A Unified Grid Approach Using Hamiltonian Paths for Computing Aerodynamic Flows

AbstractA solution algorithm using Hamiltonian paths is presented as a unified grid approach for rotorcraft applications. Hidden line structures are robustly identified on general two- and three-dimensional unstructured grids with mixed elements, providing a framework for line-based solvers. A pure quadrilateral/hexahedral mesh is a prerequisite for line identification and enables approximate factorisation along the lines. The numerical efficiency obtained using the line-implicit method on various unstructured grids is better than that of the point-implicit method. Both finite-difference and gradient reconstructions are possible regardless of grid type. A combined reconstruction method is applied, which uses different reconstructions simultaneously but for different grid directions. Finally, the solution convergence rate is further improved using a preconditioned generalized minimal residual method (GMRES), where the preconditioning step is performed using the efficient line-implicit method.Keywords: Rotorcraft aerodynamicsunstructured gridcomputational efficiencyline-implicit methodgeneralized minimal residual method AcknowledgementsThe authors would like to acknowledge Dr. Roger Strawn (Army AFDD) and Dr. Rajneesh Singh (ARL) for their continued support of HAMSTR development. This work was supported by the National Supercomputing Center with supercomputing resources including technical support (KSC-2022-CRE-0197).Disclosure statementNo potential conflict of interest was reported by the author(s).