INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9788847028920
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52300
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Computing Qualitatively Correct Approximations of Balance Law
General Material Designation
[Book]
Other Title Information
:Exponential-Fit, Well-Balanced and Asymptotic-Preserving
First Statement of Responsibility
/ by Laurent Gosse
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Milano
Name of Publisher, Distributor, etc.
: Springer Milan :Imprint: Springer,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XIX, 340 p., online resource.
SERIES
Series Title
(SIMAI Springer Series,2280-840X
Volume Designation
; 2)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
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 Schr?╢dinger 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.
Text of Note
Introduction and chronological perspective -- Lifting a non-resonant scalar balance law -- Lyapunov functional for linear error estimates -- Early well-balanced derivations for various systems -- Viscosity solutions and large-time behavior for non-resonant balance laws -- Kinetic scheme with reflections and linear geometric optics -- Material variables, strings and infinite domains -- The special case of 2-velocity kinetic models -- Elementary solutions and analytical discrete-ordinates for radiative transfer -- Aggregation phenomena with kinetic models of chemotaxis dynamics -- Time-stabilization on flat currents with non-degenerate Boltzmann-Poisson models -- Klein-Kramers equation and Burgers/Fokker-Planck model of spray -- A model for scattering of forward-peaked beams -- Linearized BGK model of heat transfer -- Balances in two dimensions: kinetic semiconductor equations again -- Non-conservative products and locally Lipschitzian paths -- A tiny step toward hypocoercivity estimates for well-balanced schemes on 2x2 models -- Preliminary analysis of the errors for Vlasov-BGK.?╗╣
SERIES
Title
SIMAI Springer Series,2280-840X
Volume Number
2
TOPICAL NAME USED AS SUBJECT
Mathematics
Differential equations, partial
Computer science, Mathematics
Engineering mathematics
Electronic books
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Gosse, Laurent.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9788847028913.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9788847028913.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
