Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics

Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
Total Pages: 28
Release: 2018-06-19
Genre:
ISBN: 9781721516513

Numerical simulation has now become an integral part of engineering design process. Critical design decisions are routinely made based on the simulation results and conclusions. Verification and validation of the reliability of the numerical simulation is therefore vitally important in the engineering design processes. We propose to develop theories and methodologies that can automatically provide quantitative information about the reliability of the numerical simulation by estimating numerical approximation error, computational model induced errors and the uncertainties contained in the mathematical models so that the reliability of the numerical simulation can be verified and validated. We also propose to develop and implement methodologies and techniques that can control the error and uncertainty during the numerical simulation so that the reliability of the numerical simulation can be improved. Zhu, J. Z. and He, Guowei and Bushnell, Dennis M. (Technical Monitor) Langley Research Center NASA/CR-2002-211744, NAS 1.26:211744, ICASE-IR-41

Spectral Methods for Uncertainty Quantification

Spectral Methods for Uncertainty Quantification
Author: Olivier Le Maitre
Publisher: Springer Science & Business Media
Total Pages: 542
Release: 2010-03-11
Genre: Science
ISBN: 9048135206

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Uncertainty Quantification in Computational Fluid Dynamics

Uncertainty Quantification in Computational Fluid Dynamics
Author: Hester Bijl
Publisher: Springer Science & Business Media
Total Pages: 347
Release: 2013-09-20
Genre: Mathematics
ISBN: 3319008854

Fluid flows are characterized by uncertain inputs such as random initial data, material and flux coefficients, and boundary conditions. The current volume addresses the pertinent issue of efficiently computing the flow uncertainty, given this initial randomness. It collects seven original review articles that cover improved versions of the Monte Carlo method (the so-called multi-level Monte Carlo method (MLMC)), moment-based stochastic Galerkin methods and modified versions of the stochastic collocation methods that use adaptive stencil selection of the ENO-WENO type in both physical and stochastic space. The methods are also complemented by concrete applications such as flows around aerofoils and rockets, problems of aeroelasticity (fluid-structure interactions), and shallow water flows for propagating water waves. The wealth of numerical examples provide evidence on the suitability of each proposed method as well as comparisons of different approaches.

Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines

Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines
Author: Francesco Montomoli
Publisher: Springer
Total Pages: 204
Release: 2018-06-21
Genre: Technology & Engineering
ISBN: 3319929437

This book introduces design techniques developed to increase the safety of aircraft engines, and demonstrates how the application of stochastic methods can overcome problems in the accurate prediction of engine lift caused by manufacturing error. This in turn addresses the issue of achieving required safety margins when hampered by limits in current design and manufacturing methods. The authors show that avoiding the potential catastrophe generated by the failure of an aircraft engine relies on the prediction of the correct behaviour of microscopic imperfections. This book shows how to quantify the possibility of such failure, and that it is possible to design components that are inherently less risky and more reliable. This new, updated and significantly expanded edition gives an introduction to engine reliability and safety to contextualise this important issue, evaluates newly-proposed methods for uncertainty quantification as applied to jet engines. Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines will be of use to gas turbine manufacturers and designers as well as CFD practitioners, specialists and researchers. Graduate and final year undergraduate students in aerospace or mathematical engineering may also find it of interest.

Applied and Computational Fluid Mechanics

Applied and Computational Fluid Mechanics
Author: Scott Post
Publisher: Jones & Bartlett Publishers
Total Pages: 548
Release: 2010-01-30
Genre: Technology & Engineering
ISBN: 144965584X

Designed for the fluid mechanics course for mechanical, civil, and aerospace engineering students, or as a reference for professional engineers, this up to date text uses computer algorithms and applications to solve modern problems related to fluid flow, aerodynamics, and thermodynamics. Algorithms and codes for numerical solutions of fluid problems, which can be implemented in programming environments such as MATLAB, are used throughout the book. The author also uses non-language specific algorithms to force the students to think through the logic of the solution technique as they translate the algorithm into the software they are using. The text also includes an introduction to Computational Fluid Dynamics, a well-established method in the design of fluid machinery and heat transfer applications. A DVD accompanies every new printed copy of the book and contains the source code, MATLAB files, third-party simulations, color figures, and more.

Research Directions in Computational Mechanics

Research Directions in Computational Mechanics
Author: National Research Council
Publisher: National Academies Press
Total Pages: 145
Release: 1991-02-01
Genre: Technology & Engineering
ISBN: 0309046483

Computational mechanics is a scientific discipline that marries physics, computers, and mathematics to emulate natural physical phenomena. It is a technology that allows scientists to study and predict the performance of various productsâ€"important for research and development in the industrialized world. This book describes current trends and future research directions in computational mechanics in areas where gaps exist in current knowledge and where major advances are crucial to continued technological developments in the United States.

Experimentation, Validation, and Uncertainty Analysis for Engineers

Experimentation, Validation, and Uncertainty Analysis for Engineers
Author: Hugh W. Coleman
Publisher: John Wiley & Sons
Total Pages: 384
Release: 2018-05-08
Genre: Technology & Engineering
ISBN: 1119417511

Helps engineers and scientists assess and manage uncertainty at all stages of experimentation and validation of simulations Fully updated from its previous edition, Experimentation, Validation, and Uncertainty Analysis for Engineers, Fourth Edition includes expanded coverage and new examples of applying the Monte Carlo Method (MCM) in performing uncertainty analyses. Presenting the current, internationally accepted methodology from ISO, ANSI, and ASME standards for propagating uncertainties using both the MCM and the Taylor Series Method (TSM), it provides a logical approach to experimentation and validation through the application of uncertainty analysis in the planning, design, construction, debugging, execution, data analysis, and reporting phases of experimental and validation programs. It also illustrates how to use a spreadsheet approach to apply the MCM and the TSM, based on the authors’ experience in applying uncertainty analysis in complex, large-scale testing of real engineering systems. Experimentation, Validation, and Uncertainty Analysis for Engineers, Fourth Edition includes examples throughout, contains end of chapter problems, and is accompanied by the authors’ website www.uncertainty-analysis.com. Guides readers through all aspects of experimentation, validation, and uncertainty analysis Emphasizes the use of the Monte Carlo Method in performing uncertainty analysis Includes complete new examples throughout Features workable problems at the end of chapters Experimentation, Validation, and Uncertainty Analysis for Engineers, Fourth Edition is an ideal text and guide for researchers, engineers, and graduate and senior undergraduate students in engineering and science disciplines. Knowledge of the material in this Fourth Edition is a must for those involved in executing or managing experimental programs or validating models and simulations.