Comparison Between Geometric and Linearized Wall-Modeling Approaches for Immersed Boundary Methods

An in-depth comparison and analysis of the two wall-modeling approaches for RANS of high Reynolds number flows for the immersed boundary method (IBM) is presented. The two wall-modeling approaches are the geometrical approach (GA) proposed by Constant et al. [1] and the linear approach (LA) proposed by Tamaki et al. [2] and correspond to the two most promising methods to obtain oscillation free and accurate results for wall-modeling RANS in an immersed boundary context. To provide an unbiased and accurate comparison, an iso-grid, iso-solver, and iso-numerical method approach is pursued and various 2D and 3D test cases are considered. For 2D, the canonical NACA 0012 and multi-element airfoil are considered whilst the 3D test case considered is an ellipsoid. Given that the GA has been developed for external aerodynamic flows with target applications such as wings and airplanes, it tends to yield more accurate results for these test cases given appropriate user-input parameters. However, the user-input independent approach of the LA provides a more general method that is able to consistently provide accurate results for a large range of flows. Though not as accurate as the GA for airfoils, wings, and airplanes, it tends to yield more accurate results for test cases outside of the target application and best practice guidelines of the GA.