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Anisotropic adaptation on unstructured grids

by 1973- Xia, Guoping

Abstract (Summary)
The objective of the present research is to assess the use of grid adaptation to improve Computational Fluid Dynamics calculations. Many issues of the quality discretization of a flow domain are discussed. The representation of the highly directional features in a flow field, such as shocks and boundary layers, forms the focus of the analysis. Anisotropic adaptation, which uses stretched elements to resolve directional features, is more effective than isotropic adaptation. Anisotropic adaptation requires more degrees of freedom from the mesh and demands the use of unstructured grids in the adaptation. The size and orientation of an anisotropic element require a matrix-like local feature indicator. The Hessian, a matrix composed of the second derivatives of an appropriate flow variable, is defined and used as a feature indicator in the adaptation. The Hessian provides a metric that defines the length of an edge and the lengths of all edges are equal in the optimized mesh. The techniques to minimize the differences among edge lengths are discussed and those chosen include node enrichment, node removal, edge swapping and point smoothing. A unified procedure based on the advancing front method is implemented to reconstruct the local connectivity that has been removed in the node removal and edge swapping processes. iii The results indicate that the mesh in which the edge lengths are equalized is not correct for three major flow features one frequently encounters. The inflections existing near the wall in a boundary layer result in coarse grids there. A “wall” Hessian is defined to replace the second derivatives and give a more appropriate spacing for high Reynolds number flow modeling. Difficulties in the adaptation of discontinuities are addressed. These include the infinite refinement that tries to pull all the points close to the discontinuity and the deviation of the shock from the refinement region because it is too thin. Remedies proposed are to limit the minimum physical edge length and smooth the Hessian such that the refinement encompasses more layers of elements. The strength of a discontinuity is defined and methodology to refine the discontinuity equally is proposed. The invalidity of the Hessian in a free stream is corrected to give a reasonable grid size in that region. It is demonstrated that these suggested modifications improve the overall quality of the adapted mesh as well as the solution. The concepts involved in the extension of the length-based approach to three dimensions are addressed. The difference and difficulties in three-dimensional adaptation are discussed. Barriers exist which prevent the equidistribution of the edge lengths, the goal of the current approach. iv
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School:The University of Tennessee at Chattanooga

School Location:USA - Tennessee

Source Type:Master's Thesis

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