Gradient-based Methods for Rapid Uncertainty Quantification in Hypersonic Flows

Brian Lockwood, University of Wyoming

With the proliferation of computational modeling within the design and analysis of engineering systems, uncertainty quantification has become increasingly important, providing valuable information for assessing the reliability of simulations and a means for improving these results. In this presentation, methods for rapid uncertainty quantification within the context of hypersonic computational fluid dynamics are examined. The simulation of hypersonic flows relies on numerous constitutive relations to account for chemical reactions, internal energy modes and molecular transport. Within these constitutive relations are hundreds of constants and parameters, which are often the result of experimental measurements. The goal of uncertainty quantification in this context is determining the variability of simulation outputs resulting from the uncertainty associated with these model parameters. Traditional methods for uncertainty quantification typically rely on exhaustive sampling, where hundreds to thousands of simulations are performed and relevant statistics are computed based on these results. For complex simulations, these exhaustive approaches are prohibitively expensive and well beyond the computational budget of most projects. To address this issue, gradient-based methods are used to reduce the expense of uncertainty quantification. Using an adjoint-based approach, the derivative of an output with respect to simulation parameters can be computed in a constant amount of work, providing more information about the simulation output without a significant increase in cost. This additional information can then be leveraged in novel ways, such as gradient-enhanced surrogate models or optimization, to accelerate the process of uncertainty quantification. This presentation examines the suitability of these gradient-based methods for hypersonic flow simulations and analyzes the performance of these methods relative to traditional uncertainty quantification strategies in terms of accuracy and computational cost.

Abstract Author(s): Brian A. Lockwood and Dimitri J. Mavriplis