Details

Autor(en) / Beteiligte

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

Titel

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

Ist Teil von

• Computational geosciences, 2019-04, Vol.23 (2), p.207-224

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2019

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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. Various numerical experiments are used to demonstrate the robustness of the proposed solver.