Commun. Comput. Phys.,
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Volume 4.


Semi-Implicit Interior Penalty Discontinuous Galerkin Methods for Viscous Compressible Flows

Vit Dolejsi 1*

1 Charles University Prague, Faculty of Mathematics and Physics, Sokolovska 83, 186 75 Prague, Czech Republic.

Received 15 July 2007; Accepted (in revised version) 6 February 2008
Available online 14 March 2008

Abstract

We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible fluids. In order to obtain a sufficiently stable higher order scheme with respect to the time and space coordinates, we develop a combination of the discontinuous Galerkin finite element (DGFE) method for the space discretization and the backward difference formulae (BDF) for the time discretization. Since the resulting discrete problem leads to a system of nonlinear algebraic equations at each time step, we employ suitable linearizations of inviscid as well as viscous fluxes which give a linear algebraic problem at each time step. Finally, the resulting BDF-DGFE scheme is applied to steady as well as unsteady flows and achieved results are compared with reference data.

AMS subject classifications: 76M10, 76N15, 35Q35, 65L06

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Key words: Compressible Navier-Stokes equations, discontinuous Galerkin finite element method, backward difference formulae, linearization.

*Corresponding author.
Email: dolejsi@karlin.mff.cuni.cz (V. Dolejsi)
 

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