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Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics
UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA.;Saudi Arabian Oil Co, Dhahran, Saudi Arabia..
Univ Bergen, Math Inst, N-5020 Bergen, Norway..
Saudi Arabian Oil Co, Dhahran, Saudi Arabia..
UT Austin, Ctr Subsurface Modeling, ICES, Austin, TX 78712 USA..
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2016 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 311, p. 180-207Article in journal (Refereed) Published
Abstract [en]

We consider multirate iterative schemes for the Biot system modeling coupled flow and geomechanics in a poro-elastic medium. The multirate iterative coupling scheme exploits the different time scales for the mechanics and flow problems by taking multiple finer time steps for flow within one coarse mechanics time step. We adapt the fixed stress split algorithm that decouples the flow and mechanics equations for the multirate case and perform an iteration between the two problems until convergence. We provide a fully discrete scheme that uses Backward Euler time discretization and mixed spaces for flow and conformal Galerkin for mechanics. Our analysis is based on studying the equations satisfied by the difference of iterates and using Banach contraction argument to prove that the corresponding scheme is a fixed point contraction. The analysis provides the value of an adjustable coefficient used in the proposed iterative coupling algorithms. Furthermore, we show that the converged quantities satisfy the variational weak form for the coupled discrete system. (C) 2016 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 311, p. 180-207
Keywords [en]
Poroelasticity, Biot system, Fixed-stress split iterative coupling, Multirate scheme, Contraction mapping
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-69253DOI: 10.1016/j.cma.2016.07.036ISI: 000387520000009OAI: oai:DiVA.org:kau-69253DiVA, id: diva2:1254262
Available from: 2018-10-08 Created: 2018-10-08 Last updated: 2019-12-12Bibliographically approved

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Kumar, Kundan

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