Fully Anisotropic Goal-oriented Mesh Adaptation for the Euler Equations

A main advantage of unstructured meshes, i.e., tetrahedral meshes, is their flexibility for generating elements with large shape and size variations everywhere in the domain. Moreover, an adequate adaptation of the mesh impacts favorably numerical schemes. Consequently, an automatic process to control the mesh generation is of main importance. This document describes a goal-oriented anisotropic mesh adaptation approach. It impacts the accuracy and the convergence of scalar outputs for the conservative Euler equations. The goal-oriented error analysis is carried out for the steady Euler model discretized by an upwind finite volume approximation. This analysis proposes a complete anisotropic formulation of the problem that differentiates it from previous works such as. This formulation involves the notion of metric widely used in mesh adaptation. The numerical results point out the gain in accuracy achieved on the scalar output for simulations with complex geometries.