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Uncertainty Quantification In Computational Fluid Dynamics Lecture Notes

Cormac McCarthy

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Computational Fluid Dynamics (CFD) has revolutionized the way engineers and scientists analyze and design fluid flows. However, CFD models are often subject to various uncertainties that can impact the accuracy and reliability of their predictions. Uncertainty Quantification (UQ) emerged as a critical discipline in CFD, providing a systematic framework to assess and quantify these uncertainties.

Uncertainty Quantification in Computational Fluid Dynamics (Lecture Notes in Computational Science and Engineering 92)

Uncertainty Quantification in Computational Fluid Dynamics (Lecture Notes in Computational Science and Engineering Book 92)

5 out of 5

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These Lecture Notes offer a comprehensive exploration of Uncertainty Quantification in Computational Fluid Dynamics, guiding readers through the fundamental concepts, methodologies, and cutting-edge applications of this transformative approach. Delve into the intricacies of uncertainty analysis, unravel the complexities of model verification and validation, and uncover the power of Bayesian inference and Monte Carlo methods.

Fundamentals of Uncertainty Quantification

Chapter 1 lays the groundwork for UQ in CFD. Explore the types of uncertainties encountered in CFD models, including model form uncertainties, input parameter uncertainties, and numerical uncertainties. Gain insights into the importance of uncertainty characterization and quantification, paving the way for reliable and accurate CFD predictions.

Verification, Validation, and Sensitivity Analysis

Chapter 2 delves into the essential aspects of CFD model verification, validation, and sensitivity analysis. Discover the rigorous steps involved in verifying the correctness of the CFD model, ensuring that it accurately represents the physical system being studied. Learn how to validate the model by comparing its predictions against experimental data or high-fidelity simulations, establishing confidence in its accuracy.

Uncover the power of sensitivity analysis in identifying the most influential input parameters and understanding their impact on the CFD predictions. Master the techniques for performing local and global sensitivity analysis, empowering you to optimize CFD models and enhance their predictive capabilities.

Uncertainty Propagation and Quantification

Chapter 3 introduces the concepts of uncertainty propagation and quantification in CFD. Explore the Monte Carlo method, a cornerstone of UQ, and its variants for efficiently propagating uncertainties through complex CFD models. Gain proficiency in applying advanced techniques such as Latin Hypercube Sampling and Quasi-Monte Carlo methods.

Delve into the theory of probability and statistics, equipping yourself with the mathematical tools for uncertainty quantification. Understand the role of probability distributions in representing uncertain inputs and quantify the uncertainty in CFD predictions using statistical measures such as mean, variance, and confidence intervals.

Bayesian Inference and Stochastic Modeling

Chapter 4 introduces the powerful Bayesian framework for updating uncertainties based on experimental data or additional information. Discover how Bayesian inference can be seamlessly integrated with CFD simulations, leading to more accurate and reliable predictions. Explore the principles of Bayesian statistics and learn how to apply Bayesian methods to CFD UQ problems.

Uncover the benefits of stochastic modeling in capturing the inherent randomness and variability in fluid flows. Gain insights into stochastic processes, random fields, and their applications in CFD UQ. Enhance your understanding of uncertainty propagation in stochastic models and develop robust CFD predictions in the face of complex uncertainties.

Applications in Engineering and Science

Chapter 5 showcases the transformative impact of Uncertainty Quantification in Computational Fluid Dynamics across a wide range of engineering and scientific disciplines. Witness how UQ empowers engineers to design more efficient and reliable aircraft, optimize combustion processes, and enhance the safety of nuclear reactors.

Discover how UQ enables scientists to unravel the complexities of weather forecasting, study climate change, and explore the frontiers of astrophysics. Delve into real-world case studies that demonstrate the practical applications of UQ in CFD, providing invaluable insights into its transformative potential.

These Lecture Notes on Uncertainty Quantification in Computational Fluid Dynamics provide a comprehensive foundation for mastering this essential discipline. With a deep understanding of UQ fundamentals, methodologies, and applications, engineers and scientists can unlock the full potential of CFD modeling, navigating the complexities of fluid flows with unprecedented accuracy and confidence. Embrace the transformative power of Uncertainty Quantification and elevate your CFD simulations to new heights.

Uncertainty Quantification in Computational Fluid Dynamics (Lecture Notes in Computational Science and Engineering Book 92)

5 out of 5