AN ODE-BASED WALL MODEL FOR RANS SIMULATIONS ON CARTESIAN GRIDS

In the simulation of high-Reynolds-number turbulent flows, the use of Cartesian grids for accurately resolving near-wall regions often leads to a large number of grid points, which significantly reduces the computational efficiency of the numerical solver. To address this issue, this study introduces a two-layer wall-modeling approach. The computational domain is divided into an outer region dominated by the Reynolds-averaged Navier-Stokes (RANS) equations and a near-wall subgrid region modeled and solved using a wall model. Within the near-wall subgrid region, the simplified boundary layer momentum equation is discretized and solved on a set of virtual subgrid points using a second-order central difference scheme. Based on the model solution, the flow quantities in the near-wall modeled cells are reconstructed to strictly satisfy the wall boundary conditions. Finally, the two-layer wall model is integrated into the framework of the Cartesian-grid immersed boundary (IB) method. This strategy employs the wall model to simulate the boundary layer at a relatively large distance from the wall, greatly relaxing the grid resolution requirements in the near-wall region. As a result, the total number of grid points is significantly reduced, and computational efficiency is improved. Validation cases—including the flat-plate T3b, a turbulent bump, and flow around a NACA0012 airfoil—demonstrate that the developed two-layer wall-modeling method effectively alleviates grid-related challenges in Cartesian-grid-based turbulent flow simulations. It allows the size of the first grid layer near the wall to be increased by one to two orders of magnitude while maintaining simulation accuracy for key flow characteristics under various typical flow conditions. The proposed approach thus provides a practical and effective solution to the computational efficiency bottleneck in high-Reynolds-number turbulent flow simulations using Cartesian grids.