In recent years, there has been growing interest in making computational fluid dynamics (CFD) predictions with quantifiable uncertainty. Tangent-mode sensitivity analysis and uncertainty propagation are integral components of the uncertainty quantification process. Generalized polynomial chaos (gPC) is a viable candidate for uncertainty propagation, and involves representing the dependant variables in the governing partial differential equations (pdes) as expansions in an orthogonal polynomial basis in the random variables. Deterministic coupled non-linear pdes are derived for the coefficients of the expansion, which are then solved using standard techniques. A significant drawback of this approach is its intrusiveness. In this paper, we develop a unified approach to automatic code differentiation and Galerkin-based gPC in a new finite volume solver, MEMOSA-FVM, written in C++. We exploit templating and operator overloading to perform standard mathematical operations, which are overloaded either to perform code differentiation or to address operations on polynomial expansions. The resulting solver is capable of either performing sensitivity or uncertainty propagation, with the choice being made at compile time. It is easy to read, looks like a deterministic CFD code, and can address new classes of physics automatically, without extensive re-implementation of either sensitivity or gPC equations. We perform tangent (forward) mode sensitivity analysis and Galerkin gPC-based uncertainty propagation in a variety of problems, and demonstrate the effectiveness of this approach.
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ASME 2010 International Mechanical Engineering Congress and Exposition
November 12–18, 2010
Vancouver, British Columbia, Canada
Conference Sponsors:
- ASME
ISBN:
978-0-7918-4448-9
PROCEEDINGS PAPER
A Unified Unintrusive Discrete Approach to Sensitivity Analysis and Uncertainty Propagation in Fluid Flow Simulations
Sanjay R. Mathur,
Sanjay R. Mathur
Purdue University, West Lafayette, IN
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Aarti Chigullapalli,
Aarti Chigullapalli
Purdue University, West Lafayette, IN
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Jayathi Y. Murthy
Jayathi Y. Murthy
Purdue University, West Lafayette, IN
Search for other works by this author on:
Sanjay R. Mathur
Purdue University, West Lafayette, IN
Aarti Chigullapalli
Purdue University, West Lafayette, IN
Jayathi Y. Murthy
Purdue University, West Lafayette, IN
Paper No:
IMECE2010-37789, pp. 213-224; 12 pages
Published Online:
April 30, 2012
Citation
Mathur, SR, Chigullapalli, A, & Murthy, JY. "A Unified Unintrusive Discrete Approach to Sensitivity Analysis and Uncertainty Propagation in Fluid Flow Simulations." Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition. Volume 11: New Developments in Simulation Methods and Software for Engineering Applications; Safety Engineering, Risk Analysis and Reliability Methods; Transportation Systems. Vancouver, British Columbia, Canada. November 12–18, 2010. pp. 213-224. ASME. https://doi.org/10.1115/IMECE2010-37789
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