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Publication: An accurate gradient and Hessian reconstruction method for cell-centered finite-volume discretizations on unstructured grids

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Title An accurate gradient and Hessian reconstruction method for cell-centered finite-volume discretizations on unstructured grids
Authors/Editors* Betchen, LJ, Straatman, AG
Where published* Int. J. Numerical Methods in Fluids
How published* Journal
Year* 2009
Volume
Number
Pages
Publisher
Keywords gradient reconstruction, finite volume
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Abstract
In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell centered finite volume framework, is presented. The reconstruction, based upon the application of Gauss' theorem, provides a fully second-order accurate estimate of the gradient, along with a first-order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods.
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