Abstract:

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.

Key words: unsteady flow, flexible flapping-wing, mesh deformation, overset grids, Delaunay graph