Penalized Wall Function Method for Turbulent Flow Modeling

A novel penalized wall function method for simulations of wall-bounded compressible turbulent flows is proposed. The new approach based on the Reynolds-averaged Navier–Stokes (RANS) equations to model outer region boundary layer, while inner part approximated by equilibrium model. differential formulation match external and solutions reformulated in a form generalized characteristic-based volume penalization transfer shear stress from layer impose wall-stress conditions RANS solution. exchange location specified implicitly through localized source term equation, written as normalized distance wall. condition determined solving an auxiliary equation wall-stress, ensuring correct matching at layer. proposed noticeably reduces near-wall mesh resolution requirements without significant modification solver removes ill-defined explicit procedure, commonly used traditional function-based methods. implemented using vertex-centered control unstructured computational grids. effectiveness developed demonstrated twodimensional bump-in-channel flow Spalart–Allmaras turbulence