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Second‐order time discretization for a coupled quasi‐Newtonian fluid‐poroelastic system
Author(s) -
Kunwar Hemanta,
Lee Hyesuk,
Seelman Kyle
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4801
Subject(s) - poromechanics , biot number , discretization , nonlinear system , decoupling (probability) , mathematics , newtonian fluid , fluid–structure interaction , mathematical analysis , mechanics , finite element method , physics , porous medium , engineering , geotechnical engineering , quantum mechanics , control engineering , porosity , thermodynamics
Summary Numerical methods are proposed for the nonlinear Stokes‐Biot system modeling interaction of a free fluid with a poroelastic structure. We discuss time discretization and decoupling schemes that allow the fluid and the poroelastic structure computed independently using a common stress force along the interface. The coupled system of nonlinear Stokes and Biot is formulated as a least‐squares problem with constraints, where the objective functional measures violation of some interface conditions. The local constraints, the Stokes and Biot models, are discretized in time using second‐order schemes. Computational algorithms for the least‐squares problems are discussed and numerical results are provided to compare the accuracy and efficiency of the algorithms.