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1	Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows Ricchiuto, Mario 12 December 2011 (has links) (PDF) In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach. [SDE] Environmental Sciences Numerical analysis hyperbolic problems unstructured grids finite elements residual based schemes high order schemes time dependent problems free surface flow shallow water equations positivity preservation source terms C-property super consistency long wave run up simulations tsunami simulations