Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

Castelletto, Nicola; Klevtsov, Sergey; Hajibeygi, Hadi; Tchelepi, Hamdi A.

doi:10.1007/s10596-018-9791-z

Title: Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

Journal Article · 09 November 2018 · Computational Geosciences

DOI: https://doi.org/10.1007/s10596-018-9791-z · OSTI ID:1548341

Castelletto, Nicola ^[1]; Klevtsov, Sergey ^[2]; Hajibeygi, Hadi ^[3];

^[2]

Stanford Univ., CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Stanford Univ., CA (United States)
Delft Univ. of Technology (Netherlands)

In this paper, we propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Lastly, various numerical experiments are used to demonstrate the robustness of the proposed solver.

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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:: 1548341

Report Number(s):: LLNL-JRNL-747875; 932724

Journal Information:: Computational Geosciences, Vol. 23, Issue 2; ISSN 1420-0597

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

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