Computational Algorithms for Shallow Water Equations

Eleuterio F. Toro is currently Emeritus Professor of Mathematics at the University of Trento, Italy, and formerly Professor of Numerical Analysis (Professore Chiara Fama) at the same University. He holds an Honours B.Sc. in pure mathematics, an M.Sc. in functional analysis and differential equations, and a Ph.D. in computational mathematics. Since 1982, and prior to his appointment in Italy (2002), he held several academic positions in the UK, including a full professorship; he has also held many visiting appointments in various countries, such as Japan, Russia, China, and USA; he is Recipient of several honours and distinctions in various countries. His research has for many years focused on the construction of computational methods for solving time-dependent evolutionary partial differential equations, with emphasis on hyperbolic balance laws and applications to industrial, aerospace, environmental, and medical problems. He is Author/Editor of several books and Author of more than 300 publications.

• The 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.