Hybrid Cartesian Grid Method for Unsteady Flow Problems

Grid generation in the simulation of unsteady compressible flows is more difficult than that of steady ones. In this paper, the near body region was discretized by using body-fitted structured grids, while the remaining computational domain was tessellated with generated Cartesian grids. By using the alternating digital tree (ADT) algorithm, the computational time of hole-cutting and identification of donor cells during grid generation could be decreased significantly. A compressible solver for unsteady flow problems is then developed. A cell-centered, 2 nd -order accurate finite volume method is employed in spatial discretization, and an implicit dual-time stepping LU-SGS approach is employed in temporal discretization. Feature-based adaptation is used for unsteady flows with stationary boundary. Geometry adaptation is used during simulation steps for moving-boundary problems and the flow solution is interpolated from the old grid to the new grid. Both laminar and turbulent unsteady cases are tested to demonstrate the accuracy and efficiency of the proposed method.