An efficient immersed boundary–dynamic wall function model based on adaptive cartesian grids

Compared to traditional body-fitted moving grids and overset grids, adaptive Cartesian grids offer significant advantages, including no need for grid deformation, highly automated generation process, natural adaptability to complex geometries, and ease of implementing solution-based adaptive mesh refinement. However, in high Reynolds number simulations involving large motions, these grids face the issue of “grid catastrophe” due to the extreme grid resolution required for turbulent boundary layer simulation. To address this, we employ the immersed boundary-dynamic wall function model combined with an implicit dual-time-stepping method, effectively resolving near-wall flow structures without significantly increasing grid count. To handle the assignment of newly emerged Eulerian cells during motion, a three-point interpolation method is used for flow field initialization. This computational framework has been validated through a series of steady-state benchmark cases. Through simulations of typical dive processes and typical pitching airfoil benchmarks, we demonstrate the high efficiency and fidelity of our method in solving turbulent flow fields under dynamic boundary conditions at subsonic and critical sonic speeds. This method provides efficient and reliable numerical simulation support for the aerodynamic design and optimization of various new aircraft.