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Implementation of the Lagrange‐Galerkin method for the incompressible Navier‐Stokes equations
Author(s) -
Buscaglia Gustavo C.,
Dari Enzo A.
Publication year - 1992
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.1650150103
Subject(s) - discretization , mathematics , polygon mesh , galerkin method , finite element method , navier–stokes equations , discontinuous galerkin method , scheme (mathematics) , vortex shedding , cylinder , compressibility , square (algebra) , vortex , mathematical analysis , geometry , physics , turbulence , reynolds number , mechanics , thermodynamics
This paper is concerned with the implementation of Lagrange‐Galerkin finite element methods for the Navier‐Stokes equations. A scheme is developed to efficiently handle unstructed meshes with local refinement, using a quad‐tree‐based algorithm for the geometric search. Several difficulties that arise in the construction of the right‐hand side are discussed in detail and some useful tricks are proposed. The resulting method is tested on the lid‐driven square cavity and the vortex shedding behind a rectangular cylinder and is found to give satisfactory agreement with previous works. A detailed analysis of the effect of time discretization is included.