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Virtual Control Volumes for Two-Dimensional UnstructuredElliptic Smoothing

Steve L. Karman Jr.

Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.121-142, October 3-6 2010


19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

SimCenter: National Center for Computational Engineering
University of Tennessee at Chattanooga
Chattanooga TN, USA

A two-dimensional unstructured elliptic smoothing method is described where the Winslow equations are discretized using a finite volume approach. Virtual control volumes for each node are constructed with element shapes that are nearly ideal. Green-Gauss theorem is used to formulate gradients over an element or a collection of elements for a node, which ultimately leads to a coupled non-linear system of equations. Modifications enable the scheme to reproduce results similar to structured mesh schemes. Results are included that demonstrate basic mesh smoothing and boundary motion. In addition, layers of quadrilateral elements can be added to selected boundaries and the interior point positions are determined via elliptic smoothing.

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