Resolving turbulent boundary layer on coarse grid using function enrichment based on variational reconstructions

An improved finite volume scheme based on variational reconstruction and function enrichment has been proposed in this paper. By incorporating the law-of-the-wall into the variational reconstruction, the proposed method can resolve turbulent flow accurately on grids much coarser than those needed by traditional methods. The usual reconstruction in a finite volume scheme assumes that the solution is belonging to a polynomial function space, which is inaccurate to resolve the velocity profile within the turbulent boundary layer unless the grid in wall-normal direction is fine enough. In the present paper, this function space is “enriched” by adding a basis function that is derived from the logarithmic law of the turbulent boundary layer. Then variational reconstruction procedure is applied to find the “best” solution belonging to the expanded function space. The advantage of the present method over the traditional wall function model is that the turbulent flow within the boundary layer is resolved rather than modeled. The algorithms and the implementations are discussed in detail. The proposed method is applied to the turbulent flow over a flat plate at a Reynolds number of [Formula: see text] and the turbulent flow over a plate with a bump at a Reynolds number of [Formula: see text]. The results of second- and third-order schemes are presented for the turbulent velocity profile and the skin friction coefficients. The numerical results suggest that this approach not only resolves the near wall turbulent accurately on very coarse grids but also reduces the computational time significantly.