柔性扑翼非定常流场的数值计算方法

Numerical Method for Unsteady Flows of Flexible Flapping-wings

提出一种将Delaunay图映射网格变形技术和非结构嵌套网格方法结合使用的策略,解决网格变形和嵌套网格单独用于柔性扑翼流场计算时需要网格再生的问题。该方法为嵌套网格中的每个嵌于背景网格的贴体非结构网格生成Delaunay背景图;每个时间步,根据扑翼的运动和变形规律移动背景图,再根据网格点和背景图的映射关系移动网格点,之后自动完成嵌套边界的定义和插值关系的建立。为方便嵌套关系的建立,嵌套网格进行分层管理。也研究了一种内存消耗少、效率较高的搜索算法,以及格心格式和格点格式统一的边界拓宽算法。非定常可压缩Navier-Stokes方程在非结构的动态网格上用有限体积法离散,并用预处理的双时间步推进、隐式LU-SGS迭代求解。几个扑翼算例的结果表明,该方法充分利用了Delaunay图映射网格变形方法的高效率,同时也发挥了嵌套网格处理大幅运动的优势;用于既有整体大幅扑动又有局部小变形的柔性扑翼流场计算,可取得令人满意的精度和效率。

As solution of unsteady flows due to flexible flapping-wings is not possible by mesh deformation and overset grids alone unless grid regeneration is employed, an effective strategy which combines mesh deformation based on Delaunay graph mapping and unstructured overset grids is proposed in this article. A Delaunay graph is generated for each body-fitted grid cluster which overlaps or is embedded within an off-body background grid cluster. At each time step, the graph moves according to the wing＇s motion and deformation, and the grids move to new positions according to a one-to-one mapping between the graph and the grid. Then, intergrid-boundary definition is implemented automatically for computation. In order to efficiently implement the overset grid procedure, the idea of hierarchical grid organization is adopted, and an efficient data search algorithm is developed. Also an intergrid boundary redefinition algorithm is designed for both cell-centered and vertex-centered schemes in order to achieve higher spatial accuracy. The unsteady compressible Navier-Stokes equations are solved on unstructured dynamic meshes by using a preconditioned dual-time stepping procedure coupled with an implicit matrix-free LU-SGS scheme. The numerical results indicate that this algorithm provides satisfactory accuracy and efficiency for simulating unsteady flow of flexible flapping-wings.