An asymptotic preserving scheme based on a micro-macro
decomposition for Collisional Vlasov equations: diffusion and high-field scaling limits
Pages: 441 - 477,
Volume 4,
Issue 2,
June 2011
doi:10.3934/krm.2011.4.441 Abstract
References
Full text (756.6K)
Related Articles
Nicolas Crouseilles - INRIA-Nancy Grand Est and IRMA, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France (email)
Mohammed Lemou - CNRS and IRMAR, Université de Rennes 1, 263 Avenue du General Leclerc CS74205, 35042 Rennes cedex, France (email)
| 1 |
A. Arnold, J.-A. Carrillo, I. Gamba and C.-W. Shu, Low and high-field scaling limits for the Vlasov- and Wigner-Poisson-Fokker-Planck system, Transport Theory Statist. Phys., 30 (2001), 121-153. |
|
| 2 |
R. Belaouar, N. Crouseilles, P. Degond and E. Sonnendr焎ker, An asymptotically stable semi-Lagrangian scheme in the quasi-neutral limit, J. Sc. Comput., 41 (2009), 341-365. |
|
| 3 |
M. Benoune, M. Lemou and L. Mieussens, Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier-Stokes asymptotics, J. Comput. Phys., 227 (2008), 3781-3803. |
|
| 4 |
L. L. Bonilla and J. Soler, High-field limit of the Vlasov-Poisson-Fokker-Planck system for different perturbation methods, http://arxiv.org/abs/cond-mat/0007164. |
|
| 5 |
M. Bostan and T. Goudon, Electric high-electric field limit for the Vlasov-Maxwell-Fokker-Planck system, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, 25 (2008), 221-251. |
|
| 6 |
J. F. Bourgat, P. LeTallec, B. Perthame and Y. Qiu, Coupling Boltzmann and Euler equations without overlapping, Domain decomposition and Engineering, Contemporary Mathematics, AMS, 157 (1992), 377-398. |
|
| 7 |
C. Buet and S. Cordier, Numerical analysis of conservative and entropy schemes for the Fokker-Planck-Landau equation, SIAM J. Numer. Anal., 36 (1998), 953-973. |
|
| 8 |
J. A. Carrillo, T. Goudon, P. Lafitte and F. Vecil, Numerical schemes of diffusion asymptotics and moment closures for kinetic equations, J. Sci. Comput., 36 (2008), 113-149. |
|
| 9 |
S. Chandrasekhar, "Radiative Transfer," Dover Publications, New-York, 1960. |
|
| 10 |
N. Crouseilles, P. Degond and M. Lemou, A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann-BGK equation, J. Comput. Phys., 199 (2004), 776-808. |
|
| 11 |
N. Crouseilles, P. Degond and M. Lemou, A hybrid kinetic-fluid model for solving the Vlasov-BGK equations, J. Comput. Phys., 203 (2005), 572-601. |
|
| 12 |
P. Degond, F. Deluzet, L. Navoret, A-B. Sun and M-H.Vignal, Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality, J. Comput. Phys., 229 (2010), 5630-5652. |
|
| 13 |
P. Degond, G. Dimarco and L. Mieussens, A multiscale kinetic-fluid solver with dynamic localization of kinetic effects, J. Comput. Phys., 229 (2010), 4907-4933. |
|
| 14 |
P. Degond, J.-G. Liu and L. Mieussens, Macroscopic fluid models with localized kinetic upscaling effects, SIAM J. Multiscale Modeling and Simulations, 5 (2006), 940-979. |
|
| 15 |
P. Degond and B. Lucquin-Desreux, An entropy scheme for the Fokker-Planck collision operator in the Coulomb case, Numer. Math., 68 (1994), 239-262. |
|
| 16 |
R. Duclous, B. Dubroca and F. Filbet, Analysis of a high order finite volume scheme for the Vlasov-Poisson system, preprint. |
|
| 17 |
F. Filbet and S. Jin, A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comp. Phys., 229 (2010), 7625-7648. |
|
| 18 |
F. Golse and A. Klar, A numerical method for computing asymptotic states and outgoing distributions for a kinetic linear half space problem, J. Stat. Phys., 80 (1995), 1033-1061. |
|
| 19 |
L. Gosse and G. Toscani, Asymptotic-preserving and well-balanced schemes for radiative transfer and the Rosseland approximation, Numer. Math., 98 (2004), 223-250. |
|
| 20 |
S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, SIAM J. Sci. Comput., 21 (1999), 441-454. |
|
| 21 |
S. Jin and D. Levermore, The discrete-ordinate method in diffusive regimes, Transport Theory Stat. Phys., 22 (1993), 739-791. |
|
| 22 |
S. Jin and D. Levermore, Numerical schemes for hyperbolic conservation laws with stiff relaxation terms, J. Comput. Phys., 126 (1996), 449-467. |
|
| 23 |
S. Jin, L. Pareschi and G. Toscani, Uniformly accurate diffusive relaxation schemes for multiscale transport equations, SIAM J. Num. Anal., 38 (2000), 913-936. |
|
| 24 |
S. Jin and Y. Shi, A micro-macro decomposition based on asymptotic-preserving scheme for the multispecies Boltzmann equation, SIAM J. Sci. Comp., 31 (2010), 4580-4606. |
|
| 25 |
A. Klar, Asymptotic-induced domain decomposition methods for kinetic and drift diffusion semiconductors equations, SIAM J. Numer. Anal., 19 (1998), 2032-2050. |
|
| 26 |
A. Klar, An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit, SIAM J. Numer. Anal., 35 (1998), 1073-1094. |
|
| 27 |
A. Klar, A numerical method for kinetic semiconductor equations in the drift diffusion limit, SIAM J. Sci. Comp., 20 (1999), 1696-1712. |
|
| 28 |
A. Klar and C. Schmeiser, Numerical passage from radiative heat transfer to nonlinear diffusion models, Math. Models Methods Appl. Sci., 11 (2001), 749-767. |
|
| 29 |
A. Klar and A. Unterreiter, Uniform stability of a finite difference scheme for transport equations in diffusive regimes, SIAM J. Numer. Anal., 40 (2001), 891-913. |
|
| 30 |
M. Lemou, Relaxed micro-macro schemes for kinetic equations, Comptes Rendus Mathématique, 348 (2010), 455-460. |
|
| 31 |
M. Lemou and L. Mieussens, A new asymptotic preserving scheme based on micro-macro formulation for linear kinetic equations in the diffusion limit, SIAM J. Sci. Comp., 31 (2008), 334-368. |
|
| 32 |
T.-P. Liu and S.-H. Yu, Boltzmann equation: Micromacro decompositions and positivity of shock profiles, Comm. Math. Phys., 246 (2004), 133-179. |
|
| 33 |
G. Naldi and L. Pareschi, Numerical schemes for kinetic equations in diffusive regimes, Appl. Math. Lett., 11 (1998), 29-35. |
|
| 34 |
J. C. Mandal and S. M. Deshpande, Kinetic flux vector splitting for Euler equations, Comput. Fluids, 23 (1994), 447-478. |
|
| 35 |
J. Nieto, F. Poupaud and J. Soler, High-field limit for the Vlasov-Poisson-Fokker-Planck system, Arch. Ration. Mech. Anal., 158 (2001), 29-59. |
|
| 36 |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation, J. Asympt. Anal., 4 (1991), 293-317. |
|
Go to top
|