Logo - springer
Slogan - springer

Mathematics - Computational Science & Engineering | Computing Qualitatively Correct Approximations of Balance Laws - Exponential-Fit, Well-Balanced

Computing Qualitatively Correct Approximations of Balance Laws

Exponential-Fit, Well-Balanced and Asymptotic-Preserving

Series: SEMA SIMAI Springer Series, Vol. 2

Gosse, Laurent

2013, XIX, 340 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$99.00

(net) price for USA

ISBN 978-88-470-2892-0

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$129.00

(net) price for USA

ISBN 978-88-470-2891-3

free shipping for individuals worldwide

online orders shipping within 2-3 days.


add to marked items

  • Surveys both analytical and numerical aspects of hyperbolic balance laws (including the recent theory of viscosity solutions for systems)
  • Numerous derivations of both well-balanced and asymptotic-preserving schemes emphasizing relations between each other Includes original material about K-multibranch solutions for linear geometric optics or order-preserving strings
  • Several chapters about numerical approximation of chemotaxis or semiconductor kinetic models which display constant macroscopic fluxes at stationary state ("qualitatively correct" approximations)
  • Presents well-balanced techniques for linearized Boltzmann and Fokker-Planck kinetic equations
Substantial effort has been drawn for years onto the development of (possibly high-order) numerical techniques for the scalar homogeneous conservation law, an equation which is strongly dissipative in L1 thanks to shock wave formation. Such a dissipation property is generally lost when considering hyperbolic systems of conservation laws, or simply inhomogeneous scalar balance laws involving accretive or space-dependent source terms, because of complex wave interactions. An overall weaker dissipation can reveal intrinsic numerical weaknesses through specific nonlinear mechanisms: Hugoniot curves being deformed by local averaging steps in Godunov-type schemes, low-order errors propagating along expanding characteristics after having hit a discontinuity, exponential amplification of truncation errors in the presence of accretive source terms... This book aims at presenting rigorous derivations of different, sometimes called well-balanced, numerical schemes which succeed in reconciling high accuracy with a stronger robustness even in the aforementioned accretive contexts. It is divided into two parts: one dealing with hyperbolic systems of balance laws, such as arising from quasi-one dimensional nozzle flow computations, multiphase WKB approximation of linear Schrödinger equations, or gravitational Navier-Stokes systems. Stability results for viscosity solutions of onedimensional balance laws are sketched. The other being entirely devoted to the treatment of weakly nonlinear kinetic equations in the discrete ordinate approximation, such as the ones of radiative transfer, chemotaxis dynamics, semiconductor conduction, spray dynamics of linearized Boltzmann models. “Caseology” is one of the main techniques used in these derivations. Lagrangian techniques for filtration equations are evoked too. Two-dimensional methods are studied in the context of non-degenerate semiconductor models.

Content Level » Research

Keywords » Asymptotic-Preserving and Well-Balanced schemes - Diffusive approximations of kinetic equations - Hyperbolic systems of balance laws - Kinetic equations and moment approximations - Viscosity solutions containing shock-waves

Related subjects » Applications - Computational Intelligence and Complexity - Computational Science & Engineering - Dynamical Systems & Differential Equations - Theoretical, Mathematical & Computational Physics

Table of contents / Preface 

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Computational Mathematics and Numerical Analysis.

Additional information