Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. Mavriplis, D., J. In 16th AIAA Computational Fluid Dynamics Conference, 2003. AIAA Paper 2003-3986. ![Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes [pdf]](https://bibbase.org/img/filetypes/pdf.svg "pdf")
Paper doi abstract bibtex The 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, or the discretization of physical viscous terms based on these gradients has the potential for generating large but subtle discretization errors, which vanish in regions with no appreciable surface curvature. © 2003 by Dimitri J. Mavriplis. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
@inproceedings{
title = {Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes},
type = {inproceedings},
year = {2003},
publisher = {AIAA Paper 2003-3986},
id = {193b8228-8f76-3d8e-a0f5-42f4c663057d},
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abstract = {The 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, or the discretization of physical viscous terms based on these gradients has the potential for generating large but subtle discretization errors, which vanish in regions with no appreciable surface curvature. © 2003 by Dimitri J. Mavriplis. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.},
bibtype = {inproceedings},
author = {Mavriplis, Dimitri J.},
doi = {10.2514/6.2003-3986},
booktitle = {16th AIAA Computational Fluid Dynamics Conference}
}
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