Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T18:21:57.139Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic-Preserving Scheme for the M1-Maxwell System in the Quasi-Neutral Regime

Part of:Equilibrium statistical mechanicsApplications to specific types of physical systemsTime-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  01 February 2016

S. Guisset,
S. Brull,
B. Dubroca,
E. d'Humières,
S. Karpov and
I. Potapenko
S. Guisset*
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F-33405 Talence, FranceUniv. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
S. Brull
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F-33405 Talence, France
B. Dubroca
Affiliation:
Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
E. d'Humières
Affiliation:
Univ. Bordeaux, CELIA, UMR 5107, F- 33400 Talence, France
S. Karpov
Affiliation:
Keldysh Institute for Applied Mathematics, 125047 Moscow, Russian Federation
I. Potapenko
Affiliation:
Keldysh Institute for Applied Mathematics, 125047 Moscow, Russian Federation
*
*Corresponding author. Email address:guisset@celia.u-bordeaux1.fr (S. Guisset)

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This work deals with the numerical resolution of the M1-Maxwell system in the quasi-neutral regime. In this regime the stiffness of the stability constraints of classical schemes causes huge calculation times. That is why we introduce a new stable numerical scheme consistent with the transitional and limit models. Such schemes are called Asymptotic-Preserving (AP) schemes in literature. This new scheme is able to handle the quasi-neutrality limit regime without any restrictions on time and space steps. This approach can be easily applied to angular moment models by using a moments extraction. Finally, two physically relevant numerical test cases are presented for the Asymptotic-Preserving scheme in different regimes. The first one corresponds to a regime where electromagnetic effects are predominant. The second one on the contrary shows the efficiency of the Asymptotic-Preserving scheme in the quasi-neutral regime. In the latter case the illustrative simulations are compared with kinetic and hydrodynamic numerical results.

Keywords

Asymptotic-Preserving schemeFokker-Planck-Landau equationMaxwell equationsquasi-neutral limitangular M1 moments model

MSC classification

Secondary:82D10: Plasmas82B40: Kinetic theory of gases82C40: Kinetic theory of gases

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016, pp. 301 - 328
Copyright
Copyright © Global-Science Press 2016 

