In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

This article is a review of the work that we are carrying out to efficiently simulate shallow
water flows. In this paper, we focus on the efficient implementation of path-conservative Roe …

Numerical modelling of transoceanic tsunami propagation, together with the detailed
modelling of inundation of small-scale coastal regions, poses a number of algorithmic …

This paper is concerned with the numerical solution of the unified first order hyperbolic
formulation of continuum mechanics recently proposed by Peshkov and Romenski [110] …

We evaluate a new depth-averaged mathematical model that is designed to simulate all
stages of debris-flow motion, from initiation to deposition. A companion paper shows how …

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is
proposed that works for general conservative and non-conservative systems of hyperbolic …

In some previous works, the authors have introduced a strategy to develop well-balanced
high-order numerical methods for nonconservative hyperbolic systems in the framework of …

We propose a simple extension of the well-known Riemann solver of Osher and Solomon
(Math. Comput. 38: 339–374, 1982) to a certain class of hyperbolic systems in non …

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-
phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al …

In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of
the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear …