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Spectral Methods for Uncertainty Quantification

With Applications to Computational Fluid Dynamics

  • Book
  • © 2010

Overview

Authors:
  1. O. P. Le Maître

    1. LIMSI-CNRS, Université Paris-Sud XI, Orsay CX, France

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  2. Omar M. Knio

    1. Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, USA

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    You can also search for this author in PubMed   Google Scholar

  • Application-oriented introduction into spectral methods for uncertainty propagation and quantification in model-based computations.
  • With carefully selected examples on incompressible vortex-dominated flows and compressible flows at low Mach numbers.
  • Only alludes to those theoretical aspects needed to set the stage for subsequent applications.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Introduction: Uncertainty Quantification and Propagation

    • O. P. Le Maître, O. M. Knio
    Pages 1-13

  3. Basic Formulations

    1. Front Matter

      Pages 15-15
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    2. Spectral Expansions

      • O. P. Le Maître, O. M. Knio
      Pages 17-44

    3. Non-intrusive Methods

      • O. P. Le Maître, O. M. Knio
      Pages 45-72

    4. Galerkin Methods

      • O. P. Le Maître, O. M. Knio
      Pages 73-105

    5. Detailed Elementary Applications

      • O. P. Le Maître, O. M. Knio
      Pages 107-156

    6. Application to Navier-Stokes Equations

      • O. P. Le Maître, O. M. Knio
      Pages 157-283

  4. Advanced Topics

    1. Front Matter

      Pages 285-285
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  5. Advanced topics

    1. Solvers for Stochastic Galerkin Problems

      • O. P. Le Maître, O. M. Knio
      Pages 287-341

    2. Wavelet and Multiresolution Analysis Schemes

      • O. P. Le Maître, O. M. Knio
      Pages 343-389

    3. Adaptive Methods

      • O. P. Le Maître, O. M. Knio
      Pages 391-476

    4. Epilogue

      • O. P. Le Maître, O. M. Knio
      Pages 477-481

  6. Back Matter

    Pages 483-536
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Keywords

About this book

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.

Authors and Affiliations

  • LIMSI-CNRS, Université Paris-Sud XI, Orsay CX, France

    O. P. Le Maître

  • Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, USA

    Omar M. Knio

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