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Stabilization procedures in coupled poromechanics problems: A critical assessment
Author(s) -
Preisig Matthias,
Prévost Jean H.
Publication year - 2010
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.951
Subject(s) - poromechanics , nonlinear system , bilinear interpolation , spurious relationship , stability (learning theory) , simple (philosophy) , mathematics , bubble , calculus (dental) , control theory (sociology) , computer science , engineering , porous medium , geotechnical engineering , control (management) , physics , porosity , medicine , philosophy , statistics , dentistry , epistemology , quantum mechanics , machine learning , artificial intelligence , parallel computing
Numerical solutions for problems in coupled poromechanics suffer from spurious pressure oscillations when small time increments are used. This has prompted many researchers to develop methods to overcome these oscillations. In this paper, we present an overview of the methods that in our view are most promising. In particular we investigate several stabilized procedures, namely the fluid pressure Laplacian stabilization (FPL), a stabilization that uses bubble functions to resolve the fine‐scale solution within elements, and a method derived by using finite increment calculus (FIC). On a simple one‐dimensional test problem, we investigate stability of the three methods and show that the approach using bubble functions does not remove oscillations for all time step sizes. On the other hand, the analysis reveals that FIC stabilizes the pressure for all time step sizes, and it leads to a definition of the stabilization parameter in the case of the FPL‐stabilization. Numerical tests in one and two dimensions on 4‐noded bilinear and linear triangular elements confirm the effectiveness of both the FPL‐ and the FIC‐stabilizations schemes for linear and nonlinear problems. Copyright © 2010 John Wiley & Sons, Ltd.