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On the optimization of the fixed-stress splitting for Biot’s equations
University Bergen, Norway.
University Bergen, Norway.
University Bergen, Norway.
University Bergen, Norway.
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2019 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 120, no 2, p. 179-194Article in journal (Refereed) Published
Abstract [en]

In this work, we are interested in efficiently solving the quasi-static, linear Biot model for poroelasticity. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot’s equations. It is well known that the convergence properties of the method strongly depend on the applied stabilization/tuning parameter. We show theoretically that, in addition to depending on the mechanical properties of the porous medium and the coupling coefficient, they also depend on the fluid flow and spatial discretization properties. The type of analysis presented in this paper is not restricted to a particular spatial discretization, although it is required to be inf-sup stable with respect to the displacement-pressure formulation. Furthermore, we propose a way to optimize this parameter that relies on the mesh independence of the scheme’s optimal stabilization parameter. Illustrative numerical examples show that using the optimized stabilization parameter can significantly reduce the number of iterations.

Place, publisher, year, edition, pages
John Wiley & Sons, 2019. Vol. 120, no 2, p. 179-194
Keywords [en]
Biot model; convergence analysis; fixed-stress splitting; geomechanics; poroelasticity
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-73567DOI: 10.1002/nme.6130ISI: 000492031500003Scopus ID: 2-s2.0-85067514257OAI: oai:DiVA.org:kau-73567DiVA, id: diva2:1336783
Funder
The Research Council of Norway, 250223Available from: 2019-07-10 Created: 2019-07-10 Last updated: 2019-11-28Bibliographically approved

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Kumar, Kundan
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