An efficient jump-diffusion approximation of the Boltzmann equation

A jump-diffusion process along with a particle scheme is devised as an accurate and efficient solution to the Boltzmann equation. The proposed (hereafter Gamma-Boltzmann model) match evolution of all moments up heat fluxes while attaining correct Prandtl number 2/3 for monatomic gas Maxwellian molecular potential. This approximation model not subject issues associated previously developed Fokker-Planck (FP) based models; such having wrong number, limited applicability, or requiring estimation higher-order moments. An compared computationally direct simulation Monte Carlo cubic FP (Gorji et al. (2011) [10]) in several test cases including Couette flow lid-driven cavity. results indicate that yields good equation, provides more limit low particles, remains feasible even dense regimes.