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FDM solutions to linear dynamics of porous media: Efficiency, stability, and parallel solution strategy
Author(s) -
Zhang Yunpeng,
Pedroso Dorival M.,
Li Ling,
Ehlers Wolfgang
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5568
Subject(s) - porous medium , computation , displacement (psychology) , stability (learning theory) , mathematics , saturation (graph theory) , bandwidth (computing) , porosity , linear system , computer science , mathematical optimization , mathematical analysis , algorithm , materials science , telecommunications , combinatorics , psychotherapist , psychology , machine learning , composite material
Summary This paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation. The method is named parallel‐lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations. As a result, the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved. The other advantage of the scheme is the fulfilment of the inf‐sup stability condition. The scheme is developed to solve porous media formulations derived from the theory of porous media. Both the u‐p and u‐v‐p formulations are considered (u: displacement of solid, p: pressure of liquid, and v: velocity of liquid). Several simulations are performed to demonstrate the capabilities of the method.