A Numerical Model for Storm Surges that Involve the Inundation of Complex Landscapes

Abstract

A numerical model for the prediction of storm surges over complex landscapes is assembled using state-of-the-art techniques. The model is based on the full nonlinear depth- averaged long wave equations solved via an explicit finite volume scheme. The interfacial fluxes are computed from slope limited reconstructions of the state variables using Osher's approximate Riemann solver. The geometric source terms are treated in a simple manner that is well balanced and consistent with the numerical flux. The numerical solution technique has been chosen to enable the accurate simulation of flows over complex topography. Importantly, the scheme conserves both mass and momentum even when the flow involves wetting—drying fronts. This approach makes the model extremely robust in cases that involve bathymetries which include large spatial gradients and even discontinuities. Another important feature of the model is the use of a simple underlying Cartesian mesh with quad-tree-based static and dynamic refinement. This permits the simulation of highly unsteady flows over complex landscapes (including localized features such as canals) by locally increasing (or relaxing) grid resolution in a dynamic fashion. If it is deemed desirable, the numerical and physical boundaries can be aligned. This alignment is achieved by a cut-cell-type approach in combination with quad-tree-based mesh refinement. In this paper, we describe the model and then present a number of tests that have been carefully chosen to verify various aspects of the solution algorithm.