Curved mesh generation and mesh refinement using Lagrangian solid mechanics

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We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final configuration is determined by solving for the equilibrium configuration. The deformations are represented using piecewise polynomials within each element of the original mesh. When the mesh is sufficiently fine to resolve the solid deformation, this method guarantees non-intersecting elements ... continued below

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Persson, P.-O. & Peraire, J. December 31, 2008.

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We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final configuration is determined by solving for the equilibrium configuration. The deformations are represented using piecewise polynomials within each element of the original mesh. When the mesh is sufficiently fine to resolve the solid deformation, this method guarantees non-intersecting elements even for highly distorted or anisotropic initial meshes. We describe the method and the solution procedures, and we show a number of examples of two and three dimensional simplex meshes with curved boundaries. We also demonstrate how to use the technique for local refinement of non-curved meshes in the presence of curved boundaries.

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  • Journal Name: Proc. of the 47th AIAA Aerospace Sciences Meeting and Exhibit

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  • Report No.: LBNL-1426E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 946598
  • Archival Resource Key: ark:/67531/metadc893212

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  • December 31, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 8, 2016, 1:18 p.m.

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Persson, P.-O. & Peraire, J. Curved mesh generation and mesh refinement using Lagrangian solid mechanics, article, December 31, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc893212/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.