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A 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.

A Unified Grid Approach Using Hamiltonian Paths for Computing Aerodynamic Flows