In this paper, a new adaptive mesh refinement algorithm is proposed for computing viscous flows around complex geometries with high-order accuracy in space. The basic idea behind the present method is to apply immersed boundary method to cells in the vicinity of a solid boundary and a newly developed Cartesian grid method (tree-structured Building-Cube method) to all other cells in an attempt to develop a fast, low storage method for computation of the Navier-Stokes equations. The implementation of the adaptive mesh refinement is straightforward in the present approach because the adaptive refinement is applied not to cells but to cubes. Since the number of cubes is relatively small, the cube refinement is quite simple and the refinement does not cause the difficulty of the dynamic load balancing in parallel computations. In a 2D test case, this method can efficiently capture flow features such as shocks or wakes, keeping the overall grid smooth. Simulation results for 3D high Reynolds number viscous flow past Ahmed body are presented for evaluation of the present algorithm.
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