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.

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  1. Crevat, Joachim; Filbet, Francis: Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions (2021)
  2. Hu, Jingwei; Qi, Kunlun; Yang, Tong: A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation (2021)
  3. Jaiswal, Shashank: Isogeometric schemes in rarefied gas dynamics context (2021)
  4. Hu, Jingwei; Shen, Jie; Wang, Yingwei: A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions (2020)
  5. Su, Wei; Wang, Peng; Zhang, Yonghao; Wu, Lei: Implicit discontinuous Galerkin method for the Boltzmann equation (2020)
  6. Dimarco, Giacomo; Hauck, Cory; Loubère, Raphaël: A class of low dissipative schemes for solving kinetic equations (2019)
  7. Keßler, Torsten; Rjasanow, Sergej: Fully conservative spectral Galerkin-Petrov method for the inhomogeneous Boltzmann equation (2019)
  8. Narski, Jacek: Fast kinetic scheme: efficient MPI parallelization strategy for 3D Boltzmann equation (2019)
  9. Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas: An efficient numerical method for solving the Boltzmann equation in multidimensions (2018)
  10. Eskandari, M.; Nourazar, S. S.: On the time relaxed Monte Carlo computations for the flow over a flat nano-plate (2018)
  11. Filbet, Francis; Shu, Chi-Wang: Discontinuous Galerkin methods for a kinetic model of self-organized dynamics (2018)
  12. Aoki, Kazuo; Baranger, Céline; Hattori, Masanari; Kosuge, Shingo; Martalò, Giorgio; Mathiaud, Julien; Mieussens, Luc: Slip boundary conditions for the compressible Navier-Stokes equations (2017)
  13. Gamba, Irene M.; Haack, Jeffrey R.; Hauck, Cory D.; Hu, Jingwei: A fast spectral method for the Boltzmann collision operator with general collision kernels (2017)
  14. Cho, H.; Venturi, D.; Karniadakis, G. E.: Numerical methods for high-dimensional probability density function equations (2016)
  15. Liu, Chang; Xu, Kun; Sun, Quanhua; Cai, Qingdong: A unified gas-kinetic scheme for continuum and rarefied flows. IV: Full Boltzmann and model equations (2016)
  16. Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek: Towards an ultra efficient kinetic scheme. part III: high-performance-computing (2015)
  17. Dimarco, Giacomo; Loubère, Raphaël; Rispoli, Vittorio: A multiscale fast semi-Lagrangian method for rarefied gas dynamics (2015)
  18. Alekseenko, A.; Josyula, E.: Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space (2014)
  19. Dimarco, G.; Pareschi, L.: Numerical methods for kinetic equations (2014)
  20. Dimarco, Giacomo; Loubere, Raphaël: Towards an ultra efficient kinetic scheme. II: The high order case (2013)

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