Application of the Finite Pointset Method to moving boundary problems for the BGK model of rarefied gas dynamics

  • The overall goal of the work is to simulate rarefied flows inside geometries with moving boundaries. The behavior of a rarefied flow is characterized through the Knudsen number \(Kn\), which can be very small (\(Kn < 0.01\) continuum flow) or larger (\(Kn > 1\) molecular flow). The transition region (\(0.01 < Kn < 1\)) is referred to as the transition flow regime. Continuum flows are mainly simulated by using commercial CFD methods, which are used to solve the Euler equations. In the case of molecular flows one uses statistical methods, such as the Direct Simulation Monte Carlo (DSMC) method. In the transition region Euler equations are not adequate to model gas flows. Because of the rapid increase of particle collisions the DSMC method tends to fail, as well Therefore, we develop a deterministic method, which is suitable to simulate problems of rarefied gases for any Knudsen number and is appropriate to simulate flows inside geometries with moving boundaries. Thus, the method we use is the Finite Pointset Method (FPM), which is a mesh-free numerical method developed at the ITWM Kaiserslautern and is mainly used to solve fluid dynamical problems. More precisely, we develop a method in the FPM framework to solve the BGK model equation, which is a simplification of the Boltzmann equation. This equation is mainly used to describe rarefied flows. The FPM based method is implemented for one and two dimensional physical and velocity space and different ranges of the Knudsen number. Numerical examples are shown for problems with moving boundaries. It is seen, that our method is superior to regular grid methods with respect to the implementation of boundary conditions. Furthermore, our results are comparable to reference solutions gained through CFD- and DSMC methods, respectevly.

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Verfasserangaben:Maria Kobert
URN (Permalink):urn:nbn:de:hbz:386-kluedo-41824
Betreuer:Axel Klar
Sprache der Veröffentlichung:Englisch
Veröffentlichungsdatum (online):25.09.2015
Jahr der Veröffentlichung:2015
Veröffentlichende Institution:Technische Universität Kaiserslautern
Titel verleihende Institution:Technische Universität Kaiserslautern
Datum der Annahme der Abschlussarbeit:22.07.2015
Datum der Publikation (Server):28.09.2015
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX)
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vom 30.07.2015