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Numerical comparison of hybridized discontinuous Galerkin and finite volume methods for incompressible flow
Author(s) -
Ahnert T.,
Bärwolff G.
Publication year - 2014
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.3938
Subject(s) - discontinuous galerkin method , mathematics , finite volume method , pressure correction method , compressibility , galerkin method , incompressible flow , convergence (economics) , flow (mathematics) , stability (learning theory) , finite element method , navier–stokes equations , computational fluid dynamics , mathematical analysis , geometry , mechanics , physics , computer science , machine learning , economics , thermodynamics , economic growth
SUMMARY In this study, a hybridizable discontinuous Galerkin method is presented for solving the incompressible Navier–Stokes equation. In our formulation, the convective part is linearized using a Picard iteration, for which there exists a necessary criterion for convergence. We show that our novel hybridized implementation can be used as an alternative method for solving a range of problems in the field of incompressible fluid dynamics. We demonstrate this by comparing the performance of our method with standard finite volume solvers, specifically the well‐established finite volume method of second order in space, such as the icoFoam and simpleFoam of the OpenFOAM package for three typical fluid problems. These are the Taylor–Green vortex, the 180‐degree fence case and the DFG benchmark. Our careful comparison yields convincing evidence for the use of hybridizable discontinuous Galerkin method as a competitive alternative because of their high accuracy and better stability properties. Copyright © 2014 John Wiley & Sons, Ltd.