An adaptive direct-forcing immersed boundary method with subcycled time advancement for compressible flows over irregular solid boundaries

Abstract

An adaptive direct-forcing immersed boundary method (IBM) is developed for numerical simulation of compressible flows involving irregular solid boundaries. The method is constructed on block-structured adaptive mesh refinement (AMR) and achieves computational efficiency through the coupling of subcycled time advancement with the direct-forcing IBM workflow. In the proposed framework, the solid surface is represented by Lagrangian points on the finest AMR level, where immersed-boundary momentum and energy source terms are evaluated to approximately enforce the prescribed boundary conditions. For AMR time advancement, a subcycling strategy is introduced in which different levels of grids advance with different time steps. The effect of the immersed boundary is transferred to coarser levels through fine-to-coarse averaging operations at synchronization times. This treatment improves computational efficiency while preserving the coarse-fine consistency of the immersed boundary forcing. The method is applicable to representative compressible flows such as shock reflection and diffraction, subsonic and supersonic body flows, aerodynamic force evolution, and viscous boundary-layer effects. Numerical tests are conducted to validate the proposed method, and the results are in good agreement with reference data such as shock diffraction, surface pressure distributions, and aerodynamic force coefficients. Computational cost comparisons demonstrate the efficiency improvement obtained from AMR and the subcycling strategy. Finally, a downburst wind-field simulation over a conical hill is presented to illustrate the capability of the proposed approach for practical complex-flow applications.