Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

Abstract

Summary An enhanced goal‐oriented mesh adaptation method is presented based on aerodynamic functional total derivatives with respect to mesh nodes in a Reynolds‐Averaged Navier‐Stokes (RANS) finite‐volume mono‐block and non‐matching multi‐block‐structured grid framework. This method falls under the category of methods involving the adjoint vector of the function of interest. The contribution of a Spalart–Allmaras turbulence model is taken into account through its linearization. Meshes are adapted accordingly to the proposed indicator. Applications to 2D RANS flow about a RAE2822 airfoil in transonic, and detached subsonic conditions are presented for the drag coefficient estimation. The asset of the proposed method is patent. The obtained 2D anisotropic mono‐block mesh well captures flow features as well as global aerodynamic functionals. Interestingly, the constraints imposed by structured grids may be relaxed by the use of non‐matching multi‐block approach that limits the outward propagation of local mesh refinement through all of the computational domain. The proposed method also leads to accurate results for these multi‐block meshes but at a fraction of the cost. Finally, the method is also successfully applied to a more complex geometry, namely, a mono‐block mesh in a 3D RANS transonic flow about an M6 wing. Copyright © 2016 John Wiley & Sons, Ltd.

Sequential feature‐based mesh movement and adjoint error‐based mesh refinement

“…A final method that ought to be considered, is that of References 44‐47. In this case, they employed the mesh adjoint functional sensitivity to the grid coordinates to be able to adapt the mesh.…”

Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations

“…the drag or lift of an airfoil). In this case goal-oriented error estimates for functional outputs may be used to drive the mesh adaptation [34,42,48,18,46]. These error estimates require the solution of an adjoint problem which takes into account the QoI.…”