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A symmetric weak form of Biot's equations based on redundant variables representing the fluid, using a Helmholtz decomposition of the fluid displacement vector field
Author(s) -
Hörlin N.E.
Publication year - 2010
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.2956
Subject(s) - biot number , displacement (psychology) , poromechanics , displacement field , conservative vector field , finite element method , scalar (mathematics) , mathematical analysis , mathematics , helmholtz free energy , classical mechanics , physics , mechanics , porous medium , geometry , materials science , porosity , thermodynamics , psychology , compressibility , composite material , psychotherapist
A novel symmetric weak formulation of Biot's equations for linear acoustic wave propagation in layered poroelastic media is presented. The primary variables used are the frame displacement, the acoustic pore pressure, the scalar potential and the vector potential obtained from a Helmholtz decomposition of the fluid displacement. Also a symmetric weak form based on the frame displacement, the pore pressure and the fluid displacement is obtained as an intermediate result. hp finite element simulations of a double leaf partition based on this new weak formulation is verified against simulation results from the classical frame displacement, fluid displacement formulation and a frame displacement pore pressure formulation. All three formulations simulated, displays the same rate of convergence with respect to finite element bases polynomial degree. The novel formulation also extends a previously published frame displacement, pore pressure, scalar fluid displacement potential formulation with an implicit irrotational fluid displacement assumption to a full representation of Biot's equations. Copyright © 2010 John Wiley & Sons, Ltd.