Non-systematic grid refinement procedures for computational fluid dynamics

Verification of fluid flow simulations is usually carried out through grid convergence studies, in which either simultaneous or independent coordinate refinement is applied. For simultaneous or systematic grid refinement, the grid is successively refined using the same ratio for all coordinates. For independent coordinate refinement, the grid is successively refined in one direction only. In the present study, a third and more generalized grid refinement procedure is introduced, which allows the flexibility of different refinement ratios for each coordinate. The new procedure could even accommodate grids of the same average grid size but with different aspect ratios. For two-dimensional simulations, the procedure utilizes numerical results on four grids to demonstrate asymptotic convergence. Numerical uncertainty is quantified using a Richardson extrapolation-based error estimator. Moreover, the new refinement approach identifies an optimal cell aspect ratio that would minimize the discretization error for a fixed average grid size. As the grid aspect ratio departs from this optimal value, finer grids would be required to enter the asymptotic convergence range. Finally, extensions of the new procedure to numerical methods of mixed-order accuracy and to three-dimensional flow simulations are discussed.