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

DOI: 10.1016/j.jcp.2023.112308

arXiv

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.