Friday, 28 March, 2014
Speaker: Prof. Alexander Kurganov (Tulane University)
Host: Y. Xing
Title: Central-Upwind Schemes for Shallow Water Models
Abstract: I will first give a brief review on simple and robust central-upwind schemes for hyperbolic conservation laws. I will then discuss their application to the Saint-Venant system of shallow water equations. This can be done in a straightforward manner, but then the resulting scheme may suffer from the lack of balance between the fluxes and (possibly singular) geometric source term, which may lead to a so-called numerical storm, and from appearance of negative values of the water height, which may destroy the entire computed solution. To circumvent these difficulties, we have developed a special technique, which guarantees that the designed second-order central-upwind scheme is both well-balanced and positivity preserving.
Finally, I will show a number of extensions of the central-upwind scheme to more complicated shallow water models including the Saint-Venant system with friction terms, two-layer shallow water equations and Savage-Hutter type model of submarine landslides and generated tsunami waves.