Polynomial Chaos Methods for Hyperbolic Partial Differential Equations - Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties
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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.
Detalles de producto
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.
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
"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)