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Computing Qualitatively Correct Approximations of Balance Laws
Laurent Gosse
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Description for Computing Qualitatively Correct Approximations of Balance Laws
Hardback. This book book explores the ways that elaborate flux functions can be constructed, mainly in a one-dimensional context for hyperbolic systems admitting shock-type solutions and also for kinetic equations in the discrete-ordinate approximation. Series: SEMA SIMAI Springer Series. Num Pages: 360 pages, biography. BIC Classification: PBKJ; PBKS; PBW; PHU; TBJ. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 23. Weight in Grams: 816.
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, ... Read more
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, ... Read more
Product Details
Format
Hardback
Publication date
2013
Publisher
Springer Verlag Italy
Number of pages
360
Condition
New
Series
SEMA SIMAI Springer Series
Number of Pages
341
Place of Publication
Milan, Italy
ISBN
9788847028913
SKU
V9788847028913
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
About Laurent Gosse
Laurent Gosse received the M.S. and Ph.D. degrees both in Mathematics from Universities of Lille 1 and Paris IX Dauphine in 1991 and 1997 respectively. Between 1997 and 1999 he was a TMR postdoc in IACM-FORTH (Heraklion, Crete) mostly working on well-balanced numerical schemes and a posteriori error estimates with Ch. Makridakis. From 1999 to 2001, he was postdoc in Universtity of L'Aquila ... Read more
Reviews for Computing Qualitatively Correct Approximations of Balance Laws
From the reviews: “The overall goal of the book is therefore to explain how to derive accurate numerical approximations of solutions to balance laws. … Each chapter includes comments and historical notes, as well as a list of references. … should be of interest to researchers willing to learn well-balanced techniques.” (Jean-François Coulombel, Mathematical Reviews, January, 2014) “This ... Read more