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E-book
Author Pettersson, Mass Per, author

Title Polynomial chaos methods for hyperbolic partial differential equations : numerical techniques for fluid dynamics problems in the presence of uncertainties / Mass Per Pettersson, Gianluca Iaccarino, Jan Nordström
Published Cham : Springer, 2015
©2015

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Description 1 online resource (xi, 214 pages) : illustrations (some color)
Series Mathematical engineering, 2192-4732
Mathematical engineering.
Contents Random Field Representation -- Polynomial Chaos Methods -- Numerical Solution of Hyperbolic Problems -- Linear Transport -- Nonlinear Transport -- Boundary Conditions and Data -- Euler Equations -- A Hybrid Scheme for Two-Phase Flow -- Appendices
Summary 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
Analysis engineering
numerieke methoden
numerical methods
vloeistoffen (fluids)
fluids
aerodynamics
Engineering (General)
Techniek (algemeen)
Bibliography Includes bibliographical references and index
Notes English
Online resource; title from PDF title page (SpringerLink, viewed March 20, 2015)
Subject Differential equations, Hyperbolic -- Numerical solutions.
Galerkin methods.
Numerical analysis.
Fluid mechanics.
Mechanics of fluids.
MATHEMATICS -- Numerical Analysis.
Differential equations, Hyperbolic -- Numerical solutions
Galerkin methods
Form Electronic book
Author Iaccarino, Gianluca, author.
Nordström, Jan, 1953- author.
ISBN 9783319107141
3319107143
3319107135
9783319107134