R13/R26矩方法的介观尺度壁面边界条件

Wall boundary condition for the R13/R26 moment method at mesoscopic level

宏观尺度NSF(Navier-Stokes-Fourier)、R13/R26矩方程边界条件在中、大克努森数Kn来流条件下计算精度大幅度降低,也极易发散。针对这一难题,提出R13/R26矩方程的介观尺度边界条件,在靠近壁面处重构速度分布函数,并输入介观尺度Boltzmann模型方程;基于离散速度法求解宏观参数,所得到的宏观参数作为R13/R26矩方程的壁面边界条件。仿真结果表明:基于介观尺度边界条件的R13/R26矩方法相较原边界条件计算精度最大提高59.84%,同时,所提出的边界条件将矩方法对Kn的适用范围拓展到1.0。

Wall boundary conditions for the macroscopic equations,i.e.the NSF(Navier-Stokes-Fourier)equations,R13/R26 moment equations,lose their accuracy dramatically and are easy to diverge,especially in the middle and high Knudsen number regimes.To overcome these difficulties,a wall boundary condition for the R13/R26 moment method was proposed at the mesoscopic level.The velocity distribution function was reconstructed and feedback into the Boltzmann model equation in the near-wall region,and the wall boundary condition for the R13/R26 moment method was calculated on the basis of solving the Boltzmann equation with the discrete velocity method.Results indicate that:the proposed wall boundary condition is able to increase the computational accuracy up to 59.84%compared with the classical approach.Meanwhile,it is able to get the steady-state solution for the Knudsen number up to 1.0.