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Dynamic Parallel Adaption for Three Dimensional Unstructured Meshes: Applicationto Interface Tracking

Mesri, Youssef, Walid Zerguine, Hugues Digonnet,Luisa Silva, and Thierry Coupez

Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.195-212, October 12-15 2008


17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008

CIM Group, Center for Material Forming/ MINES ParisTech, Rue Claude Daunesse
BP 207 06904 Sophia Antipolis cedex France

First Paragraph of Introduction
The anisotropic mesh adaption techniques in the last decade have dramatically improved the numerical simulations accuracy of complex problems. An optimal anisotropic mesh adaption consists in refining and coarsening the mesh, by using a metric to specify stretching directions, in order to accurately capture physical anisotropy such as shock waves, contact discontinuities, vortexes, boundary layers and free surfaces. Thus, we propose in this paper, an anisotropic a posteriori error estimator that controls the error due to mesh discretization in all space directions. From the a posteriori error analysis, we obtain an optimal metric (optimal mesh) as a minimum of an error indicator function and for a given number of elements. The optimal metric obtained is used to build an optimal mesh for the given number of elements. Furthermore, solutions for the physical problems illustrated here are often more accurate on adapted meshes than those obtained on globally-refined meshes and at a much lower cost.

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