Summary
This article is devoted to domain decomposition schemes for kinetic and hydrodynamic equations. A convergence proof for an alternating scheme is given and coupling conditions at the interface between the equations are developed and investigated. In particular for nonequilibrium situations at the interface new coupling conditions are developed by considering interface layers. This leads to kinetic linear half space problems. A fast procedure to solve these problems is given.
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References
J.F. Bourgat, P. Le Tallec, D.Tidriri, Y. Qiu, Numerical Coupling of Nonconservative or Kinetic Models with the Conservative Compressible Navier Stokes Equations, Fifth International Symposium on Domain Decomposition methods for P.D.E., SIAM, Philadelphia 1991.
F. Coron, F. Golse, C. Sulem, A Classification of Well-posed Kinetic Layer Problems, CPAM, Vol. 41, p. 409, 1988.
F. Golse, Applications of the Boltzmann Equation Within the Context of Upper Atmosphere Vehicle Aerodynamics, Computer Meth. in Engineer. and Appl. Mech. Vol. 75, p. 299, 1989.
F. Golse, Knudsen Layers from a Computational Viewpoint, TTS P 21 (3), 211, 1992.
F. Golse, A. Klar, A Numerical Method for the Computation of Asymptotic States and Outgoing Distributions for Kinetic Linear Half Space Problems,to appear in J. Stat. Phys..
H. Grad, Asymptotic Theory of the Boltzmann Equation II,Rarefied gas dynamics, Proceedings of the 3. International symposium 1962, ed. J.A. Laurman, Academic Press, p. 26, 1963
R.. Illner, H. Neunzert, Domain Decomposition: Linking Kinetic and Aerodynamic Descriptions, AGTM preprint 90, Kaiserslautern, 1993.
A. Klar, Domain Decomposition for Kinetic Problems with Nonequilibrium States,to appear in Eur. J. Mech./B Fluids.
A. Klar, Convergence of Alternating Domain Decomposition Schemes for Kinetic and Aerodynamic Equations to appear in Math. Meth. Appl. Sci..
A. Klar, Coupling conditions for kinetic and drift diffusion semiconductor equations in preparation.
S.K. Loyalka, Approximate Method in the Kinetic Theory in Phys. Fluids 11, Vol. 14, 1971.
A. Lukschin, H. Neunzert, J. Struckmeier, Interim Report for the Hermes Project DPH 6174 /91, 1992.
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© 1995 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Klar, A. (1995). Domain Decomposition Schemes and Coupling Conditions for Kinetic and Hydrodynamic Equations. In: Hackbusch, W., Wittum, G. (eds) Numerical Treatment of Coupled Systems. Notes on Numerical Fluid Mechanics (NNFM), vol 51. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86859-6_12
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DOI: https://doi.org/10.1007/978-3-322-86859-6_12
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-86861-9
Online ISBN: 978-3-322-86859-6
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