Commun. Comput. Phys.,
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
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
Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Compressible Navier-Stokes equations, discontinuous Galerkin finite element method, backward difference formulae, linearization.
Email: email@example.com (V. Dolejsi)