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Computational Mechanics
Erschienen in: Computational Mechanics 2/2017

14.11.2016 | Original Paper

Von Neumann stability analysis of the u–p reproducing kernel formulation for saturated porous media

verfasst von: Sheng-Wei Chi, Thanakorn Siriaksorn, Shih-Po Lin

Erschienen in: Computational Mechanics | Ausgabe 2/2017

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Abstract

This paper introduces the von Neumann method to investigate the temporal stability of the displacement–pressure \((u{-}p)\) reproducing kernel formulation for saturated porous media. Both dynamic and quasi-static formulations are considered and the critical time steps are derived. The effect of lumped and consistent matrices on temporal stability is analyzed under explicit temporal discretization. It is shown that lumped matrices have better temporal stability than consistent matrices. The study also shows that nodal support size greatly affects the critical time step size of the formulations. For consistent matrices, larger support size results in smaller critical time step size; however, opposite relation occurs if lumped scheme is used. The numerical study shows that stabilization parameter of the stabilized nodal integration methods reduces the critical time step size. Transient analyses are performed to verify the results from von Neumann analysis.
Vorheriger Artikel Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method

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Metadaten
Titel
Von Neumann stability analysis of the u–p reproducing kernel formulation for saturated porous media
verfasst von
Sheng-Wei Chi
Thanakorn Siriaksorn
Shih-Po Lin
Publikationsdatum
14.11.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 2/2017
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-016-1349-0

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