Virtual control volumes for two-dimensional unstructured elliptic smoothing

Steve L. Karman

doi:10.1007/978-3-642-15414-0_8

Virtual control volumes for two-dimensional unstructured elliptic smoothing

Steve L. Karman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 19th International Meshing Roundtable, IMR 2010
Pages	121-142
Number of pages	22
DOIs	https://doi.org/10.1007/978-3-642-15414-0_8
State	Published - 2010
Externally published	Yes
Event	19th International Meshing Roundtable, IMR 2010 - Chattanooga, TN, United States Duration: Oct 3 2010 → Oct 6 2010

Publication series

Name	Proceedings of the 19th International Meshing Roundtable, IMR 2010

Conference

Conference	19th International Meshing Roundtable, IMR 2010
Country/Territory	United States
City	Chattanooga, TN
Period	10/3/10 → 10/6/10

Keywords

Finite-volume control volume
Mesh quality improvement
Unstructured elliptic smoothing
Winslow smoothing

Access to Document

10.1007/978-3-642-15414-0_8

Cite this

@inproceedings{f11642749f2c4525909e904b705a8b07,

title = "Virtual control volumes for two-dimensional unstructured elliptic smoothing",

abstract = "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.",

keywords = "Finite-volume control volume, Mesh quality improvement, Unstructured elliptic smoothing, Winslow smoothing",

author = "Karman, \{Steve L.\}",

year = "2010",

doi = "10.1007/978-3-642-15414-0\_8",

language = "English",

isbn = "9783642154133",

series = "Proceedings of the 19th International Meshing Roundtable, IMR 2010",

pages = "121--142",

booktitle = "Proceedings of the 19th International Meshing Roundtable, IMR 2010",

note = "19th International Meshing Roundtable, IMR 2010 ; Conference date: 03-10-2010 Through 06-10-2010",

}

Karman, SL 2010, Virtual control volumes for two-dimensional unstructured elliptic smoothing. in Proceedings of the 19th International Meshing Roundtable, IMR 2010. Proceedings of the 19th International Meshing Roundtable, IMR 2010, pp. 121-142, 19th International Meshing Roundtable, IMR 2010, Chattanooga, TN, United States, 10/3/10. https://doi.org/10.1007/978-3-642-15414-0_8

TY - GEN

T1 - Virtual control volumes for two-dimensional unstructured elliptic smoothing

AU - Karman, Steve L.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Finite-volume control volume

KW - Mesh quality improvement

KW - Unstructured elliptic smoothing

KW - Winslow smoothing

UR - https://www.scopus.com/pages/publications/84878231077

U2 - 10.1007/978-3-642-15414-0_8

DO - 10.1007/978-3-642-15414-0_8

M3 - Conference contribution

AN - SCOPUS:84878231077

SN - 9783642154133

T3 - Proceedings of the 19th International Meshing Roundtable, IMR 2010

SP - 121

EP - 142

BT - Proceedings of the 19th International Meshing Roundtable, IMR 2010

T2 - 19th International Meshing Roundtable, IMR 2010

Y2 - 3 October 2010 through 6 October 2010

ER -

Virtual control volumes for two-dimensional unstructured elliptic smoothing

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