The purpose of the present paper is to solve the lid-driven cavity problem for a non-Newtonian power-law shear thinning and shear thickening fluid by a meshless method. Results are presented for $\text{Re}=100$ and $\text{Re}=1000$, where different levels of shear thinning and thickening are considered. Furthermore, the lid-driven cavity case is made geometrically more complex by adding several circular-shaped obstacles in the geometry. The Navier-Stokes equations are solved with the local meshless diffuse approximate method. The weighted least squares approximation is structured by using the second-order polynomial basis vector and the Gaussian weight function. The explicit Euler scheme is used to perform the artificial time stepping. The non-incremental pressure correction scheme is used to couple the pressure and the velocity fields. Results are presented in terms of viscosity contours, stream function, velocity vectors, mid-plane velocity and viscosity profiles for the steady state. The numerical method is verified by a comparison with the results obtained from the literature, which are computed with the least squares finite element formulation. Furthermore, an investigation of the node density and node distribution type is performed. A near perfect match with the reference solution and between the structured and unstructured node distribution is found.

本文的目的是通过无网格方法解决非牛顿幂律剪切变稀和剪切稠化流体的盖子驱动空腔问题。结果显示为$\text{关于}=100$ 和 $\text{关于}=1000$，其中考虑了不同程度的剪切变稀和变稠。此外，通过在几何形状中添加几个圆形障碍物，盖子驱动的腔体在几何形状上变得更加复杂。Navier-Stokes 方程使用局部无网格漫反射近似方法求解。加权最小二乘近似是通过使用二阶多项式基向量和高斯权重函数构造的。显式欧拉方案用于执行人工时间步进。非增量压力校正方案用于耦合压力场和速度场。结果以稳态的粘度等值线、流函数、速度矢量、中平面速度和粘度曲线表示。通过与从文献中获得的结果进行比较来验证数值方法，这些结果是用最小二乘有限元公式计算的。此外，还对节点密度和节点分布类型进行了调查。找到了与参考解决方案以及结构化和非结构化节点分布之间的近乎完美的匹配。