Numerical experiments on application of Richardson extrapolation with nonuniform grids

Some unresolved problems related to Richardson extrapolation (RE) are elucidated via examples, and possible remedies are suggested. The method is applied to the case of turbulent flow past a backward facing step using nonuniform grid distributions. It is demonstrated that RE can be used to obtain grid independent solutions using the same grid refinement factors in both coordinate directions. The use of generalized wall functions together with the standard k-epsilon model seems to work well even if the grid refinement extends into the viscous sublayer. In addition, the grid convergence index and other standard uncertainty measures are compared and a new uncertainty measure is suggested which seems to be a better indicator for the grid convergence error.