Robin-type wall functions and their numerical implementation

The paper is devoted to numerical implementation of the wall functions of Robin-type for modeling near-wall turbulent flows. The wall functions are based on the transfer of a boundary condition from a wall to some intermediate boundary near the wall. The boundary conditions on the intermediate boundary are of Robin-type and represented in a differential form. The wall functions are formulated in an analytical easy-to-implement form, can take into account the source terms, and do not include free parameters. The relation between the wall functions of Robin type and the theory of Calderon–Ryaben'kii's potentials is demonstrated. A universal robust approach to the implementation of the Robin-type wall functions in finite-volume codes is provided. The example of an impinging jet is considered.