Inhalt des Dokuments
Preprint 04-2004
Modeling and analysis of a cylinder flow including heat transfer
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