基于MRT-LBM的方腔流动局部加密算法

摘要 使用多参数弛豫模型的格子玻尔兹曼方法及D2Q9模型，对方腔流顶盖下方左右奇异角落处应用局部网格加密模拟方腔流动特性.在粗细网格界面上，建立了分布函数的转换公式，采用3次样条插值计算加密界面上插值点的参量，根据Chapman-Enskog分析，给出了应力计算公式.数值计算结果表明:对雷诺数1000的方腔流动，沿腔中心线的速度分布与经典文献结果对比效果良好，压力、涡量轮廓图的噪声明显降低，应力振荡明显减少，证实了所提局部加密方法的有效性.
Abstract：Employing the D2Q9 model， grids at the double singular corners were locally refined to investigate the flow peculiarity of the lid driven cavity based on the multi-relaxation time of lattice Boltzmann method (MRT-LBM). The transferring formulae of the distribution functions were established between the coarse and fine grids. Parameters were interpolated with cubic spline implementation on the refined layers， and the stress expressions were given on the basis of the Chapman-Enskog. For the cavity flow with the Reynolds number 1000， the simulation results showed that the velocity distribution along the cavity mid plane agrees with that of the classical benchmark very well， the noises on the pressure and vortex contours are significantly reduced， and the stress fluctuation obviously decreases. The computational results showed validation of the present method.