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Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured MeshesThe accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.
Document ID
Document Type
Contractor Report (CR)
Mavriplis, Dimitri J. (National Inst. of Aerospace Research Hampton, VA, United States)
Thomas, James L. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
September 7, 2013
Publication Date
December 1, 2003
Subject Category
Numerical Analysis
Report/Patent Number
Funding Number(s)
OTHER: 762-20-11-03-00
Distribution Limits
Work of the US Gov. Public Use Permitted.

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