Abstract
Aim of this work is the examination of numerical methods for the solution of large systems of PDE's. The equations under consideration arise from chemically reacting flows. A focal point is the analysis of a finite element discretization with stabilized finite elements of degree two. Aspects of error estimation, solution techniques and mesh adaptivity are discussed with regard to the Navier-Stokes equations. Using a well established Navier-Stokes benchmark flow the discussed methods are verified. To cope with the huge systems arising from reactive flow problems a parallel multigrid method on locally refined meshes is presented. Finally, we will perform a simulation of a methane burner in a complex three dimensional geometry. We will use a detailed reaction mechanism with 39 chemical species.
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