Committee Chair

Karman, Steve L.

Committee Member

Anderson, W. Kyle; Swafford, Timothy W.; Matthews, John V., III; Power, Greg D.


Dept. of Computational Science


College of Engineering and Computer Science


University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)


In any engineering endeavor, it is important to have the ability to efficiently and intelligently break up a region of interest in order to explore and investigate the interesting and dynamic aspects of the system enclosed in the region. In the field of fluid mechanics - and, in particular, computational fluid dynamics - this region breakup (known as discretization) has traditionally been done using structured meshes but, because of their flexibility with capturing real-world geometry, unstructured meshes are being increasingly utilized. Not surprisingly, techniques that have traditionally been reserved for structured meshes are migrating to the world of unstructured meshing as well. One such technique is the application of the Winslow elliptic smoothing equations to an unstructured mesh. The Winslow equations have proven to be powerful tools for smoothing unstructured meshes and some early difficulty using the Winslow equations with unstructured meshes was alleviated when it was determined that it was not necessary for the entire computational mesh to be constructed as an overarching system of nodes and elements, but rather, each node in computational space could be treated as an individual virtual control volume. Winslow equations have been shown to be ideal for smoothing non-boundary nodes in inviscid regions but of limited use in other situations. This presented two opportunities to improve and extend the usefulness of the Winslow equations in relation to unstructured meshes. Research documented herein allowed the Winslow equations to be applied to boundary nodes which, traditionally, have been held static while interior mesh points are smoothed. In addition, several methods were tested to make the Winslow equations applicable to highly anisotropic viscous regions of a mesh. The most successful methodology that was developed and explored in relation to a viscous region was to use an iteratively adapted computational space for each of the nodes in the viscous region. This technique allowed a mesh with an amenable connectivity structure to be smoothed in such a way that it could match a desired viscous profile based on an initial off-body spacing and the geometric progression of the viscous layers of the mesh.


Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.




Computational fluid dynamics


Winslow elliptic smoothing equations


Computational Engineering

Document Type

Doctoral dissertations




xxii, 215 leaves



Call Number

LB2369.1 .M377 2010