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Non-Intrusive Polynomial Chaos Methods for Uncertainty Quantification in Fluid Dynamics

66 citations0/0 files storedAIAA Aerospace Sciences Meeting

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Probabilistic and Robust Engineering Design Computational Fluid Dynamics and Aerodynamics Model Reduction and Neural Networks

Abstract

This paper examines uncertainty quantification in computational fluid dynamics (CFD) with non-intrusive polynomial chaos (NIPC) methods which require no modification to the existing deterministic models. The NIPC methods have been increasingly used for uncertainty propagation in high-fidelity CFD simulations due to their non-intrusive nature and strong potential for addressing the computational efficiency and accuracy requirements associated with large-scale complex stochastic simulations. We give the theory and description of various NIPC methods used for non-deterministic CFD simulations. We also present several stochastic fluid dynamics examples to demonstrate the application and effectiveness of NIPC methods for uncertainty quantification in fluid dynamics. These examples include stochastic computational analysis of a laminar boundary layer flow over a flat plate, supersonic expansion wave problem, and inviscid transonic flow over a three-dimensional wing with rigid and aeroelastic assumptions.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2005High-Order Collocation Methods for Differential Equations with Random Inputs 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes

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