Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics

Castelletto, N.; White, J. A.; Tchelepi, H. A.

doi:10.1002/nag.2400

Title: Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics

Journal Article · 21 June 2015 · International Journal for Numerical and Analytical Methods in Geomechanics

DOI: https://doi.org/10.1002/nag.2400 · OSTI ID:1463026

Castelletto, N. ^[1]; White, J. A. ^[2]; Tchelepi, H. A. ^[1]

Stanford Univ., Stanford, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Here, the paper deals with the numerical solution of Biot's equations of coupled consolidation obtained by a mixed formulation combining continuous Galerkin finite–element and multipoint flux approximation finite–volume methods. The solution algorithm relies on the recently developed fixed–stress solution scheme, in which first the flow problem and then the mechanical one are addressed iteratively. We show that the algorithm can be interpreted as a particular block triangular preconditioning strategy applied within a Richardson iteration. The key component to the success of the preconditioner is the sparse approximation to the Schur complement based on a pressure space mass matrix scaled by a weighting factor that depends element–wise on the inverse of a suitable bulk modulus. The accuracy of the method is assessed, making use of well–known analytical solutions from the literature. Numerical results demonstrate robustness and low computational cost of the fixed–stress scheme in accurately capturing the two–way coupling between deformation and pressure.

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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:: 1463026

Report Number(s):: LLNL-JRNL--737002; 889943

Journal Information:: International Journal for Numerical and Analytical Methods in Geomechanics, Journal Name: International Journal for Numerical and Analytical Methods in Geomechanics Journal Issue: 14 Vol. 39; ISSN 0363-9061

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics

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