Mesh Adaptation for Computational Fluid Dynamics, Volume 2

5Goal-Oriented Adaptation for Viscous Steady Flows

Chapter 4 introduces for the steady Euler flow model the different steps of a method for goal-oriented anisotropic adaptation. A continuous adjoint and a continuous error analysis are used for exhibiting an intermediate optimal continuous metric. The final optimal metric is solution of a (continuous) fixed point. A way of discretizing this fixed point is then introduced and constitutes the goal-oriented anisotropic mesh adaptation algorithm. This chapter extends the goal-oriented anisotropic adaptation to viscous steady compressible flows. Only the error analysis is different. With viscous terms, it is more complex. Further, due to the thin boundary layers in the flow, the efficiency of adaptation is much more influenced by the quality of the error estimate. The central principle of this kind of analysis is again to express the right-hand side of the error equation, often referred as the local error, as a function of the interpolation error of a collection of fields present in the nonlinear partial differential equations. Two approaches are considered and compared. Applications to mesh adaptive calculations of flows past airfoils and a wing-body combination are discussed.

5.1. Introduction

This chapter focuses on the building of an anisotropic goal-oriented mesh adaptation method for viscous flows. The way to derive such a method for inviscid flows was described in the previous chapter. In order to extend it to an elliptic ...