Acceleration scheme for the mesoscopic numerical simulation in the kinetic theory of rarefied gas

To overcome the difficulty that DVM(discrete velocity method) for solving the Boltzmann equation has extremely slow convergence speed and high computational resource consumption in the slip flow and early transition flow regimes, an acceleration scheme which coupling the mesoscopic/macroscopic equations in the full flow area was proposed. Boltzmann model equation could be solved based on the DVM using finite difference method at the mesoscopic level, and the moment equations could be solved based on the semi-implicit method for pressure linked equations using finite volume method at the macroscopic level. Fast convergence characteristic of the Navier-Slokes-Fourier/R26 moment equations in the low Knudsen number regime was fully utilized to accelerate mesoscopic equation. The distribute function could be reconstructed from the high-order Hermile polynomial function, so that the data transfer between the macroscopic and the mesoscopic equations could be done. Simulation results indicate that: the acceleration scheme, coupling the mesoscopic/macroscopic equations in the full flow area, shows great acceleration performance in the slip and early transition regime, which is able to save up to 95.28% computational lime cost. However, the acceleration performance decreases significantly in the middle and large Knudsen number regime. © 2024 National University of Defense Technology. All rights reserved.