A well-balanced finite volume non-linear shallow water equations model for extreme flood wave propagation and run-up

Abstract

Natural extreme flows such as tsunami waves, bore propagation or glacial lake outburst often take place over rough and complex topographies with arbitrary boundaries giving rise to complex unsteady free-surface dynamics where rapid changes in physical variables may arise. Nonlinear Shallow Water Equations (NSWE) can be used to model these flows. Numerical strategies for solving the NSWE should be able to deal with complicated geometries and the complex dynamics of breaking and run-up.In this work we present a robust numerical model that solves the nonlinear shallow water equations with friction in a non-orthogonal boundary-fitted curvilinear coordinate system based on the work of Marche et al. (2007) and Lackey & Sotiropoulos (2005).