Efficient wall-modeling diffused-interface immersed boundary method for solving turbulent flows with high-order finite difference schemes

This study presents a novel approach that integrates explicit non-equilibrium wall modeling with the diffused-interface immersed boundary method (IBM) and couples it with high-order compact finite difference method (FDM). This framework efficiently models high Reynolds number turbulent flows over obstacles. The major contributions of this study are as follows: (1) the adaptation of explicit non-equilibrium wall functions within the diffused-interface IBM to create a slip condition, which strikes an effective balance between computational efficiency and accuracy for complex flow scenarios and (2) the incorporation of wall-modeling diffused-interface IBM with high-order compact FDM, leveraging its high computational efficiency during parallel computations and its capability to handle the multiscale nature of turbulent flows. The efficacy of these combined methods is validated through three high Reynolds number test cases: turbulent flow over a circular cylinder, a square cylinder, and a large-span flat roof. The results demonstrate that these methods achieve satisfactory accuracy with coarser grids compared to traditional wall-resolving approaches, underscoring their potential for efficient and practical applications.