Numerical models solving the full 2‐D shallow water equations (SWEs) have been
increasingly used to simulate overland flows and better understand the transient flow …

Extensions to the Roe and HLL method have been previously formulated in order to solve
the Shallow Water equations in the presence of source terms. These were named the …

A new exact Riemann solver for the shallow water equations with a discontinuous bottom is
proposed. The algorithm is based on the approach to overcome the non-uniqueness of the …

We extend recently proposed flux globalization based well-balanced path-conservative
central-upwind schemes to several shallow water models including the Saint-Vevant system …

The Riemann problem for the shallow water equations with discontinuous topography is
considered. In a general case the exact solution of this problem is not unique, which …

This work is devoted to the derivation of a fully well-balanced numerical scheme for the well-
known shallow-water model. During the last two decades, several well-balanced strategies …

In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation
method is implemented to solve one-dimensional shallow water wave equations. In general …

This paper compares various topography discretization approaches for Godunov-type
shallow water numerical models. Many different approaches have emerged popular with …

This paper presents a finite volume scheme on structured grids to simulate shallow flows
over complex terrain. The situation of shallow downhill flow over a step is particularly …

Powerful numerical methods have to consider the presence of source terms of different
nature, that intensely compete among them and may lead to strong spatiotemporal …