气体运动论BGK格式的翼型绕流数值模拟

以气体运动论BGK(Bhatnagaar-Gross-Krook)格式为基础,通过改进非均匀网格下的通量计算方法,把气体运动论BGK方法应用到二维贴体网格上模拟了可压缩的无黏和黏性流动。在重构阶段,以交界面周围4个网格单元为一组,先把每个网格单元的宏观量(密度、动量和总能量)转换在相对于交界面的坐标系下,然后使用van Leer限制器插值求出交界面的宏观量,在求解阶段再使用BGK理论求出流过交界面的通量。通过上述方法使贴体网格和均匀网格,在计算格式上一致,与其他求解二维贴体网格的气体运动论BGK方法相比,该方法相对简单,计算量减小。结合贴体网格通量计算和气体运动论BGK格式方法理论,分别对亚、跨、超声速下的NACA0012翼型绕流进行了数值模拟和对比研究,所得可压缩无黏流动的数值结果与北大西洋公约组织航天研究与发展咨询组(AGARD)的结果吻合良好。本文还模拟了低雷诺数状态下的可压缩黏性流动,所得结果与文献中的数值计算结果吻合良好,证明了该方法在数值模拟及激波捕捉方面具有鲁棒性,为在复杂流动中的应用提供了一种简单的途径。

Numerical Simulation of Flow Around an Airfoil with Gas-kinetic BGK Scheme

This article presents a method for the numerical solution of compressible viscid and inviscid flow with two dimensional body-fitted grids based on an improved gas-kinetic BGK (Bhatnagaar-Gross-Krook) scheme. This method has been improved in flux computation on a non-uniform grid. In the reconstruction stage,four cells around the cell interface are grouped into one. The macroscopic variables including density, momentum and energy of group cells are transferred to a local coordinate system on the cell interface. The macroscopic variables of the cell interface are interpolated via the van Leer limiter and the fluxes across the cell interface can be computed with the BGK scheme. In this method the computing scheme does not change between the two dimensional body-fitted grids and the uniform grids. The computation load is reduced and the method is simple compared with the other gas-kinetic BGK methods on non-umiform grid. Simulation and research are carried out respectively for a subsonic,transonic and supersonic flow around an airfoil NACA0012. The results of the compressible in viscid flow by the present method agree well with advisory group for aerospace research and development (AGARD) results. The numerical simulation results for a compressible viscid flow agree well with numerical results of references. Thus it is proved that this method has excellent robustness in numerical simulation and shock-capturing aspect. This scheme provides a simple way of calculation for complex flows.