Certifiable Computational Fluid Dynamics Through Mesh Optimization

Abstract

The accuracy and reliability of computational fluid dynamics (CFD) are addressed by proposing a novel, efficient, and generic mesh optimization approach. By using an appropriate directional error estimator, coupled with an effective mesh adaptation technique that is tied closely to the solver, it can be demonstrated that, for each flow condition and geometry combination, a controllable error level and an optimal mesh can be obtained. It is further demonstrated that such an optimal mesh can be reached from almost any reasonable initial grid and, more astonishingly, that the order of accuracy of well-posed numerical algorithms has a considerably reduced impact on solution accuracy if the mesh is well adapted. Thus, the proposed approach can be considered a first step toward user-, mesh-, and solver-independent, and thus certifiable, CFD.