基于AMG法及多块非正交网格的三维方腔流场数值模拟

Numerical simulation of 3D lib-driven cavity flow based on AMG method and multi-block non-orthogonal grid

为了将AMG法与多块非正交结构网格结合起来,应用于求解基于多块格离散的三维N-S方程离散系统,针对经典算例三维顶盖驱动直方腔和45°倾斜方腔流动问题,构建了三维多块非正交结构网格系统,设计了三维N-S方程块结构网格离散系统系数矩阵CSR存贮格式;根据非正交同位网格SIMPLE耦合算法,建立了N-S方程的AMG数值求解方法,编制了用AMG法计算的三维数值仿真程序,并采用AMG法求解控制方程中所有流动参数;同已有的结果做了比较,给出了三维方腔流场内复杂的涡系图像,并对算法的有效性进行了验证.结果表明:AMG法及相关算法可用于复杂区域流动问题的数值模拟,为大规模的CFD数值模拟问题奠定了基础.

To apply AMG method in fast solving FVM-based discrete systems of Navier-Stokes equations, the non-orthogonal hexahedron collocated grid system was set up to numerically simulate lib-driven flow in vertical and 45° inclined wall cavity. Based on the SIMPLE algorithm of non-orthogonal hexahedron collo- cated grid, the structure and the compressed sparse row（CSR） storage scheme of coefficient matrix were obtained by N -S equation and multi-block grid. Numerical simulation programs were designed to solve the flow parameters of governing equations by AMG method. Compared computing results with existing re- sults, the flow structure figures of 3 D lib-driven cavity flow were obtained, and the algorithm was veri- fied. The results show that AMG and the related algorithms can be applied in the numerical simulations of fluid flow in complex field, and are suitable for large-scale numerical simulation of fluid flow.