Spectral Methods for Uncertainty Quantification

With Applications to Computational Fluid Dynamics

  • O. P. Le Maître
  • Omar M. Knio

Part of the Scientific Computation book series (SCIENTCOMP)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. O. P. Le Maître, O. M. Knio
    Pages 1-13
  3. Basic Formulations

    1. Front Matter
      Pages 15-15
    2. O. P. Le Maître, O. M. Knio
      Pages 17-44
    3. O. P. Le Maître, O. M. Knio
      Pages 45-72
    4. O. P. Le Maître, O. M. Knio
      Pages 73-105
    5. O. P. Le Maître, O. M. Knio
      Pages 107-156
    6. O. P. Le Maître, O. M. Knio
      Pages 157-283
  4. Advanced Topics

    1. Front Matter
      Pages 285-285
    2. O. P. Le Maître, O. M. Knio
      Pages 287-341
    3. O. P. Le Maître, O. M. Knio
      Pages 343-389
    4. O. P. Le Maître, O. M. Knio
      Pages 391-476
    5. O. P. Le Maître, O. M. Knio
      Pages 477-481
  5. Back Matter
    Pages 483-536

About this book


This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundations associated with probability and measure spaces. A brief discussion is provided of only those theoretical aspects needed to set the stage for subsequent applications. These are demonstrated through detailed treatments of elementary problems, as well as in more elaborate examples involving vortex-dominated flows and compressible flows at low Mach numbers. Some recent developments are also outlined in the book, including iterative techniques (such as stochastic multigrids and Newton schemes), intrusive and non-intrusive formalisms, spectral representations using mixed and discontinuous bases, multi-resolution approximations, and adaptive techniques. Readers are assumed to be familiar with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral approximation is helpful but not essential.


CFD book Navier-Stokes equation algorithms fluid dynamics application spectral methods computational fluid dynamics fluid dynamics linear optimization models flui models for simulation of fluid flows simulation of fluids spectral methods uncertainty propagation uncertainty quantification

Authors and affiliations

  • O. P. Le Maître
    • 1
  • Omar M. Knio
    • 2
  1. 1.LIMSI-CNRSUniversité Paris-Sud XIOrsay CXFrance
  2. 2.Department of Mechanical EngineeringThe Johns Hopkins UniversityBaltimoreUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2010
  • Publisher Name Springer, Dordrecht
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-90-481-3519-6
  • Online ISBN 978-90-481-3520-2
  • Series Print ISSN 1434-8322
  • Buy this book on publisher's site