This paper presents the decoupled hydrological discretization (DHD) scheme for solving the
shallow water equations in hydrological applications involving surface runoff in rural and …

In this paper, we present a new two-layer model of Savage–Hutter type to study submarine
avalanches. A layer composed of fluidized granular material is assumed to flow within an …

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 …

We propose a stabilized Residual Distribution (RD) scheme for the simulation of shallow
water flows. The final discretization is obtained combining the stabilized RD approach …

An unstructured high-resolution, node-centered finite volume algorithm for triangular grids is
developed in order to simulate unsteady, two-dimensional, shallow water flows over …

This review paper describes a class of scheme named “residual distribution schemes” or
“fluctuation splitting schemes”. They are a generalization of Roe's numerical flux in …

In this paper, we survey our recent work on designing high order positivitypreserving well-
balanced finite difference and finite volume WENO (weighted essentially non-oscillatory) …

This chapter is devoted to the description of recently developed efficient tools for the
numerical resolution of shallow water models, and in particular for the case of Coriolis force …

The finite volume discretisation of the shallow water equations has been the subject of many
previous studies, most of which deal with a well-balanced conservative discretisation of the …

In this paper, we construct spatially consistent explicit second order discretizations for time
dependent hyperbolic problems, starting from a given residual distribution (RD) discrete …