Derigs, Dominik ORCID: 0000-0002-9687-2035 (2018). Ideal GLM-MHD - a new mathematical model for simulating astrophysical plasmas. PhD thesis, Universität zu Köln.

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Magnetic fields are ubiquitous in space. As there is strong evidence that magnetic fields play an important role in a variety of astrophysical processes, they should not be neglected recklessly. However, analytic models in astrophysical either do often not take magnetic fields into account or can do this after limiting simplifications reducing their overall predictive power. Therefore, computational astrophysics has evolved as a modern field of research using sophisticated computer simulations to gain insight into physical processes. The ideal MHD equations, which are the most often used basis for simulating magnetized plasmas, have two critical drawbacks: Firstly, they do not limit the growth of numerically caused magnetic monopoles, and, secondly, most numerical schemes built from the ideal MHD equations are not conformable with thermodynamics. In my work, at the interplay of math and physics, I developed and presented the first thermodynamically consistent model with effective inbuilt divergence cleaning. My new Galilean-invariant model is suitable for simulating magnetized plasmas under extreme conditions as those typically encountered in astrophysical scenarios. The new model is called the "ideal GLM-MHD" equations and supports nine wave solutions. The accuracy and robustness of my numerical implementation are demonstrated with a number of tests, including comparisons to other schemes available within in the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code FLASH. A possible astrophysical application scenario is discussed in detail.

Item Type: Thesis (PhD thesis)
Translated title:
Ideale GLM-MHD - ein neues mathematisches Modell zur Beschreibung astrophysikalischer PlasmenGerman
Translated abstract:
Magnetfelder sind in der Astrophysik allgegenwärtig. Aufgrund vielfältiger Hinweise, dass sie in einer großen Zahl von astrophysikalischen Prozessen eine dominante Rolle einnehmen können, sollten ihre Auswirkungen nicht leichtfertig vernachlässigt werden. Analytische Modelle berücksichtigen hingegen oftmals keine Magnetfelder oder nur unter starker Modellvereinfachung, die dann jedoch ihre Aussagefähigkeit deutlich reduzieren kann. Aufgrund dessen hat sich die Computerphysik als modernes Forschungsgebiet entwickelt. Mithilfe hochentwickelter Simulationen komplexer numerischer Modelle gewinnt sie Einblicke in ansonsten nicht zugängliche physikalische Prozesse. Das am häufigsten verwendete Modell zur Simulation von Plasma, die idealen MHD-Gleichungen, hat zwei entscheidende Nachteile: Es begrenzt weder das Wachstum von numerisch verursachten magnetischen Monopolen, noch sind die meisten auf ihr basierenden numerischen Schema konform mit den Gesetzen der Thermodynamik, speziell dem zweiten Hauptsatz. In meiner Arbeit, die ich interdisziplinär zwischen Mathematik und theoretischer Physik durchgeführt habe, entwickelte ich das erste thermodynamisch konsistente Modell mit wirkungsvoller eingebauter Korrektur von Divergenzfehlern in magnetischen Feldern. Mein neues Galilei-invariante Modell eignet sich für die Simulation magnetisierter Plasmen unter extremen Bedingungen wie sie typischerweise in astrophysikalischen Szenarien auftreten. Es wird als die "idealen GLM-MHD Gleichungen" bezeichnet und beschreibt neun charakteristische Plasmawellen. Die Genauigkeit und Robustheit meines Verfahrens wird anhand einer Reihe von Tests mithilfe des adaptiven Multi-Physik Simulationscode FLASH demonstriert. Ein astrophysikalisches Anwendungsszenario wird ausführlich diskutiert.German
CreatorsEmailORCIDORCID Put Code
URN: urn:nbn:de:hbz:38-84427
DOI: 10.18716/kups.8442
Date: 14 September 2018
Place of Publication: Köln
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Physics > Institute of Physics I
Subjects: Mathematics
Uncontrolled Keywords:
Ideal GLM-MHDEnglish
Entropy stabilityEnglish
Entropy consistencyEnglish
Date of oral exam: 14 September 2018
NameAcademic Title
Walch-Gassner, StefanieProf. Dr.
Trebst, SimonProf. Dr.
Funders: Sonderforschungsbereich 956 "Conditions and Impact of Star Formation", Bonn-Cologne Gradate School of Physics and Astronomy
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Refereed: Yes


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