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020 _a9783031613951
_9978-3-031-61395-1
024 7 _a10.1007/978-3-031-61395-1
_2doi
050 4 _aQA297-299.4
072 7 _aPBKS
_2bicssc
072 7 _aMAT041000
_2bisacsh
072 7 _aPBKS
_2thema
100 1 _aToro, Eleuterio F.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_981675
245 1 0 _aComputational Algorithms for Shallow Water Equations
_h[electronic resource] /
_cby Eleuterio F. Toro.
250 _a2nd ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXV, 408 p. 161 illus., 22 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aThe Shallow Water Equations -- Notions on Hyperbolic Equations -- Linear Shallow Water Equations -- Properties of the Nonlinear Equations -- Elementary Waves in Shallow Water -- Exact Riemann Solver: Wet Bed -- Exact Riemann Solver: Dry Bed -- Tests with Exact Solution -- Notions on Numerical Methods -- First-Order Methods for Systems -- Approximate Riemann Solvers -- Second-Order Non-Linear Methods -- Sources and Multidimensions -- Ader High-Order Methods -- Dam-Break Modelling -- Mach Reflection in Tsunamis -- Concluding Remarks.
520 _aThis book is a thoroughly revised and enlarged version of “Shock-capturing methods for free-surface shallow flows", first published by Wiley and Sons, 2001. The book describes mathematically free-surface flows through partial differential equations and includes modern shock-capturing methods to solve them, with strong emphasis on finite volume upwind and centred methods. Such equations and methods are fundamental in simulating shallow water flows but also atmospheric flows, dispersion of dense gases and the dynamics of mixtures of materials. The book is accompanied by numerical software in the form of sample computer programs as supplementary material. In this new edition, additional sections have been introduced to existing chapters. Also, new chapters have been included; one contains a review of the mathematics of hyperbolic partial differential equations, another introduces the numerical analysis of partial differential equations and another one deals with advanced very-high order numerical methods in the finite volume and discontinuous Galerkin frameworks. Furthermore, comprehensive modifications and corrections have been made throughout various sections of the text, and numerous figures depicting numerical results have been enhanced. This book is primarily intended for environmental scientists, applied mathematicians and engineers in academia, research laboratories, industry and consultancy organisations. Senior undergraduate and postgraduate students involved with mathematical modelling and computational methods for environmental problems will benefit from studying this book. Lecturers could use most of the material for courses on numerical methods for wave propagation problems in hydraulics, oceanography, atmospherics and other geophysical fluid dynamics contexts.
650 0 _aNumerical analysis.
650 0 _aFluid mechanics.
650 0 _aEngineering geology.
650 0 _aGeotechnical engineering.
_966388
650 0 _aGeophysics.
_969226
650 1 4 _aNumerical Analysis.
650 2 4 _aEngineering Fluid Dynamics.
650 2 4 _aGeoengineering.
650 2 4 _aGeotechnical Engineering and Applied Earth Sciences.
_966389
650 2 4 _aGeophysics.
_969226
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031613944
776 0 8 _iPrinted edition:
_z9783031613968
776 0 8 _iPrinted edition:
_z9783031613975
856 4 0 _uhttps://doi.org/10.1007/978-3-031-61395-1
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c62117
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