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).


Room 623, Séminaire d'analyse numérique

Organisé par

Section de mathématiques


Scott MacLachlan, Memorial University, Canada

entrée libre


Catégorie: Séminaire

Mots clés: analyse numérique