Mesh adaptation and higher order extrapolation of the Reynolds-averaged Navier-Stokes equations using τ-estimation

The aim of this article is to use an accurate truncation error estimate in order to perform -extrapolation and mesh adaptation in an unstructured finite volume computational fluid dynamics solver, in the context of a posteriori error estimation. The truncation error is approximated by the so-called -estimation technique, in which a special criterion is defined in order to account for the finite volume discretisation. It is shown that an accurate truncation error evaluation can be obtained on arbitrary geometries as long as restriction of the solution from the fine-to-coarse grid is accurate and the coarse grid possesses the same quality requirements as the fine grid. The accuracy of the truncation error estimation is successfully verified on Euler and Reynolds-averaged Navier-Stokes equations using the method of manufactured solutions. Then, mesh adaptation is performed on aerodynamic configurations where a good improvement of the force coefficients with respect to a classic feature-based indicator is obtained, at a lower cost than performing global refinement.