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 present a novel quasi-conservative arbitrary high order accurate ADER (Arbitrary-
Derivative) discontinuous Galerkin method allowing to efficiently use a non-conservative …

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 …

We extend recently proposed flux globalization based well-balanced path-conservative
central-upwind schemes to several shallow water models including the Saint-Vevant system …

In this work a non-conservative balance law formulation is considered that encompasses the
rotating, compressible Euler equations for dry atmospheric flows. We develop a semi …

A fluid-dynamic approach to charm-quark diffusion in the quark-gluon plasma (QGP) is
developed for the first time. Results for integrated yields and momentum distributions of …

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 …

This paper deals with the development of efficient incomplete multidimensional Riemann
solvers for hyperbolic systems. Departing from a four-waves model for the speeds of …

We develop fifth-order A-WENO finite-difference schemes based on the path-conservative
central-upwind method for nonconservative one-and two-dimensional hyperbolic systems of …

We herein present a novel methodology to construct very high order well-balanced schemes
for the computation of the Euler equations with gravitational source term, with application to …