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On steady-state preserving spectral methods for homogeneous Boltzmann equations

Francis Filbet 1, 2 Lorenzo Pareschi 3 Thomas Rey 4, 5 
1 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
2 KALiFFE - Kinetic models AppLIed for Future of Fusion Energy
Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne], INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
4 RAPSODI - Reliable numerical approximations of dissipative systems
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : In this note, we present a general way to construct spectral methods for the collision operator of the Boltzmann equation which preserves exactly the Maxwellian steady state of the system. We show that the resulting method is able to approximate with spectral accuracy the solution uniformly in time.
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Francis Filbet, Lorenzo Pareschi, Thomas Rey. On steady-state preserving spectral methods for homogeneous Boltzmann equations. Comptes Rendus. Mathématique, Académie des sciences (Paris), 2015, 353 (4), pp.309-314. ⟨10.1016/j.crma.2015.01.015⟩. ⟨hal-01053930⟩

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