A coarse-to-fine approach for efficient deformation of curved high-order meshes

We propose a coarse-to-fine approach for generating fine and curved highorder tetrahedral meshes. The proposed approach is performed in three steps: (1) generate a coarse reference mesh; (2) map this to a coarse and curved highorder mesh; and (3) refine the curved high-order mesh. The approach provides high-order meshes that are valid, have the desired interpolation degree, and can be computed with a greatly reduced computational cost. Moreover, it enables the direct conversion of isotropic meshes (e.g. an Euler mesh) into anisotropic meshes (e.g. a Navier-Stokes boundary layer mesh). The key application of this method is to generate sequences of largeamplitude deformed meshes over time. These mesh sequences are required for high-order simulations with time-dependent geometries, such as in fluid dynamic simulations of flapping wings using the Arbitrary Lagrangian-Eulerian method [1]. For these problems, a reference mesh is typically deformed to accommodate several different wing configurations. To this end, a Lagrangian solid mechanics equation is solved on the same mesh, taking the wing displacement state as a Dirichlet boundary condition [2]. Generating fine deformed meshes in this manner is expensive since flow simulations of flapping wings often require ∼ 10 high-order elements, including the highly refined regions in the boundary layer. With our approach, the number of degrees of freedom required to perform mesh deformation can be reduced more than 500 times. In the sections that follow, we describe further details of our methodology (Section 2), an application of our method to the meshing problem for a 3D flapping bat wing (Section 3), and concluding remarks (Section 4).