In this paper, a high Reynolds number compressible flow simulation method based on the immersed boundary method (IBM) is developed on the adaptive Cartesian grids to address two problems: one is the ability of large-scale Cartesian grid generation, and the other is the resolution of thin shear layers. For the former, an efficient automatic parallel generation method of adaptive Cartesian grids is proposed based on the k-d tree theory. The method has good parallel scalability and computational efficiency, e.g., the generation of 1.41 × 109 cells by 2048 cores takes only 0.40 min. For the latter, an IBM-wall function coupling method is designed to simulate geometrical configurations with high Reynolds numbers in the parallel framework. Numerical experiments show that the presented method can yield results consistent with the use of body-fitted grids. In conclusion, the presented method can realize a fully automatic simulation of high Reynolds number compressible flows, significantly reducing the labor cost in the computational fluid dynamics process, and can improve the accuracy and efficiency of engineering applications.
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