Domain decomposition for near-wall turbulent flows

Modeling near-wall high-Reynolds-number turbulent flows is a time-consuming problem. A domain decomposition approach is developed to overcome the problem. The original computational domain is split into a near-wall (inner) subdomain and an outer subdomain. The developed approach is applied to a model 2D equation simulating major peculiarities of near-wall high-Reynolds-number flows. On the base of the Calderon–Ryaben’kii potential theory it is possible to consider the near-wall (inner) problem independently on the outer problem. The influence of the inner problem can exactly be represented by a pseudo-differential equation formulated on the intermediate boundary. In a 1D case, it leads to the wall functions represented by Robin boundary conditions, which can be determined either analytically or numerically. It is important that the wall functions (or boundary conditions) are mesh independent and can be realized in a separate routine. Thus, the original problem can only be solved in the outer domain with some specific nonlocal boundary conditions called nonlocal wall functions. The technique can be extended to 3D problems straightforward.