University of Texas at Austin

Past Event: Babuška Forum

PECOS Verification Tools: Manufactured Analytical Solutions Abstraction (MASA) and Bayesian Richardson Extrapolation (BRExtrap)

Todd A. Oliver, Institute for Computational Engineering and Sciences, The University of Texas at Austin

10 – 11AM
Friday Jan 26, 2018

POB 6.304

Abstract

Computational simulations are commonly used to probe the physics of complex phenomena and to inform critical design and operational decisions for complex systems. Given these uses, it is essential that the software implementation of the models that form the basis of such simulations be correct and that the effects of numerical approximations are understood. Verification encompasses both of these activities. The process of assessing software correctness is code verification, while the process of assessing solution accuracy is solution verification. In this talk, we examine two tools aimed at enabling verification studies. The first tool is a software library for generating and using manufactured solutions: the MASA (Manufactured Analytical Solution Abstraction) library (https://github.com/manufactured-solutions/MASA). MASA serves as a centralized repository for manufactured solutions and accompanying source terms. It currently contains solutions for a number of equation sets, including the Euler, Navier-Stokes, and Reynolds-averaged Navier-Stokes equations. The library provides C, C++, Fortran, and python interfaces, enabling use across a wide range of scientific codes. Further, it provides automatic differentiation capabilities to ease the generation of new solutions. We will show examples of bugs discovered using MASA, describe how to incorporate MASA support into an existing software package, and discuss how to generate new manufactured solutions using MASA. The second tool aims to enable solution verification for statistics computed from simulations of chaotic systems, as encountered in large eddy or direct numerical simulation (DNS). In such simulations, due to the presence of non-trivial statistical error, standard techniques for estimating discretization error, such as Richardson extrapolation, fail or are unreliable. In this work, we develop an extension of Richardson extrapolation that accounts for the effects of sampling error. The result is a Bayesian inference problem in which the uncertain discretization error parameters are estimated given statistical results from simulations with varying resolution. The performance of the method is demonstrated on multiple problems, including DNS of channel flow. Bio Todd Oliver is a Research Scientist at the Center for Predictive Engineering and Computational Science within the Institute of Computational Engineering and Sciences at UT-Austin. He received his Ph.D. in Aerospace Engineering from MIT in 2008. He joined ICES at a Postdoctoral Researcher shortly after and has been at UT since that time. His research interests include uncertainty quantification, model inadequacy, and computational fluid dynamics.

Event information

Date
10 – 11AM
Friday Jan 26, 2018
Location POB 6.304
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