Nonlinear Multigrid for Reservoir Simulation

Max la Cour Christensen, Klaus Langgren Eskildsen, Allan Peter Engsig-Karup, Mark Wakefield

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A feasibility study is presented on the effectiveness of applying nonlinear multigrid methods for efficient reservoir simulation of subsurface flow in porous media. A conventional strategy modeled after global linearization by means of Newton’s method is compared with an alternative strategy modeled after local linearization, leading to a nonlinear multigrid method in the form of the full-approximation scheme (FAS). It is demonstrated through numerical experiments that, without loss of robustness, the FAS method can outperform the conventional techniques in terms of algorithmic and numerical efficiency for a black-oil model. Furthermore, the use of the FAS method enables a significant reduction in memory usage compared with conventional techniques, which suggests new possibilities for improved large-scale reservoir simulation and numerical efficiency. Last, nonlinear multilevel preconditioning in the form of a hybrid-FAS/Newton strategy is demonstrated to increase robustness and efficiency.
Original languageEnglish
Article numberSPE-178428-PA
JournalS P E Journal
Issue number3
Pages (from-to)888-898
Publication statusPublished - 2016

Cite this

Christensen, M. L. C., Eskildsen, K. L., Engsig-Karup, A. P., & Wakefield, M. (2016). Nonlinear Multigrid for Reservoir Simulation. S P E Journal, 21(3), 888-898. [SPE-178428-PA].