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

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

doi:10.1016/j.jcp.2024.113163

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

Journal Article · 04 June 2024 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2024.113163· OSTI ID:2407228

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

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

A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed here. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.

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:: 2407228

Report Number(s):: LLNL--JRNL-851214; 1077624

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 513; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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