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 …

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

Finite volume (FV) numerical solvers of the two-dimensional shallow water equations are
core to industry-standard flood models. The second-order Discontinuous Galerkin (DG2) …

In Vuik and Ryan [J. Comput. Phys., 270 (2014), pp. 138--160] we studied the use of
troubled-cell indicators for discontinuity detection in nonlinear hyperbolic partial differential …

In Gerhard et al.(2015a) a new class of adaptive Discontinuous Galerkin schemes has been
introduced for shallow water equations, including the particular necessary properties, such …

We present a comprehensive assessment of nodal and hybrid modal/nodal discontinuous
Galerkin (DG) finite element solutions on a range of unstructured meshes to nonlinear …

In the modelling of hydrodynamics, the Discontinuous Galerkin (DG) approach constitutes a
more complex and modern alternative to the well-established finite volume method. The …

The high-order numerical solution of the non-linear shallow water equations is susceptible
to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by …

Numerical modelling of wide ranges of different physical scales, which are involved in
Shallow Water (SW) problems, has been a key challenge in computational hydraulics …

We provide an adaptive strategy for solving shallow water equations with dynamic grid
adaptation including a sparse representation of the bottom topography. A challenge in …