A simple criterion for estimating the grid level of detail for RANS methods

A simple criterion for evaluating the grid resolution needed to obtain a grid-independent solution of turbulent flow problems in the framework of statistical approach to turbulence simulation is proposed. The criterion is derived on the basis of an a posteriori estimate of the local interpolation error of the field of turbulent kinetic energy. A good resolution should ensure a small local interpolation error of the discrete turbulent kinetic energy. The equation for the transport of turbulent kinetic energy and realizability conditions for the turbulent stress tensor made it possible to reduce the estimation of relative interpolation error to an explicit formula for the estimate of the maximal grid step required for obtaining a grid-independent solution. The proposed criterion is applied to a steady problem for a flow past a backward facing step and to the problem of unsteady flow around a half-circular profile arranged at a zero angle of attack for the Reynolds number $\operatorname{Re}=45000$. A numerical study showed that the proposed criterion gives a good estimate of the grid resolution required for obtaining a grid-independent solution away from a wall. This criterion can be used both for estimating the grid independence of the solution and for adapting the computation grid.