Authors
Jakub Wiktor Both, Kundan Kumar, Jan Martin Nordbotten, Florin Adrian Radu
Publication date
2019/3/15
Journal
Computers & Mathematics with Applications
Volume
77
Issue
6
Pages
1479-1502
Publisher
Pergamon
Description
In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, generalizing the classical Biot equations. In practice a monolithic solver is not always available, defining the requirement for a linearization scheme to allow the use of separate simulators. It is not met by the classical Newton method. We propose three different linearization schemes incorporating the fixed-stress splitting scheme, coupled with an L-scheme, Modified Picard and Newton linearization of the flow equations. All schemes allow the efficient and robust decoupling of mechanics and flow equations. In particular, the simplest scheme, the Fixed-Stress-L-scheme, employs solely constant diagonal stabilization, has low cost per iteration, and is very robust. Under mild, physical assumptions, it is theoretically shown to be a …
Total citations
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Scholar articles
JW Both, K Kumar, JM Nordbotten, FA Radu - Computers & Mathematics with Applications, 2019