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URN: urn:nbn:de:bsz:25-opus-7923
URL: http://www.freidok.uni-freiburg.de/volltexte/792/


Wesenberg, Matthias

Efficient finite-volume schemes for magnetohydrodynamic simulations in solar physics

Effiziente Finite-Volumen-Verfahren für Magnetohydrodynamische Simulationen in der Sonnenphysik

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Kurzfassung in Deutsch

We present efficient finite-volume schemes for solving
the equations of (compressible) magnetohydrodynamics (MHD) in one, two, and
three spatial dimensions. We introduce a new approximate Riemann solver for the
ideal gas MHD equations (MHD-HLLEM) that outperforms all other solvers
considered. We present and compare several Riemann solvers that are suitable
for the real gas case of an arbitrary equation of state (EOS) (e.g., RGDW and
RGMHD-HLLEM). If the evaluation of the EOS is expensive, we suggest using an
adaptively-refined table for the EOS. Our error indicator facilitates a
significant enhancement of the codes' efficiencies by using locally-adapted
grids. We introduce a new limiter (DEOmod) for linear reconstructions on
unstructured triangular grids in 2d that represents a clear improvement of
the approaches commonly used. Simulations in physically-unbounded domains are
enabled by the proposed transparent boundary conditions. We show that the new
hyperbolic divergence cleaning technique is a highly effective and efficient
approach for reducing errors in the divergence of the numerical approximation
to the magnetic field. Our 3d code is parallelized for distributed-memory
machines and comprises dynamic load balancing and local grid adaption on
unstructured hexahedral or tetrahedral grids.

All our comparisons of solvers are based on considering their efficiencies,
i.e., the computational time required for reaching the same errors.
We construct one- and two-dimensional
Riemann problems whose exact solution is known at least in parts of the
computational domain. The suitability and efficiency of our multidimensional
codes for applications from solar physics is demonstrated by simulations of
magnetic fluxtubes. However, neither our new approaches nor their
implementations are restricted to solar physics. Furthermore, our new limiter
and the error indicator can be used for arbitrary time-dependent hyperbolic
systems of conservation laws.


SWD-Schlagwörter: Magnetohydrodynamik , Finite-Volumen-Methode , Nichtlineares hyperbolisches System , Computersimulation , Astrophysik
Freie Schlagwörter (deutsch): Allgemeine Zustandsgleichung , Approximative Riemannlöser , Lineare Rekonstruktion , Lokale Adaption , Effizienzvergleich
Freie Schlagwörter (englisch): solar physics , conservation laws , approximate Riemann solvers , high-resolution techniques , general equation of state
MSC Klassifikation 65Y20 Comp , 76W05 Magn , 76M12 Fini
Institut: Institut für Angewandte Mathematik
Fakultät: Mathematische Fakultät (bis Sept. 2002)
DDC-Sachgruppe: Mathematik
Dokumentart: Dissertation
Erstgutachter: Kröner, Dietmar (Prof. Dr.)
Sprache: Englisch
Tag der mündlichen Prüfung: 31.07.2003
Erstellungsjahr: 2003
Publikationsdatum: 13.08.2003
Bemerkung: Appendix: E.1: Movies
E.2: Posters
E.3: Sources
[E.4: Thesis]
E.5: Webpages
Indexliste