Wallfunctions

Wall functions are a set of empirical or semi-empirical correlations used in computational fluid dynamics (CFD) to approximate the behavior of the flow near a solid boundary, specifically a wall. Instead of resolving the very thin viscous sublayer and buffer region directly with a very fine mesh, wall functions bridge the gap between the wall and the first computational cell away from it. This approach significantly reduces the computational cost by allowing for a coarser mesh near the wall.

The fundamental idea behind wall functions is to use the known physics of turbulent flow in the near-wall region to predict the values of flow variables, such as velocity, temperature, and turbulence quantities, at the center of the first cell. These correlations typically relate the wall shear stress, heat flux, or mass transfer to the flow variables in this first cell based on the logarithmic law of the wall for turbulent boundary layers.

Different types of wall functions exist, tailored for different flow regimes and turbulence models. For instance, standard wall functions are commonly used with the k-epsilon turbulence model, while enhanced wall treatments or scalable wall functions are employed with models like k-omega. The accuracy of wall functions depends on several factors, including the quality of the mesh near the wall, the flow regime, and the specific wall function implementation. They are a compromise between computational efficiency and accuracy, and their use requires careful consideration of the problem being solved.