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Preprint 04-2004

Modeling and analysis of a cylinder flow including heat transfer

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Author(s) : Michael Schmidt

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 04-2004

MSC 2000

34A09 Implicit equations, differential-algebraic equations
76D05 Navier-Stokes equations

Abstract :
Exemplarily, in this diploma thesis a descriptor system arising from the spatial discretization of a PDE model of an extruder is considered. A corresponding finite volume discretization on a staggered grid is presented in detail. The application of the strangeness-index concept by Kunkel and Mehrmann provides the following results. First, the coupling of the unsteady incompressible Navier-Stokes equations with the heat equation via a temperature-depending viscosity does not lead to an additional increase of the differentiation index beyond two. Second, an equivalent index-one reformulation of the initial descriptor system in terms of the original solution components and of the same size is derived. Finally, the index-reduction process of the semi-discretized system indicates how to obtain a numerically preferable continuous model. In particular, it provides a good mathematical interpretation why formulations explicitely including the pressure-correction equation may lead to better numerical results.

Keywords : Navier-Stokes equations, heat equation, coupling of PDEs, differential-algebraic equations, strangeness-index, index reduction, finite volume method

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