We review numerical methods for direct numerical simulation (DNS) and large-eddy
simulation (LES) of turbulent compressible flow in the presence of shock waves. Ideal …

This review paper concerns the application of numerical methods of the Godunov type to the
computation of approximate solutions to free-surface gravity flows modelled under a shallow …

In 1917, the British scientist LF Richardson made the first reported attempt to predict the
weather by solving partial differential equations numerically, by hand! It is generally …

Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

The purpose of this work is to propose a novel a posteriori finite volume subcell limiter
technique for the Discontinuous Galerkin finite element method for nonlinear systems of …

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new
but have gained rapid popularity in numerical solutions of hyperbolic partial differential …

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for
solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions …

In this article, a conservative least-squares polynomial reconstruction operator is applied to
the discontinuous Galerkin method. In a first instance, piecewise polynomials of degree N …

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 …

We design arbitrarily high-order accurate entropy stable schemes for systems of
conservation laws. The schemes, termed TeCNO schemes, are based on two main …