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A sensitivity analysis on the parameter of the GLS method for a second‐gradient theory of incompressible flow
Author(s) -
Barbosa da Cruz Antônio G.,
Dutra do Carmo Eduardo G.,
Duda Fernando P.
Publication year - 2015
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.4033
Subject(s) - mathematics , discretization , galerkin method , finite element method , discontinuous galerkin method , compressibility , incompressible flow , mathematical analysis , degree of a polynomial , basis function , polynomial basis , square (algebra) , robustness (evolution) , flow (mathematics) , polynomial , geometry , mechanics , physics , thermodynamics , biochemistry , chemistry , gene
Summary Using a non‐conforming C 0 ‐interior penalty method and the Galerkin least‐square approach, we develop a continuous–discontinuous Galerkin finite element method for discretizing fourth‐order incompressible flow problems. The formulation is weakly coercive for spaces that fail to satisfy the inf‐sup condition and consider discontinuous basis functions for the pressure field. We consider the results of a stability analysis through a lemma which indicates that there exists an optimal or quasi‐optimal least‐square stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, and on the geometry of the finite element in the mesh. We provide several numerical experiments illustrating such dependence, as well as the robustness of the method to deal with arbitrary basis functions for velocity and pressure, and the ability to stabilize large pressure gradients. We believe the results provided in this paper contribute for establishing a paradigm for future studies of the parameter of the Galerkin least square method for second‐gradient theory of incompressible flow problems. Copyright © 2015 John Wiley & Sons, Ltd.