchelepi, Hamdi A. Computational Geosciences, Vol. 20, Issue 5 https://doi.org/10.1007/s10596-016-9569-0	journal	April 2016
Nonlinear solver for three-phase transport problems based on approximate trust regions Møyner, Olav Computational Geosciences, Vol. 21, Issue 5-6 https://doi.org/10.1007/s10596-017-9660-1	journal	July 2017
Efficient reordered nonlinear Gauss–Seidel solvers with higher order for black-oil models Klemetsdal, Øystein S.; Rasmussen, Atgeirr F.; Møyner, Olav Computational Geosciences, Vol. 24, Issue 2 https://doi.org/10.1007/s10596-019-09844-5	journal	July 2019
Two-Scale Preconditioning for Two-Phase Nonlinear Flows in Porous Media Skogestad, Jan Ole; Keilegavlen, Eirik; Nordbotten, Jan M. Transport in Porous Media, Vol. 114, Issue 2 https://doi.org/10.1007/s11242-015-0587-5	journal	October 2015
Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto Journal of Computational and Applied Mathematics, Vol. 340 https://doi.org/10.1016/j.cam.2017.10.029	journal	October 2018
Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems Lee, Chak Shing; Hamon, François; Castelletto, Nicola Computer Methods in Applied Mechanics and Engineering, Vol. 372 https://doi.org/10.1016/j.cma.2020.113432	journal	December 2020
Potential-based reduced Newton algorithm for nonlinear multiphase flow in porous media Kwok, Felix; Tchelepi, Hamdi Journal of Computational Physics, Vol. 227, Issue 1 https://doi.org/10.1016/j.jcp.2007.08.012	journal	November 2007
Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements Natvig, Jostein R.; Lie, Knut-Andreas Journal of Computational Physics, Vol. 227, Issue 24 https://doi.org/10.1016/j.jcp.2008.08.024	journal	December 2008
Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions Jenny, Patrick; Tchelepi, Hamdi A.; Lee, Seong H. Journal of Computational Physics, Vol. 228, Issue 20 https://doi.org/10.1016/j.jcp.2009.06.032	journal	November 2009
Domain decomposition strategies for nonlinear flow problems in porous media Skogestad, Jan Ole; Keilegavlen, Eirik; Nordbotten, Jan M. Journal of Computational Physics, Vol. 234 https://doi.org/10.1016/j.jcp.2012.10.001	journal	February 2013
Trust-region based solver for nonlinear transport in heterogeneous porous media Wang, Xiaochen; Tchelepi, Hamdi A. Journal of Computational Physics, Vol. 253 https://doi.org/10.1016/j.jcp.2013.06.041	journal	November 2013
Nonlinear analysis of multiphase transport in porous media in the presence of viscous, buoyancy, and capillary forces Li, Boxiao; Tchelepi, Hamdi A. Journal of Computational Physics, Vol. 297 https://doi.org/10.1016/j.jcp.2015.04.057	journal	September 2015
Dissipation-based continuation method for multiphase flow in heterogeneous porous media Jiang, Jiamin; Tchelepi, Hamdi A. Journal of Computational Physics, Vol. 375 https://doi.org/10.1016/j.jcp.2018.08.044	journal	December 2018
Decoupling and Block Preconditioning for Sedimentary Basin Simulations Scheichl, R.; Masson, R.; Wendebourg, J. Computational Geosciences, Vol. 7, Issue 4 https://doi.org/10.1023/B:COMG.0000005244.61636.4e	journal	January 2003
Multi-level adaptive solutions to boundary-value problems Brandt, Achi Mathematics of Computation, Vol. 31, Issue 138 https://doi.org/10.1090/S0025-5718-1977-0431719-X	journal	May 1977
On the Use of a Mixed Multiscale Finite Element Method for GreaterFlexibility and Increased Speed or Improved Accuracy in Reservoir Simulation Aarnes, Jorg E. Multiscale Modeling & Simulation, Vol. 2, Issue 3 https://doi.org/10.1137/030600655	journal	January 2004
A Hierarchical Multiscale Method for Two-Phase Flow Based upon Mixed Finite Elements and Nonuniform Coarse Grids Aarnes, Jorg E.; Krogstad, Stein; Lie, Knut-Andreas Multiscale Modeling & Simulation, Vol. 5, Issue 2 https://doi.org/10.1137/050634566	journal	January 2006
Multigrid Smoothers for Ultraparallel Computing Baker, Allison H.; Falgout, Robert D.; Kolev, Tzanio V. SIAM Journal on Scientific Computing, Vol. 33, Issue 5 https://doi.org/10.1137/100798806	journal	January 2011
Field-Split Preconditioned Inexact Newton Algorithms Liu, Lulu; Keyes, David E. SIAM Journal on Scientific Computing, Vol. 37, Issue 3 https://doi.org/10.1137/140970379	journal	January 2015
Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method Dolean, V.; Gander, M. J.; Kheriji, W. SIAM Journal on Scientific Computing, Vol. 38, Issue 6 https://doi.org/10.1137/15M102887X	journal	January 2016
Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation Barker, Andrew T.; Gelever, Stephan V.; Lee, Chak S. SIAM Journal on Scientific Computing, Vol. 43, Issue 4 https://doi.org/10.1137/19M1296343	journal	January 2021
Nonlinearly Preconditioned Inexact Newton Algorithms Cai, Xiao-Chuan; Keyes, David E. SIAM Journal on Scientific Computing, Vol. 24, Issue 1 https://doi.org/10.1137/S106482750037620X	journal	January 2002
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs Karypis, George; Kumar, Vipin SIAM Journal on Scientific Computing, Vol. 20, Issue 1 https://doi.org/10.1137/S1064827595287997	journal	January 1998
Sensitivity of the impact of geological uncertainty on production from faulted and unfaulted shallow-marine oil reservoirs: objectives and methods Manzocchi, T.; Carter, J. N.; Skorstad, A. Petroleum Geoscience, Vol. 14, Issue 1 https://doi.org/10.1144/1354-079307-790	journal	February 2008
Adaptively Localized Continuation-Newton Method—Nonlinear Solvers That Converge All the Time Younis, R. M. . M.; Tchelepi, H. A. . A.; Aziz, K. . SPE Journal, Vol. 15, Issue 02 https://doi.org/10.2118/119147-PA	journal	December 2009
Nonlinear Multigrid for Reservoir Simulation Christensen, Max la; Eskildsen, Klaus Langgren; Engsig-Karup, Allan Peter SPE Journal, Vol. 21, Issue 03 https://doi.org/10.2118/178428-PA	journal	June 2016
Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques Christie, M. A.; Blunt, M. J. SPE Reservoir Evaluation & Engineering, Vol. 4, Issue 04 https://doi.org/10.2118/72469-PA	journal	August 2001

Similar Records

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

Journal Article · Mon Jun 03 20:00:00 EDT 2024 · Journal of Computational Physics · OSTI ID:2407228

NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

Technical Report · Thu Jan 21 23:00:00 EST 2016 · OSTI ID:1237574

Related Subjects

58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
algebraic multigrid
full approximation scheme
generalized upwind flux
nonlinear multigrid
two-phase flow and transport
unstructured

An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media

Citation Formats

References (32)

Similar Records

Related Subjects