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Preprint 08-2013

Numerical comparison of hybridized discontinuous Galerkin and finite volume methods for incompressible flow

Source file is available as :   Portable Document Format (PDF)

Author(s) : Tobias Ahnert , Günter Bärwolff

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 08-2013

MSC 2000

65M12 Stability and convergence of numerical methods
65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract :
A numerical comparison of a hybridizable discontinuous Galerkin method proposed by Nguyen et al. and the well established finite volume method of second order in space represented by the icoFoam and simpleFoam solver of OpenFOAM is given. The hybridizable iscontinuous Galerkin method has been reformulated as Picard iteration, hybridized and implemented from scratch. The methods are introduced and four numerical standard simulations are used in order to benchmark and evaluate the solver - the Taylor-Green vortex, the 180 degrees fence case as well as a two-dimensional stationary and non-stationary DFG benchmark. The numerical examples suggests hybridized discontinuous Galerkin methods are a competitive alternative to finite volume solvers for incompressible fluid simulations due to high accuracy and better stability properties.

Keywords : iscontinuous Galerkin method, finite volume method, incompressible Navier-Stokes equations, DFG benchmark, implicit Euler

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