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Computational Science, Engineering & Technology Series
ISSN 1759-3158 CSETS: 12
PROGRESS IN ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, C.A. Mota Soares
Chapter 3
Automatic Mesh Adaption: Towards User-Independent CFD F. Suerich-Gulick*, C.Y. Lepage+ and W.G. Habashi*+
*Department of Mechanical Engineering, McGill University, Montreal, Canada Full Bibliographic Reference for this chapter
F. Suerich-Gulick, C.Y. Lepage, W.G. Habashi, "Automatic Mesh Adaption: Towards User-Independent CFD", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Progress in Engineering Computational Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 3, pp 43-55, 2004. doi:10.4203/csets.12.3
Keywords: computational fluid dynamics, mesh adaptation, anisotropy, unstructured meshes, turbulence models, boundary layer flow.
Summary
In the work presented here, a mesh adaptation module is extended to account for
the requirements of turbulence models on 3-D unstructured tetrahedral meshes.
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Most turbulence models require that the distribution of grid points in the
boundary layer fall within a specific range of
Many turbulence models require that near-wall elements be orthogonal to the
wall, necessitating the use of hexahedral meshes or hybrid tetrahedral meshes with
layers of prisms on the walls. It should be noted that the capacity to produce anisotropic meshes is particularly important in this case, because the turbulence model requires an extremely high mesh density in the direction normal to the wall. The adaptation software produces elements that are stretched in the directions parallel to the wall, so the adapted mesh has a much smaller number of nodes than an equivalent isotropic mesh with the same boundary layer resolution. However, adapting these stretched elements presents additional difficulties, especially for 3-D meshes.
The standard mesh adaptation process is governed by the error metric, in the form
of a Hessian matrix H, which is computed from the second derivatives of the
adaptation scalar.
In order to modify the metric in the direction normal to the no-slip wall, the
Hessian is decomposed into its eigenvectors such that
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