Central scheme for systems of shallow water equations with wet and dry states -

Abstract

In this thesis we present a new well-balanced, non-oscillatory, second-order accurate central scheme for the numerical solution of the two-dimensional shallow water equations (SWE) with wet and dry states. The numerical scheme is a central scheme that follows a classical Riemannfree finite volume method and that evolves the numerical solution on a single Cartesian grid. Most numerical schemes generate numerical instabilities, such as negative water heights, when considered with wet and dry regions. The developed well-balanced numerical scheme is capable of maintaing, when necessary, the steady state requirement of SWE systems, along with a proper and clean interaction between wet and dry states whenever water run-ups are present. The developed scheme is then validated and the numerical solution of recent two-dimensional SWE problems is reported.