LEADER 04916nam 22008055 450 001 9910878981503321 005 20260112134521.0 010 $a9783031613951$b(electronic bk.) 010 $z9783031613944 024 7 $a10.1007/978-3-031-61395-1 035 $a(MiAaPQ)EBC31579292 035 $a(Au-PeEL)EBL31579292 035 $a(CKB)33623754000041 035 $a(MiAaPQ)EBC31580408 035 $a(Au-PeEL)EBL31580408 035 $a(DE-He213)978-3-031-61395-1 035 $a(EXLCZ)9933623754000041 100 $a20240801d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComputational Algorithms for Shallow Water Equations /$fby Eleuterio F. Toro 205 $a2nd ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (413 pages) 311 08$aPrint version: Toro, Eleuterio F. Computational Algorithms for Shallow Water Equations Cham : Springer,c2024 9783031613944 320 $aIncludes bibliographical references and index. 327 $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. 330 $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. 606 $aNumerical analysis 606 $aFluid mechanics 606 $aEngineering geology 606 $aGeotechnical engineering 606 $aGeophysics 606 $aNumerical Analysis 606 $aEngineering Fluid Dynamics 606 $aGeoengineering 606 $aGeotechnical Engineering and Applied Earth Sciences 606 $aGeophysics 606 $aModels matemātics$2thub 606 $aOnes de xoc$2thub 606 $aProblemes de Riemann-Hilbert$2thub 606 $aOnades$2thub 606 $aModels matemātics$2thub 608 $aLlibres electrōnics$2thub 615 0$aNumerical analysis. 615 0$aFluid mechanics. 615 0$aEngineering geology. 615 0$aGeotechnical engineering. 615 0$aGeophysics. 615 14$aNumerical Analysis. 615 24$aEngineering Fluid Dynamics. 615 24$aGeoengineering. 615 24$aGeotechnical Engineering and Applied Earth Sciences. 615 24$aGeophysics. 615 7$aModels matemātics 615 7$aOnes de xoc 615 7$aProblemes de Riemann-Hilbert 615 7$aOnades 615 7$aModels matemātics 676 $a531.1133 700 $aToro$b E. F.$01770156 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910878981503321 996 $aComputational Algorithms for Shallow Water Equations$94247476 997 $aUNINA