Polynomial Chaos Methods for Hyperbolic Partial Differential Equations: Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

• A timely and innovative text which supports computational scientists in keeping abreast of new developments • Useful for fluid dynamics researchers to incorporate uncertainty in their models • Provides the reader with an understanding of numerical methods for general stochastic hyperbolic problems This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but not necessary. Content Level » Research Keywords » Computational Fluid Dynamics - Hyperbolic Partial Differential Equations - Numerical Analysis - Stochastic Galerkin Methods - Uncertainty Quantification Related subjects » Classical Continuum Physics - Computational Science & Engineering

Author(s): Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström
Series: Mathematical Engineering
Publisher: Springer
Year: 2015

Language: English
Pages: C, XI, 214
Tags: Механика;Механика жидкостей и газов;Гидрогазодинамика;

Front Matter
Pages i-xi


Introductory Concepts and Background
Front Matter
Pages 1-1

Book Chapter
Pages 3-9
Introduction
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström

Book Chapter
Pages 11-21
Random Field Representation
Mass Per Pettersson, Jan Nordström, Gianluca Iaccarino

Book Chapter
Pages 23-29
Polynomial Chaos Methods
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström

Book Chapter
Pages 31-44
Numerical Solution of Hyperbolic Problems
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström


Scalar Transport Problems
Front Matter
Pages 45-45

Book Chapter
Pages 47-80
Linear Transport Under Uncertainty
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström

Book Chapter
Pages 81-109
Nonlinear Transport Under Uncertainty
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström

Book Chapter
Pages 111-121
Boundary Conditions and Data
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström


Euler Equations and Two-Phase Flow
Front Matter
Pages 123-123

Book Chapter
Pages 125-148
gPC for the Euler Equations
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström

Book Chapter
Pages 149-172
A Hybrid Scheme for Two-Phase Flow
Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström

Back Matter
Pages 173-214