An a priori anisotropic Goal-Oriented Error Estimate for Viscous Compressible Flow and Application to Mesh Adaptation

A. Belme 1 F. Alauzet 2 A. Dervieux 3
1 TROPICS - Program transformations for scientific computing
CRISAM - Inria Sophia Antipolis - Méditerranée
2 Gamma3 - Automatic mesh generation and advanced methods
ICD - Institut Charles Delaunay, Inria Saclay - Ile de France
Abstract : We present a goal-oriented error analysis for the calculation of low Reynolds steady compressible flows with anisotropic mesh adaptation. The error analysis is of a priori type. Its central principle is 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. This goal-oriented error analysis is the extension of [39] done for inviscid flows to laminar viscous flows by adding viscous terms. The main benefits of this approach, in comparison to other error estimates in the literature, is that the optimal anisotropy of the mesh directly appears in the error analysis and is not obtained from an ad hoc variable nor a local analysis. As a consequence, an optimum is obtained and the convergence of the mesh adaptive process is very fast, i.e., generally the convergence is obtained after 5 to 10 mesh adaptation cycle. Then, using the continuous mesh framework, an optimal metric is analytically obtained from the error estimation. Applications to mesh adaptive calculations of flows past airfoils are presented.
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https://hal.inria.fr/hal-01927113
Contributor : Alain Dervieux <>
Submitted on : Monday, November 19, 2018 - 4:09:51 PM
Last modification on : Friday, April 19, 2019 - 4:55:06 PM
Long-term archiving on : Wednesday, February 20, 2019 - 3:27:09 PM

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A. Belme, F. Alauzet, A. Dervieux. An a priori anisotropic Goal-Oriented Error Estimate for Viscous Compressible Flow and Application to Mesh Adaptation. 2018. ⟨hal-01927113⟩

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