A Hamiltonian-Strand Approach for Aerodynamic Flows Using Overset and Hybrid Meshes

A solution framework using Hamiltonian paths and strand grids (HAMSTR) is presented for three-dimensional flows on overset and hybrid meshes. The methodology creates a volume mesh starting from an unstructured surface mesh that can be comprised of mixed triangular-quadrilateral elements. "Linelets" through the meshes are found in a robust manner and the solver uses line-implicit schemes and high-order reconstruction schemes along these linelets, similar to a structured solver. The mesh system is also extended to utilize overset meshes. This overset technique allows for multiple mesh systems, which consists of a near-body Hamiltonian/Strand grid and off-body Cartesian nested meshes. The generalized approach to obtaining the Hamiltonian paths allows for initially structured and unstructured meshes to be quilted together to form a unified grid. In such cases, Hamiltonian paths can cross themselves; however, no changes are necessary for the flow solver. Finally, the integration framework between the various components of the code suite is performed using Python to allow for ease of integration in the future to other codes. Aerodynamic flows past an airfoil, sphere, wing and non-lifting rotor are presented using the Hamiltonian/Strand approach and good agreement was observed against experimental results as well as solutions obtained from traditional structured solvers.