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Symmetric extensions of normal discrete velocity models
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Kinetisk teori)
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Kinetisk teori)
2012 (English)In: 28th International Symposium on Rarefied Gas Dynamics 2012 / [ed] Michel Mareschal, Andrés Santos, American Institute of Physics (AIP), 2012, 1, Vol. 1501, no 1, 254-261 p.Conference paper, (Refereed)
Abstract [en]

In this paper we discuss a general problem related to spurious conservation laws for discrete velocity models (DVMs) of the classical (elastic) Boltzmann equation. Models with spurious conservation laws appeared already at the early stage of the development of discrete kinetic theory. The well-known theorem of uniqueness of collision invariants for the continuous velocity space very often does not hold for a set of discrete velocities. In our previous works we considered the general problem of the construction of normal DVMs, we found a general algorithm for the construction of all such models and presented a complete classification of normal DVMs with small number n of velocities (n<11). Even if we have a general method to classify all normal discrete kinetic models (and in particular DVMs), the existing method is relatively slow and the amount of possible cases to check increases rapidly with n. We remarked that many of our normal DVMs appear to be axially symmetric. In this paper we consider a connection between symmetric transformations and normal DVMs. We first develop a new inductive method that, starting with a given normal DVM, leads by symmetric extensions to a new normal DVM. This method can produce very fast many new normal DVMs with larger number of velocities, showing that the class of normal DVMs contains a large subclass of symmetric models. We finally apply the method to several normal DVMs and construct new models that are not only normal, but also symmetric relatively to more and more axes. We hope that such symmetric velocitysets can be used for DSMC methods of solving Boltzmann equation.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2012, 1. Vol. 1501, no 1, 254-261 p.
Series
AIP Conference Proceedings, ISSN 1551-7616 ; 1501
Keyword [en]
Kinetic theory, discrete kinetic (velocity) models, conservation laws
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-16072DOI: 10.1063/1.4769516ISI: 000312411200032ISBN: 978-0-7354-1115-9 (print)OAI: oai:DiVA.org:kau-16072DiVA: diva2:573775
Conference
28th International Symposium on Rarefied Gas Dynamics 2012, July 9 - 13, Zaragoza
Available from: 2012-12-03 Created: 2012-12-03 Last updated: 2017-07-07Bibliographically approved

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Publisher's full texthttp://proceedings.aip.org/resource/2/apcpcs/1501/1/254_1

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