This review paper concerns the application of numerical methods of the Godunov type to the
computation of approximate solutions to free-surface gravity flows modelled under a shallow …

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 …

Shallow water equations with a non-flat bottom topography have been widely used to model
flows in rivers and coastal areas. An important difficulty arising in these simulations is the …

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 present a global, closed‐loop, multiscale mathematical model for the human circulation
including the arterial system, the venous system, the heart, the pulmonary circulation and the …

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 …

A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial
equilibrium solutions, where the effects of convective fluxes and source terms cancel each …

In this work, we design an arbitrary high order accurate nodal discontinuous Galerkin
spectral element type method for the one dimensional shallow water equations. The novel …