Cost vs Accuracy: DNS of turbulent flow over a sphere using structured immersed-boundary, unstructured finite-volume, and spectral-element methods

We report a comparative study of three numerical solvers for the direct numerical simulation of the flow over a sphere at Re = 3700. A high-order spectral-element code (Nek5000), a general purpose, unstructured finite-volume solver (OpenFOAM) and an in-house Cartesian solver using the immersed-boundary method (IBM) are employed for the analysis; results are compared against previous numerical and experimental data. Numerical results show that Nek5000 and the IBM code operate within a similar computational performance range, in terms of cost-vs-accuracy analysis, for both global parameters as well as local flow features. On the other hand, OpenFOAM needed a significantly higher number of degrees of freedom (and, overall, a higher cost) to match some of the basic features of the flow, such as the length of the recirculation bubble forming downstream the sphere. For the finest grid resolutions, the three codes are in good agreement for most of the analyzed flow metrics. Overall, our results suggest that high-order methods and second-order, energy-conserving approaches based on the IBM may be both viable options for high-fidelity scale-resolving simulations of turbulent flows with separation.