An overset mesh approach for 3D mixed element high-order discretizations

Achieving higher accuracy and fidelity in aerodynamic simulations using higher-order methods has received significant attention over the last decade. High-order methods are attractive because they provide higher accuracy with fewer degrees of freedom and at the same time relieve the burden of generating very fine meshes. Discontinuous Galerkin (DG) methods1 have received particular attention for aerodynamic problems; these methods combine the ideas of finite-element and finite-volume methods allowing for high-order approximations and geometric flexibility. The goal of this work is to devise an accurate, e cient and robust three-dimensional high-order method based on DG discretizations2 for simulating a wide variety of aerodynamic flows in an overset grid framework. This is achieved with a three-dimensional DG solver that incorporates many of the techniques previously demonstrated by our group and others in the two-dimensional setting.3–5 The DG solver supports hybrid, mixed-element, unstructured meshes including arbitrary combinations of tetrahedra, prisms, pyramids, and hexahedra. The solver has been designed to incorporate both p-enrichment and h-refinement capabilities using non-conforming elements (hanging nodes). Recently overset grids have been gaining popularity. Although the DG solver can handle unstructured meshes there are some situations where even an unstructured solver could benefit from an overset grid framework. Bodies in relative motion such as helicopters or wind turbines are di cult to simulate with a single grid. Typically these simulations require mesh movement or re-meshing every time step. Overset grids solve this issue by allowing multiple grids to move relative to each other. Another advantage to overset grids is the ability to combine a near-body and an o↵-body solver. For example using the DG solver as a near-body solver combined with an e cient cartesian mesh o↵-body solver would greatly increase the overall e ciency and capabilities of the solver. This has been demonstrated with success in the HELIOS6 framework which combines a near body solver NSU3D7 with an o↵-body solver SAMARC.8,9 Previous work by our group combined a hexahedral DG solver10 with NSU3D. This work has been extended to the new DG solver using a newly developed high-order overset mesh framework called TIOGA (Topology Independent Overset Grid Assembler). The novelty in this approach is that the 3D hybrid, mixed element, curved cell, hp-adaption, and high order capabilities in the DG solver2 can be used in an overset framework. This gives the ability to solve complicated relative motion problems at high order and to be