An Efficient Jump-Diffusion Approximation of the Boltzmann Equation


Journal article


Fabian Mies, Mohsen Sadr, Manuel Torrilhon
Journal of Computational Physics, vol. 490(112308), 2023


arXiv
Cite

Cite

APA   Click to copy
Mies, F., Sadr, M., & Torrilhon, M. (2023). An Efficient Jump-Diffusion Approximation of the Boltzmann Equation. Journal of Computational Physics, 490(112308). https://doi.org/10.1016/j.jcp.2023.112308


Chicago/Turabian   Click to copy
Mies, Fabian, Mohsen Sadr, and Manuel Torrilhon. “An Efficient Jump-Diffusion Approximation of the Boltzmann Equation.” Journal of Computational Physics 490, no. 112308 (2023).


MLA   Click to copy
Mies, Fabian, et al. “An Efficient Jump-Diffusion Approximation of the Boltzmann Equation.” Journal of Computational Physics, vol. 490, no. 112308, 2023, doi:10.1016/j.jcp.2023.112308.


BibTeX   Click to copy

@article{fabian2023a,
  title = {An Efficient Jump-Diffusion Approximation of the Boltzmann Equation},
  year = {2023},
  issue = {112308},
  journal = {Journal of Computational Physics},
  volume = {490},
  doi = {10.1016/j.jcp.2023.112308},
  author = {Mies, Fabian and Sadr, Mohsen and Torrilhon, Manuel}
}

A jump-diffusion process along with a particle scheme is devised as an accurate and efficient particle solution to the Boltzmann equation. The proposed process (hereafter Gamma-Boltzmann model) is devised to match the evolution of all moments up to the heat fluxes while attaining the correct Prandtl number of 2/3 for monatomic gas with Maxwellian molecular potential. This approximation model is not subject to issues associated with the previously developed Fokker-Planck (FP) based models; such as having wrong Prandtl number, limited applicability, or requiring estimation of higher-order moments. An efficient particle solution to the proposed Gamma-Boltzmann model is devised and compared computationally to the direct simulation Monte Carlo and the cubic FP model [M. H. Gorji, M. Torrilhon, and P. Jenny, J. Fluid Mech. 680 (2011): 574-601] in several test cases including Couette flow and lid-driven cavity. The simulation results indicate that the Gamma-Boltzmann model yields a good approximation of the Boltzmann equation, provides a more accurate solution compared to the cubic FP in the limit of a low number of particles, and remains computationally feasible even in dense regimes.


Tools
Translate to