稀薄气体动理论中介观尺度数值模拟的加速方法

针对滑移流、早期过渡流区域采用离散速度法(discrete velocity method, DVM)求解Boltzmann方程收敛速度极慢、计算资源消耗大的难题,提出全流场耦合介观/宏观方程加速方法。在介观层面基于有限差分的DVM求解Boltzmann方程,在宏观层面基于有限体积的压力耦合方程组半隐式方法求解矩方程,充分利用纳维-斯托克斯-傅里叶/R26矩方程在低克努森数下的快速收敛特性,对介观方程进行加速。基于高阶Hermite多项式重构分布函数,完成宏观方程与介观方程之间的数据传输。仿真结果表明:全流场耦合介观/宏观方程的加速方法在滑移流、早期过渡流区域具有显著加速性能,最大降低了95.28%的计算时长；但对中、大克努森数流域,加速性能大幅度下降。

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-Stokes-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 Hermite 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 time cost. However, the acceleration performance decreases significantly in the middle and large Knudsen number regime.