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FDM and FEM solutions to linear dynamics of porous media: stabilised, monolithic and fractional schemes
Author(s) -
Zhang Yunpeng,
Pedroso Dorival M.,
Li Ling
Publication year - 2016
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.5231
Subject(s) - finite element method , porous medium , stability (learning theory) , mathematics , computer science , mathematical analysis , engineering , porosity , structural engineering , geotechnical engineering , machine learning
Summary A number of methods have been developed for solving the dynamics of saturated porous media. However, most solutions are based on the finite element method, and only a few employ finite differences (FDM). One problem with the FDM is the difficulty in fulfilling the inf‐sup (Ladyženskaja‐Babuška‐Brezzi) condition. This paper explores solutions with the FDM, including the development of new schemes aiming at stabilised formulations. The efficiency, accuracy and stability of several FDM and finite element method algorithms are thoroughly investigated as well. A combination of primary variables from the theory of porous media is considered, including the so‐called up and uvp formulations. Six numerical schemes are produced and quantitatively studied. Simulations of 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes. Copyright © 2016 John Wiley & Sons, Ltd.