FV_HipoDiff swMATH ID: 32052 Software Authors: Bessemoulin-Chatard, Marianne; Herda, Maxime; Rey, Thomas Description: Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations. In this article, we are interested in the asymptotic analysis of a finite volume scheme for one-dimensional linear kinetic equations, with either a Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates, we establish that the proposed scheme is Asymptotic-Preserving in the diffusive limit. Moreover, we adapt to the discrete framework the hypocoercivity method proposed by J. Dolbeault, C. Mouhot, and C. Schmeiser [Trans. Amer. Math. Soc. 367, no. 6 (2015)] to prove the exponential return to equilibrium of the approximate solution. We obtain decay rates that are uniformly bounded in the diffusive limit. Finally, we present an efficient implementation of the proposed numerical schemes and perform numerous numerical simulations assessing their accuracy and efficiency in capturing the correct asymptotic behaviors of the models. Homepage: https://www.ams.org/journals/mcom/2020-89-323/S0025-5718-2019-03490-7/ Source Code: https://gitlab.com/thoma.rey/FV_HipoDiff Dependencies: Python Keywords: kinetic equations; finite volume methods; hypocoercivity; diffusion limit; asymptotic-preserving schemes Related Software: Mulprec Cited in: 10 Documents all top 5 Cited by 27 Authors 3 Herda, Maxime 2 Rey, Thomas 1 Ayi, Nathalie 1 Bernard, Étienne 1 Bessemoulin-Chatard, Marianne 1 Cancès, Clément 1 Chainais-Hillairet, Claire 1 Cheng, Yingda 1 Dujardin, Guillaume Michel 1 Fathi, Max 1 Fu, Jingyi 1 Georgoulis, Emmanuil H. 1 Hérau, Frédéric 1 Hivert, Hélène 1 Krell, Stella 1 Lafitte, Pauline 1 Levitt, Antoine 1 Li, Fengyan 1 Loy, Nadia 1 Pareschi, Lorenzo 1 Peng, Zhichao 1 Perthame, Benoît 1 Qiu, Jingmei 1 Stoltz, Gabriel 1 Tang, Min 1 Tristani, Isabelle 1 Zanella, Mattia all top 5 Cited in 8 Serials 3 SIAM Journal on Numerical Analysis 1 Journal of Statistical Physics 1 Mathematics of Computation 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Applied Mathematics Letters 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Annales Henri Lebesgue all top 5 Cited in 7 Fields 8 Numerical analysis (65-XX) 7 Partial differential equations (35-XX) 4 Statistical mechanics, structure of matter (82-XX) 1 Difference and functional equations (39-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Biology and other natural sciences (92-XX) Citations by Year