Boltzmann swMATH ID: 7008 Software Authors: Filbet, Francis; Russo, Giovanni Description: High order numerical methods for the space non-homogeneous Boltzmann equation. In this paper we present accurate methods for the numerical solution of the Boltzmann equation of rarefied gas. The methods are based on a time splitting technique. The transport is solved by a third order accurate (in space) positive and flux conservative (PFC) method. The collision step is treated by a Fourier approximation of the collision integral, which guarantees spectral accuracy in velocity, coupled with several high order integrators in time. Strang splitting is used to achieve second order accuracy in space and time. Several numerical tests illustrate the properties of the methods. Homepage: https://www.projet-plume.org/en/relier/fast-boltzmann Keywords: Boltzmann equation; Rarefied gas dynamics; Spectral methods; Splitting; algorithms Related Software: HE-E1GODF; CUDA; FINUFFT; SMILE; MPI; Kokkos; PETSc; ISOGAT; SHASTA; RODAS; MOOD; Chemotaxis; Vador; WENO Cited in: 48 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year High order numerical methods for the space non-homogeneous Boltzmann equation. Zbl 1034.82052Filbet, Francis; Russo, Giovanni 2003 all top 5 Cited by 69 Authors 10 Filbet, Francis 9 Dimarco, Giacomo 6 Loubère, Raphaël 5 Pareschi, Lorenzo 4 Hu, Jingwei 3 Martínez Gamba, Irene 3 Groppi, Maria 3 Mouhot, Clément 3 Narski, Jacek 3 Russo, Giovanni 2 Alaia, Alessandro 2 Aoki, Kazuo 2 Hauck, Cory D. 2 Jin, Shi 2 Puppo, Gabriella 2 Shen, Jie 2 Spiga, Giampiero 2 Tharkabhushanam, Sri Harsha 2 Villani, Cédric 2 Wu, Lei 2 Zhang, Yonghao 1 Aimi, Alessandra 1 Baker, Lowell L. 1 Baranger, Céline 1 Boscheri, Walter 1 Cai, Qingdong 1 Cho, Heyrim 1 Crevat, Joachim 1 Desvillettes, Laurent 1 Diligenti, Mauro 1 Gimelshein, Sergey F. 1 Guardasoni, Chiara 1 Haack, Jeffrey R. 1 Hadjiconstantinou, Nicolas G. 1 Hattori, Masanari 1 Huang, Xiaodong 1 Jaiswal, Shashank 1 Josyula, Eswar 1 Karniadakis, George Em 1 Keßler, Torsten 1 Kosuge, Shingo 1 Kowalczyk, Piotr 1 Kudryavtsev, Alexey N. 1 Liu, Chang 1 Martalò, Giorgio 1 Mathiaud, Julien 1 Mieussens, Luc 1 Nourazar, S. Salman 1 Palczewski, Andrzej 1 Qi, Kunlun 1 Reese, Jason M. 1 Rey, Thomas 1 Rispoli, Vittorio 1 Rjasanow, Sergej 1 Scanlon, Thomas J. 1 Shershnev, A. A. 1 Shu, Chi-Wang 1 Su, Wei 1 Sun, Quanhua 1 Takata, Shigeru 1 Toscani, Giuseppe 1 Tritsch, V. 1 Venturi, Daniele 1 Walenta, Zbigniew 1 Wang, Peng 1 Wang, Yingwei 1 White, Craig I. 1 Xu, Kun 1 Yang, Haizhao all top 5 Cited in 23 Serials 16 Journal of Computational Physics 4 Journal of Scientific Computing 2 SIAM Journal on Numerical Analysis 2 SIAM Journal on Scientific Computing 2 Physics of Fluids 2 European Journal of Mechanics. B. Fluids 2 Kinetic and Related Models 1 Computers and Fluids 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Statistical Physics 1 Mathematics of Computation 1 BIT 1 Inventiones Mathematicae 1 Transactions of the American Mathematical Society 1 Journal of Computational Mathematics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 International Journal of Computational Fluid Dynamics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Multiscale Modeling & Simulation 1 Communications in Mathematical Sciences 1 Acta Numerica 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Communications in Computational Physics all top 5 Cited in 12 Fields 37 Fluid mechanics (76-XX) 33 Numerical analysis (65-XX) 25 Statistical mechanics, structure of matter (82-XX) 14 Partial differential equations (35-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX) Citations by Year