We consider the issue of wave breaking closure for Boussinesq type models, and attempt at
providing some more understanding of the sensitivity of some closure approaches to the …

In this paper, we investigate an original way to deal with the problems generated by the
limitation process of high-order finite volume methods based on polynomial reconstructions …

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 extends the MOOD method proposed by the authors in [A high-order finite
volume method for hyperbolic systems: Multi-Dimensional Optimal Order Detection (MOOD) …

In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …

We consider in this work the discontinuous Galerkin discretization of the nonlinear shallow
water equations on unstructured triangulations. In the recent years, several improvements …

Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs,
coastal areas, and other situations in which the water depth is much smaller than the …

The aim of this paper is to present a novel monotone upstream scheme for conservation law
(MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to …

In this chapter we describe a general methodology for developing high-order well-balanced
schemes for hyperbolic system with nonconservative products and/or source terms. We …

We introduce a new class of two-dimensional fully nonlinear and weakly dispersive Green–
Naghdi equations over varying topography. These new Green–Naghdi systems share the …