Committee Chair

Hilbert, C. Bruce

Committee Member

Sreenivas, Kidambi; Matthews, Matt; Newman, James C., III


Dept. of Computational Engineering


College of Engineering and Computer Science


University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)


The finite element method has been shown to be a powerful tool in computational engineering with recent application to electromagnetics and fluid dynamics. However, achieving the high orders of accuracy easily available to the finite element method has proven difficult due to conforming higher-order meshes to curved geometries. If higher-order nodes are not placed on the surface of the geometry error is introduced into the simulated solution. This barrier is largely a non-issue for inviscid meshes where a mid-edge node can be projected onto the nearest geometry surface with minimal detrimental side effects. Viscous meshes however have to deform most of the boundary layers in order to avoid inverting the surface elements and to maintain an acceptable mesh quality. This research focuses on extending the application of the linear elastic analogy to this mesh movement problem by attributing orthotropic material properties individually to each node or element. This technique allows each node or element to behave differently under the stress of conforming to the boundary. These localized material properties are determined using the adjoint optimization method. To better determine mesh quality, a new mesh metric called Metric3 is introduced. This new metric resembles the included angle metric and is based on an element’s isoparametric transformation matrix.


I would like to thank my adviser Dr. Bruce Hilbert for his time, effort, and for keeping me pointed in the right direction when there are too many leads to chase, also to my committee members Dr. James C. Newman III, Dr. John V. Matthews III, and Dr. Abdollah Arabshahi. The professors and students of the SimCenter both past and present deserve recognition for creating an environment so conducive to research and higher education. I would also like to thank Ethan Hereth but more importantly Kim Sapp. Branch Technology, Inc. also deserves recognition for allowing Dr. Hilbert to serve as a graduate adviser. I would like to thank my parents, Jerry and Sandra Shoemake, and brother Brian for their encouragement to follow my interests and support in getting an advanced degree in ’squares and triangles’. And finally I would like to thank my wife, Kristen, for her love and support as we faced graduate school together.


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.




Numerical grid generation (Numerical analysis); Finite element method


Higher order finite element; Computational fluid dynamics; Curvilinear meshing; Linear elastic mesh deformation

Document Type

Doctoral dissertations




xii, 165 leaves