A parallel unstructured overset mesh method has been developed for the simulation of unsteady flows around multiple bodies in relative motion. The time integration was achieved by using a second-order accurate point Gauss-Seidel relaxation method with dual time stepping. For the spatial discretization, a cell-centered finite-volume method was used in conjunction with the Roe's flux-difference splitting. A new neighbor-to-neighbor search technique and a new data structure were developed to achieve fast and robust search of nodes on parallel distributed memory machines. A criterion of choosing a starting point for the efficient search was also suggested. In order to retain the second-order spatial accuracy of the flow solver across the overset mesh boundary, interpolations were made not only at cell faces but also for cell centers. The flow information for the cells located inside the neighboring solid bodies in close contact is obtained in a way that the flow tangency condition is satisfied on the solid surface. By doing this, the second-order temporal accuracy in dual time stepping can be preserved for unsteady flow simulations.
The present method was validated for an oscillating NACA0012 airfoil and the Douglas three-element airfoil with deflecting and retracting flap and leading-edge slat. Three-dimensional flow calculation was also made by simulating the separation trajectory of the external store of the Eglin/Pylon/Store configuration, coupled with six degree-of-freedom equations of motion. Good comparisons were obtained between the present results and the experimental data for both the predicted store trajectory and the instantaneous surface pressures on the store. It was found that the present parallel unstructured overset mesh method is an efficient tool for the simulation of unsteady flows around multiple bodies in relative motion.
