The discontinuous Galerkin method for convection-diffusion problems in time-dependent domains

• ID: 2494, RIV: 10051849
• ISSN: not specified, ISBN: 978-3-642-11795-4
• source: Numerical Mathematics and Advanced Applications 2009
• keywords: discontinuous Galerkin solution; convection-diffusion problems; time-dependent domains; ALE formulation
• authors: Václav Kučera, Miloslav Feistauer, Jaroslava Prokopová
• authors from KNM: Feistauer Miloslav, Kučera Václav

Abstract

This paper is concerned with the numerical treatment of convection-diffusion problems in time-dependent domains. A suitable formulation of the governing equations is derived using the Arbitrary Lagrangian-Eulerian (ALE) method. The equations are then discretized in space using the discontinuous Galerkin method. The resulting space-semidiscretization scheme is numerically tested on the compressible Navier-Stokes equations describing the flow of viscous gases. The particular form of these equations allows the use of a semi-implicit time discretization, which has already been extensively studied in the case of stationary computational domains.