References

[1]Batishchev, O.V, Yu Bychenkov, V., Detering, F., Rozmus, W., Sydera, R., Copjack, C.E, and Novikov, V.N.. Heat transport and electron distribution function in laser produced with hot spots. Physics of Plasmas 9 2302–2310., 2002.Google Scholar
[2]Bobylev, A.V and Potapenko, I.F. Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas. J. Comp. Phys., 246, 123–144, 2013.Google Scholar
[3]Braginskii, S.I.. Reviews of plasmaphysics. Consultant Bureau, New York, vol. 1, 1965.Google Scholar
[4]Brantov, A.V, Yu Bychenkov, V., Batishchev, O.V., and Rozmus, W.. Nonlocal heat wave propagation due to skin layer plasma heating by short laser pulses. Computer Physics communications 164 67–72, 2004.Google Scholar
[5]Brull, S., Degond, P., and Deluzet, F.. Degenerate anisotropic elliptic problems and magnetised plasma simulations. Commun. Comput. Phys. 11 pp147–178, 2012.Google Scholar
[6]Brull, S., Degond, P., Deluzet, F., and Mouton, A.. An asymptotic preserving scheme for a bi-fluid Euler-Lorentz system, Kinet. Rel. Models. Vol. 4, No. 4, 2011.Google Scholar
[7]Brull, S., Deluzet, F., and Mouton, A.. Numerical resolution of an anisotropic non linear diffusion problem. Commun. in Math. Sci., vol 13, No 1, pp 203–224, 2015.CrossRefGoogle Scholar
[8]Buet, C. and Cordier, S.. Conservative and entropy decaying numerical scheme for the isotropic Fokker-Planck-Landau equation. J. Comput. Phys. 145, No.1, 228–245 (1998).Google Scholar
[9]Chen, F.. Introduction to Plasma Physics and Controlled Fusion. Plenum Press, New York, 1984.Google Scholar
[10]Crispel, P., Degond, P., and Vignal, M.-H.. A plasma expansion model based on the full Euler-Poisson system. Math. Models Methods Appl. Sci. 17 1129–1158, 2007.Google Scholar
[11]Crispel, P., Degond, P., and Vignal, M.-H.. An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field. Math. Models Methods Appl. Sci. 17 1129–1158, 2007.Google Scholar
[12]Crispel, P., Degond, P., and Vignal, M.-H.. An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasi-neutral limit. J. Comput. Phys. 223 (2007) 208–234, 2007.Google Scholar
[13]Crouseilles, N., Lemou, M., and Méhats, F.. Asymptotic Preserving schemes for highly oscillatory Vlasov Poisson equations. J. Comp. Phys., Volume 248, Pages 287308, 1 September 2013.Google Scholar
[14]Degond, P., Deluzet, F., Navoret, L., Sun, A., and Vignal, M.H.. Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality. J. Comput. Phys, 229 no 16, 5630–5652, 2010.Google Scholar
[15]Degond, P., Deluzet, F., Sangam, A., and Vignal, M.-H.. An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field. J. Comput. Phys. Volume 228, Issue 1, 2009.CrossRefGoogle Scholar
[16]Degond, P., Deluzet, F., and Savelief, D.. Numerical approximation of the Euler-Maxwell model in the quasineutral limit. Journal of Computational Physics, 231, pp. 1917–1946, 2012.Google Scholar
[17]Degond, P., Liu, H., Savelief, D., and Vignal, M-H.. Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit. C. R. Acad. Sci. Paris, Ser. I 341 323328, 2005.Google Scholar
[18]Degond, P., Lozinski, A., Narski, J., and Negulescu, C.. An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition. J. Comp. Phys., 231 (2012), pp. 2724–2740.CrossRefGoogle Scholar
[19]Drake, J.F., Kaw, P.K., Lee, Y.C., Schmidt, G., Liu, C.S., and Rosenbluth, M.N.. Parametric instabilities of electromagnetic waves in plasmas. Phys. Fluids 17, 778, 1974.Google Scholar
[20]Dubroca, B., Feugeas, J.-L., and Frank, M.. Angular moment model for the Fokker-Planck equation. The European Phys. Journal D, Volume 60, Issue 2, pp 301–307, November 2010.Google Scholar
[21]Dubroca, B. and Feugeas, J.L.. Étude théorique et numérique d'une hiéarchie de modèles aux moments pour le transfert radiatif. C. R. Acad. Sci. Paris, t. 329, SCrie I, p. 915–920, 1999.Google Scholar
[22]Duclous, R., Dubroca, B., Filbet, F., and Tikhonchuk, V.. High order resolution of the Maxwell-Fokker-Planck-Landau model intended for ICF applications. J. Comput. Phys. 228(14): 5072–5100 (2009).Google Scholar
[23]Filbet, F. and Jin, S.. A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources. J. Comp. Phys. vol. 229, no 20 (2010).Google Scholar
[24]Hauck, C. and McLarren, R.. Positive PN closures. Siam J. Sci. Comp. Vol. 32, No. 5, pp. 2603–2626.Google Scholar
[25]Jin, S.. Efficient Asymptotic-Preserving (AP) schemes for some multi-scale kinetic equations. SIAM J. Sci. Comp. 21 441, 1999.Google Scholar
[26]Jin, S. and Yan, B.. A class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation. J. Comp. Phys. 230, 6420–6437, 2011.CrossRefGoogle Scholar
[27]Lemou, M. and Mieussens, L.. A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit. SIAM J. Sci. Comput., 31(1), 334368, 2008.Google Scholar
[28]Levermore, D.. Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83, 1996.Google Scholar
[29]Mallet, J., Brull, S., and Dubroca, B.. An entropic scheme for an angular moment model for the classical Fokker-Planck-Landau equation of electrons. Communi. Comput. Phys., Vol.15, No. 2, pp. 422–450, 2013.Google Scholar
[30]Mallet, J., Brull, S., and Dubroca, B.. General moment system for plasma physics based on minimum entropy principle. Submitted.Google Scholar
[31]Marocchino, A., Tzoufras, M., Atzeni, S., Schiavi, A., Nicola, Ph. D., Mallet, J., Tikhonchuk, V., and Feugeas, J.-L.. Nonlocal heat wave propagation due to skin layer plasma heating by short laser pulses. Phys. Plasmas 20, 022702, 2013.Google Scholar
[32]Minerbo, G.N.. Maximum entropy Eddigton Factors. J. Quant. Spectrosc. Radiat. Transfer, 20, 541, 1978, 1978.Google Scholar
[33]Schurtz, G.P., Nicolai, Ph.D., and Busquet, M.. A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes. Physics of Plasmas, 7, 4238, 2000.Google Scholar
[34]Spitzer, L. and Haarm, R.. Transport Phenomena in a Completely Ionized Gas. Phys. Rev. 89, 977, 1953.Google Scholar