Well-balanced Meshless Methods for the Shallow-Water Equations (Scott MacLachlan, Memorial University, Canada)

02.04.2019 14:00

Despite their inherent limitations, the shallow-water equations are a common model for many geophysical flow situations, including coastal and river flooding. Discretization and efficient numerical simulation of the shallow-water equations pose a significant computational challenge, particularly in situations where the flow is driven by real-world data, such as for real-time simulation of flooding events over large regions. In this talk, I will present recent work on meshless discretizations for the shallow-water equations and discuss their application to tsunami models. Meshless methods are attractive for modelling both coastal and river flooding as they naturally address the unstructured nature of real-world topographic data, but standard meshless finite-difference approaches fail even for very simple test cases. This motivates the development of a mimetic scheme for the spatial derivative and averaging operators to realize well-balanced meshless discretizations. We couple this approach with a radial basis function based extrapolation method for the inundation model, giving an accurate and efficient simulation scheme for the shallow-water equations. This is joint work with Jörn Behrens (Universität Hamburg), Alex Bihlo and Rüdiger Brecht (Memorial University of Newfoundland).

Lieu

Room 623, Séminaire d'analyse numérique

entrée libre