Numerical Implementation of Generalized Robin–type Wall Functions and Their Application to Impinging Flows

The paper is devoted to the generalized wall functions of Robin–type and their application to 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 of the momentum equation, and do not include free parameters. The log–profile assumption is not used in this approach. A robust numerical algorithm is proposed for implementation of Robin–type wall functions to both finite–difference and finite– volume numerical schemes. The algorithm of implementation of the Robin–type wall functions to existing finite-volume codes is provided. The axisymmetric impinging jet problem is numerically investigated for different regimes on the base of the wall-functions implemented to the high-Reynolds-number k − ǫ model.