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 are interested in the approximation of a steady hyperbolic problem. In some cases, the
solution can satisfy an additional conservation relation, at least when it is smooth. This is the …

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 …

The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-
volume numerical methods for 1D systems of balance laws. The strategy introduced by two …

In this paper we consider the solution of the enhanced Boussinesq equations of Madsen
and Sørensen (1992)[55] by means of residual based discretizations. In particular, we …

We provide a review of high order methods for CFD. Besides recalling some classical
methods, we show a framework allowing on one hand to see and work with these methods …

We propose and analyze an algorithm for the robust construction of curved meshes in two
and three dimensions. The meshes are made of curved simplexes. The algorithm starts from …

Abstract Newly developed reconstructed Discontinuous Galerkin (rDG) methods are
presented for solving linear advection–diffusion equations on hybrid unstructured grids …

A robust and high order accurate Residual Distribution (RD) scheme for the discretization of
the steady Navier–Stokes equations is presented. The proposed method is very flexible: it is …

In this paper, we present first, second, and third order implicit finite-volume solvers for
advection–diffusion problems based on the first-order hyperbolic system method. In …