Approximating local averages of fluid velocities: The equilibrium Navier–Stokes equations Original Research Article

In the approximation of higher Reynolds number flow problems, the usual approach is to seek to approximate suitable velocity averages rather than the pointwise fluid velocity itself. We consider an approach to this question wherein the averages are local, spatial averages computed with the Gaussian filter (as in large eddy simulation) and the averages are approximated without using either turbulent closure models or wall laws. The approach we consider is a (underresolved) direct numerical simulation followed by postprocessing to extract accurate flow averages. Á priori and a posteriori estimates are given for View the MathML source which can give guidance for the coupling between the averaging radius δ and the mesh width h. Numerical experiments support the error estimates and illustrate the adaptive grid refinement procedure. Our analysis and experiments are for the equilibrium case which is a step towards but still far from the actual case of a turbulent flow simulation.