This article reviews several unstructured grid-based high-order methods for the
compressible Euler and Navier–Stokes equations. We treat the spatial and temporal …

In recent years numerical methods have been widely used to effectively resolve complex
flow features of aerodynamics flows with meshes that are reasonable for today's computers …

Recently a new high-order formulation for 1D conservation laws was developed by Huynh
using the idea of “flux reconstruction”. The formulation was capable of unifying several …

A high order multidomain spectral difference (SD) method is developed for the three
dimensional Navier-Stokes equations on unstructured hexahedral grids. The method is easy …

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 …

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

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 …

Pour réduire la consommation en carburant et respecter des normes anti-pollution toujours
plus sévères, les motoristes font de plus en plus appel à la combustion prémélangée …

In the hyperbolic research community, there exists the strong belief that a continuous
Galerkin scheme is notoriously unstable and additional stabilization terms have to be added …

A high-order, central, essentially non-oscillatory (CENO), finite-volume scheme in
combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for …