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. Kudryavtsev, A.N.; Shershnev, A.A.: A numerical method for simulation of microflows by solving directly kinetic equations with WENO schemes (2013)
  2. 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)
  3. Alaia, Alessandro; Puppo, Gabriella: A hybrid method for hydrodynamic-kinetic flow.II: Coupling of hydrodynamic and kinetic models (2012)
  4. Filbet, Francis: On deterministic approximation of the Boltzmann equation in a bounded domain (2012)
  5. Alaia, Alessandro; Puppo, Gabriella: A hybrid method for hydrodynamic-kinetic flow. I: A particle-grid method for reducing stochastic noise in kinetic regimes (2011)
  6. Dimarco, Giacomo; Pareschi, Lorenzo: Exponential Runge-Kutta methods for stiff kinetic equations (2011)
  7. Filbet, Francis; Jin, Shi: An asymptotic preserving scheme for the ES-BGK model of the Boltzmann equation (2011)
  8. Filbet, Francis; Mouhot, Clément: Analysis of spectral methods for the homogeneous Boltzmann equation (2011)
  9. Filbet, Francis; Jin, Shi: A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources (2010)
  10. Gamba, Irene M.; Tharkabhushanam, Sri Harsha: Shock and boundary structure formation by spectral-Lagrangian methods for the inhomogeneous Boltzmann transport equation (2010)
  11. Gamba, Irene M.; Tharkabhushanam, Sri Harsha: Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states (2009)
  12. Filbet, Francis: An asymptotically stable scheme for diffusive coagulation-fragmentation models (2008)
  13. Groppi, M.; Aoki, K.; Spiga, G.; Tritsch, V.: Shock structure analysis in chemically reacting gas mixtures by a relaxation-time kinetic model (2008)
  14. Kowalczyk, Piotr; Palczewski, Andrzej; Russo, Giovanni; Walenta, Zbigniew: Numerical solutions of the Boltzmann equation: Comparison of different algorithms (2008)
  15. Aimi, A.; Diligenti, M.; Groppi, M.; Guardasoni, C.: On the numerical solution of a BGK-type model for chemical reactions (2007)
  16. Groppi, M.; Spiga, G.; Takata, S.: The steady shock problem in reactive gas mixtures (2007)
  17. Mouhot, Clément; Pareschi, Lorenzo: Fast algorithms for computing the Boltzmann collision operator (2006)
  18. Baker, Lowell L.; Hadjiconstantinou, Nicolas G.: Variance reduction for Monte Carlo solutions of the Boltzmann equation (2005)
  19. Desvillettes, L.; Villani, C.: On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation (2005)
  20. Filbet, Francis; Pareschi, Lorenzo; Toscani, Giuseppe: Accurate numerical methods for the collisional motion of (heated) granular flows (2005)

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