Summary: Optimal 3D Highly Anisotropic Mesh Adaptation
based on the Continuous Mesh Framework
, F. Alauzeta
aINRIA, Projet Gamma, Domaine de Voluceau, Rocquencourt, BP 105,
78153 Le Chesnay Cedex, France.
bGeorge Mason University, Computational Fluid Dynamics Center,
4400 university drive, MS6A2, Fairfax, VA, USA
This paper addresses classical issues that arise when applying anisotropic mesh adaptation to real-life 3D problems as the loss
of anisotropy or the necessity to truncate the minimal size when discontinuities are present in the solution. These problematics
are due to the complex interaction between the components involved in the adaptive loop: the flow solver, the error estimate and
the mesh generator. A solution based on a new continuous mesh framework is proposed to overcome these issues. We show that
using this strategy allows an optimal level of anisotropy to be reached and thus enjoy the full benefit of unstructured anisotropic
mesh adaptation: optimal distribution of the degrees of freedom, improvement of the ratio accuracy with respect to cpu time, ...
Key words: Anisotropy; multi-scale mesh adaptation; metric-based mesh adaptation; continuous mesh; convergence order;
Nowadays, there is no more need to recall the benefits of metric-based mesh adaptation when dealing with anisotropic
physical phenomena. A lot of 3D successful examples on real-life problems have already proved its efficiency [3, 6, 11, 18, 19].