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Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

Name: Polynomial Chaos Methods for Hyperbolic Partial Differential Equations
Brand: Springer International Publishing AG
SKU: 9783319107134
Price: 129.81 EUR
Availability: InStock

Numerical Techniques for Fluid Dynamics Problems in the Presence of Uncertainties

Autor: Jan Nordström, Gianluca Iaccarino, Mass Per Pettersson

Jazyk:

Väzba: Pevná

Vydavateľ: Springer International Publishing AG

Dostupnosť: Skladom u dodávateľa

Odosielame za 10-13 dní

129.81 €

This monograph presents computational techniques and numerical analysis to study conservation laws u...

Informácie o knihe

Autor

Jan Nordström, Gianluca Iaccarino, Mass Per Pettersson

Jazyk

Angličtina

Väzba

Kniha - Pevná

Vydalo

2015

Stránok

214

EAN

9783319107134

ISBN

3319107135

Enbook ID

05166353

Vydavateľ

Springer International Publishing AG

Hmotnosť

5089

Rozmery

155 x 235 x 18

Kompletný popis

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.§