Importance of Code and Solution Verification In Credible Simulations

Abstract

Current interest in verification, validation, and uncertainty quantification (VVUQ) has increased substantially over the past 30 years with increased awareness of potential inaccuracies of numerical simulations. This requires rigorous VVUQ analysis methods to correctly estimate the numeric and physics modeling uncertainties of numerical simulations for a given application. While methods exist that quantify these uncertainties, these methods are not the most rigorous in identifying code errors and estimating numerical and physical modeling uncertainties. The VVUQ methods presented in this dissertation describe three state-of-the-art improvements to current VVUQ methods: modified equation analysis method of manufactured solutions (MEAMMS) code verification, identifying and characterizing the "Asymptotic Point", and how this impacts validation and uncertainty quantification. MEAMMS code verification builds on the method of manufactured solutions (MMS) and the modified equation analysis (MEA) to identify code errors that are below, of the same order, or with certain implementations, higher than the numerical method. Previous code verification methods, such as MMS, do not identify these types of coding errors. Characterizing the asymptotic point for multiple manufactured solutions provides additional insight into how discretization error behaves for a variety of discretization sizes. This characterization is able to evaluate the performance of different discretization uncertainty methods inside the asymptotic range, near the asymptotic point, and outside the asymptotic range. Code and solution verification sensitivities show the importance of code and solution verification in validation and uncertainty quantification studies. By changing the amount of coding error and numerical uncertainty on a synthetic problem, the impact can be measured. This novel work aims at extending the field of VVUQ by developing tools and methodologies that improve the quality of computational software’s prediction capability.