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

por Mass Per Pettersson
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97,17 €
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Mass Per Pettersson Polynomial Chaos Methods for Hyperbolic Partial Differential Equations - Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties
Mass Per Pettersson - Polynomial Chaos Methods for Hyperbolic Partial Differential Equations - Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties

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Descripción

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 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 notnecessary.

Colaboradores

Autor:
Mass Per Pettersson
Gianluca Iaccarino
Jan Nordström

Detalles de producto

Ilustraciones:
XI, 214 p. 60 illus., 54 illus. in color.
Indice:

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.

Observaciones:
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


Includes supplementary material: sn.pub/extras

Tipo de medio:
Tapa blanda
Editorial:
Springer International Publishing
Revisado:

"The authors explain in the preface that the book was written for readers with knowledge of uncertainty quantification, probability theory, statistics and numerical analysis, and this knowledge is definitely required to make the best use of the book. For such readers, the book is readable and interesting, in particular because of the extensive range of numerical examples presented in later chapters." (Philipp Dörsek, Mathematical Reviews, May, 2016)

"This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. ... Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest." (Titus Petrila, zbMATH, Vol. 1325.76004, 2016)

Idioma:
Inglés
Edición:
Softcover reprint of the original 1st ed. 2015
Número de páginas:
214

Datos base

Tipo de producto:
Libro de bolsillo
Fecha de aparición:
13 de octubre de 2016
Dimensiones del paquete:
0.235 x 0.155 x 0.014 m; 0.328 kg
GTIN:
09783319356129
DUIN:
8EL067LGVD1
97,17 €
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