HIGH ACCURACY METHOD FOR TURBULENT FLOW PROBLEMS

We present a method of high-order temporal and spatial accuracy for flow problems with high Reynolds number. The method presented is stable, computationally cheap and gives an accurate approximation to the quantities sought. The direct numerical simulation of turbulent flows is computationally expensive or not even feasible. Hence, the method employs turbulence modeling. The two key ingredients are the temporal deferred correction, combined with the family of Approximate Deconvolution models, which allows for arbitrarily high order of accuracy in both spatial and temporal variables. We prove stability and accuracy for the two-step method; the method is shown to be second order accurate in time and in the filtering width.