Comparative Study of Conventional and Penalized Wall Function Methods in Turbulent Flow Modeling

This paper presents a comparative study of two classes of wall function methods—the conventional and penalized wall function approaches. Both methods are evaluated within the framework of wall-modeled Reynolds-averaged Navier–Stokes (RANS) equations under the equilibrium boundary layer approximation, and a mathematical foundation for the wall function approximation is provided. Matching conditions between the wall-modeled and outer flow solutions are established, and both explicit strong algebraic and implicit weak differential formulations for the conventional wall function method are discussed. In contrast to conventional approaches, the penalized wall function method, developed by the authors, employs a continuous formulation that introduces an auxiliary partial differential equation for friction velocity, enabling more robust and accurate matching between RANS and wall function solutions. A comparative analysis of these methods is conducted through numerical simulations of three test cases: turbulent flow over a flat plate with zero and adverse pressure gradients, and a 3D bump-in-channel verification problem.