Mesh Optimization Using Dual-Weighted Error Estimators: Application to the Periodic Hill

Simulations have matured to be an important tool in the design and analysis of many modern industrial devices, in particular in the process, vehicle and aeronautical industries. Most of the considered flows are turbulent, for which it is impossible to perform straightforward grid-convergence studies without considering long-term statistics. Therefore, when performing simulations in computational fluid dynamics (CFD), the use of adaptive mesh refinement (AMR) is an effective strategy to increase the reliability of the solution at a reduced computational cost. Such tools allow for error control, reduced simulation time, easier mesh generation, better mesh quality and better resolution of the a priori unknown physics. In the present contribution, the design of an optimal mesh, using AMR, is investigated in Nek5000 [3], a highly scalable code based on the spectral element method (SEM) [9] and aimed at the direct numerical simulation (DNS) of the incompressible Navier–Stokes equations (further discussed in section “Numerical Method”).