Computerorientiertes Problemlösen WS 2011/2012

16, Sep, 2011

Die Begleitmaterialien zur Veranstaltung “Computerorientiertes Problemlösen” im Wintersemester 2011/12 stehen auf der Kurs-Homepage zur Verfügung.

Die Leistungsnachweise sind im BOSS-System erfasst. Studierende, deren Studiengang nicht mit dem BOSS-System arbeitet, können ihre Leistungsnachweise ab dem 21.10.2011 im Sekretariat Raum 1049 bei Frau Drees (vormittags) abholen.

Talk at Hirschegg Workshop on Conservation Laws 2011

13, Sep, 2011

The slides of my talk On a failsafe flux limiting approach for the Euler equations presented at the 10th Hirschegg Workshop on Conservation Laws Conference, September 4 - 10, 2011 in Hirschegg, Austria can be downloaded here.

Preprint on high-resolution finite element schemes for an idealized Z-pinch implosion model

31, May, 2010

The following preprint has been added to my list of publications.

D. Kuzmin, M. Möller and J.N. Shadid, High-resolution finite element schemes for an idealized Z-pinch implosion model (PS, PDF). Technical Report 410, Technische Universität Dortmund, 2010.

Abstract

A high-resolution finite element method is developed for numerical simulation of Z-pinch-like implosions using a phenomenological model for the magnetic drive source term. The momentum and energy equations of the Euler system are extended by adding radial body forces proportional to the concentration of a scalar tracer field. The evolution of the tracer is governed by an additional transport equation which is solved in a segregated fashion. The finite element discretization is stabilized using a linearized flux-corrected transport (FCT) algorithm. Scalar viscosity of Rusanov type is employed to construct the underlying low-order scheme. In the process of flux limiting, node-by-node transformations from the conservative to the primitive variables are performed to ensure that all quantities of interest (density, pressure, tracer) are bounded by the physically admissible low-order values. The performance of the proposed algorithm on fully unstructured meshes is illustrated by numerical results for a power law implosion in the x-y plane.

The paper has been submitted to Computers & Fluids.

Preprint on failsafe flux limiting

21, Apr, 2010

The following preprint has been added to my list of publications.

D. Kuzmin, M. Möller, J.N. Shadid and M. Shashkov, Failsafe flux limiting and constrained data projections for systems of conservation laws (PS, PDF). Technical Report 407, Technische Universität Dortmund, 2010.

Abstract

A new approach to flux limiting for systems of conservation laws is presented. The Galerkin finite element discretization/L2 projection is equipped with a failsafe mechanism that prevents the birth and growth of spurious local extrema. Within the framework of a synchronized flux-corrected transport (FCT) algorithm, the velocity and pressure fields are constrained using node-by-node transformations from the conservative to the primitive variables. An additional correction step is included to ensure that all the quantities of interest (density, velocity, pressure) are bounded by the physically admissible low-order values. The result is a conservative and bounded scheme with low numerical diffusion. The new failsafe FCT limiter is integrated into a high-resolution finite element scheme for the Euler equations of gas dynamics. Also, bounded L2 projection operators for conservative interpolation/initialization are designed. The performance of the proposed limiting strategy and the need for a posteriori control of flux-corrected solutions are illustrated by numerical examples.

The paper has been submitted to Journal of Computational Physics.

Talk at ICFD Conference 2010

19, Apr, 2010

The slides of my talk On the design of high-resolution finite element schemes for coupled problems with application to an idealized Z-pinch implosion model presented at the 10th ICFD Conference on Numerical Methods for Fluid Dynamics, April 11-15, 2010, at the University of Reading, England can be downloaded here.

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