Interface layers and  coupling conditions on networks for  linearized kinetic BGK equation

We consider a linearized kinetic BGK equation and the associated acoustic system on a network. Coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the consideration of a fixpoint problem involving the solutions of kinetic half-space problems. This work extends the procedure developed in [13], where coupling conditions for a simplified BGK model have been derived. Numerical comparisons between different coupling conditions confirm the accuracy of the proposed approximation.

Metadaten
Author:	Ikrom Akramov, Raul Borsche, N. Eckhard, A. Klar
URN:	urn:nbn:de:hbz:386-kluedo-71040
Document Type:	Preprint
Language of publication:	English
Date of Publication (online):	2023/01/14
Year of first Publication:	2023
Publishing Institution:	Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
Date of the Publication (Server):	2023/01/16
Page Number:	21
Faculties / Organisational entities:	Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:	5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces)
	65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M08 Finite volume methods
	82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C40 Kinetic theory of gases
Licence (German):	Creative Commons 4.0 - Namensnennung (CC BY 4.0)