All ETDs from UAB

Advisory Committee Chair

Chih-Hsiung Cheng

Advisory Committee Members

Chau-Lyan Chang

Robert Nichols

Roy Koomullil

Sin-Chung Chang

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) School of Public Health


A transient viscous solver has been developed based on the novel space-time conser-vation element solution element (CESE) framework. Till date, the numerical accuracy of the CESE framework in modeling inviscid flow problems has been well documented, while very little work has been done in regards to modeling transient viscous flows. In this work, an attempt to fill that gap in literature was carried out by rigorously investigat-ing the numerical accuracy and computational performance of the CESE framework in simulating such flows. The study aims at gaining a deeper understanding on the numeri-cal accuracy and dissipation characteristics of the CESE framework, as well as its robust-ness in handling practical problems of interest. There are four major sections in this work. The first section details the fundamentals of the CESE framework, various schemes available under the framework, and a step-by-step procedure involved in constructing a Navier-Stokes solver using the framework. The second section deals with implementation of boundary conditions, with particular focus on non-slip walls - a key component of vis-cous solvers. The treatment of various boundary conditions is explored so that it is con-sistent with the fundamental aspect of the CESE framework- space-time flux conserva-tion. Two different approaches to model the viscous wall effect have been explored and presented in detail. The third section of this work investigates and assesses: 1) numerical accuracy, dissipation/dispersion characteristics of various schemes in the CESE frame-work, 2) influence of grid topology on the accuracy of viscous flow simulation results, and 3) robustness of the developed solver. Viscous flow problems under several catego-ries, which include aeroacoustics and hypersonic flows, are employed to assess those. Furthermore, the use of triangular and tetrahedral meshes for 2-D and 3-D viscous flow simulations respectively, is shown to be more accurate than their structured mesh coun-terpart under this novel framework. The original CESE framework is 2nd order accurate in both space and time. A higher-order extension to it is proposed and explored in the final section, so that it can be used to solve problems such as computational aeroacoustics, which require high numerical accuracy, without needing a very fine mesh.

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