Doctor of Philosophy, University of Toledo, 2015, Mechanical Engineering

External Verification Analysis (EVA), a new approach to verifying unsteady partial differential equation codes, is presented. After a review of the relevant code verification literature, the mathematical foundation and solution method of the EVA tool is discussed in detail. The implementation of the EVA tool itself is verified through an independent Python program. A procedure for code verification with the EVA tool is described and then applied to the three-dimensional form of a high-order non-linear computational aeroacoustics code.

Committee: Ray Hixon (Advisor); Sorin Cioc (Committee Member); James DeBonis (Committee Member); Mehdi Pourazady (Committee Member); Chunhua Sheng (Committee Member) Subjects: Aerospace Engineering; Fluid Dynamics; Mechanical Engineering

Master of Science in Mechanical Engineering, University of Toledo, 2010, College of Engineering

As Computational Aeroacoustics (CAA) codes become more complex andwidely used, robust Verification of such codes becomes more and more important. Recently, Hixon et al. proposed a variation of the Method of Manufactured Solutions of Roache especially suited for Verifying unsteady CFD and CAA codes that does not require the generation of source terms or any modification of the code being Verified. This work will present the development of the External Verification Analysis (EVA) method and the results of its application to some popular model equations of CFD/CAA and a high-order nonlinear CAA code.

Committee: Ray Hixon PhD (Committee Chair); Douglas Oliver PhD (Committee Member); Chunhua Sheng PhD (Committee Member) Subjects: Acoustics; Mechanical Engineering

Master of Science, University of Akron, 2006, Applied Mathematics

Mathematical models of physical processes often include partial differential equations (PDEs). Oftentimes solving PDEs analytically is not feasible and a numerical method is implemented to obtain an approximate solution. Too often the assumption is made that the solution should be trusted when codes are prone to implementation errors. Code verification is a field of mathematics that shows the algorithm has been implemented without mistakes and has correctly solved the problem. Currently no one method of code verification is universally accepted. The Method of Manufactured Exact Solutions (MMES) is the most commonly used, but it has a considerable disadvantage of altering the code after verification. We have developed a new method, Completely Residual Based Code Verification (CRBCV), which does not require any modification. By using several solution methods, we have shown that CRBCV is dependable when verifying the heat equation with linear and nonlinear source terms and a frontal polymerization model.

Committee: Laura Gross (Advisor) Subjects: Mathematics