A 3D goal-oriented anisotropic mesh adaptation applied to inviscid flows in aeronautics
Adrien Loseille
Fréderic Alauzet
(INRIA Rocquencourt)
Alain Dervieux
(INRIA, BP93, 06902 Sophia-Antipolis, France)
Proceedings of AIAA Aerospace Sciences Meeting and Exhibit, Orlando, Fl., 2010 (23 pages)
Abstract:
This paper studies the coupling between anisotropic mesh adaptation and goal-oriented
error estimate. The former is very well suited to the control of the interpolation error. It
is generally interpreted as a local geometric error estimate. On the contrary, the latter is
preferred when studying approximation errors for PDEs. It generally involves non local
error contributions. Consequently, a full and strong coupling between both is hard to
achieve due to this apparent incompatibility. This paper shows how to achieve this coupling.
This is done in three steps. First, a new a priori error estimate is proved in a formal
framework adapted to goal-oriented mesh adaptation for output functionals. Second, the
error estimate is applied to the set of steady compressible Euler equations which are solved
by a stabilized Galerkin finite element discretization. A goal-oriented error estimation
is derived. Third, rewritten in the continuous mesh framework, the previous estimate is
minimized on the set of continuous meshes thanks to a calculus of variations. The optimal
mesh is then derive. 3D examples of steady flows around supersonic and transsonic aircrafts
are presented to validate the current approach and to demonstrate its efficiency.
Full text (pdf)
@inproceedings{LDA10d,
author = {Loseille, A. and Dervieux, A. and Alauzet, F.},
title = {A {3D} goal-oriented anisotropic mesh adaptation applied to inviscid flows in aeronautics},
booktitle = {Proceedings of 48th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2010-1067},
location = {Orlando, FL, USA},
year = 2010
}