Boltzmann

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.


References in zbMATH (referenced in 40 articles , 1 standard article )

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  1. Su, Wei; Wang, Peng; Zhang, Yonghao; Wu, Lei: Implicit discontinuous Galerkin method for the Boltzmann equation (2020)
  2. Dimarco, Giacomo; Hauck, Cory; Loubère, Raphaël: A class of low dissipative schemes for solving kinetic equations (2019)
  3. Keßler, Torsten; Rjasanow, Sergej: Fully conservative spectral Galerkin-Petrov method for the inhomogeneous Boltzmann equation (2019)
  4. Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas: An efficient numerical method for solving the Boltzmann equation in multidimensions (2018)
  5. Eskandari, M.; Nourazar, S. S.: On the time relaxed Monte Carlo computations for the flow over a flat nano-plate (2018)
  6. Filbet, Francis; Shu, Chi-Wang: Discontinuous Galerkin methods for a kinetic model of self-organized dynamics (2018)
  7. Aoki, Kazuo; Baranger, Céline; Hattori, Masanari; Kosuge, Shingo; Martalò, Giorgio; Mathiaud, Julien; Mieussens, Luc: Slip boundary conditions for the compressible Navier-Stokes equations (2017)
  8. 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)
  9. Cho, H.; Venturi, D.; Karniadakis, G. E.: Numerical methods for high-dimensional probability density function equations (2016)
  10. 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)
  11. Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek: Towards an ultra efficient kinetic scheme. part III: high-performance-computing (2015)
  12. Dimarco, Giacomo; Loubère, Raphaël; Rispoli, Vittorio: A multiscale fast semi-Lagrangian method for rarefied gas dynamics (2015)
  13. Alekseenko, A.; Josyula, E.: Deterministic solution of the spatially homogeneous Boltzmann equation using discontinuous Galerkin discretizations in the velocity space (2014)
  14. Dimarco, G.; Pareschi, L.: Numerical methods for kinetic equations (2014)
  15. Dimarco, Giacomo; Loubere, Raphaël: Towards an ultra efficient kinetic scheme. I: Basics on the BGK equation (2013)
  16. Dimarco, Giacomo; Loubere, Raphaël: Towards an ultra efficient kinetic scheme. II: The high order case (2013)
  17. Kudryavtsev, A. N.; Shershnev, A. A.: A numerical method for simulation of microflows by solving directly kinetic equations with WENO schemes (2013)
  18. Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao: Deterministic numerical solutions of the Boltzmann equation using the fast spectral method (2013)
  19. Alaia, Alessandro; Puppo, Gabriella: A hybrid method for hydrodynamic-kinetic flow. II: Coupling of hydrodynamic and kinetic models (2012)
  20. Filbet, Francis: On deterministic approximation of the Boltzmann equation in a bounded domain (2012)

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