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 …

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

This paper is concerned with the numerical solution of the unified first order hyperbolic
formulation of continuum mechanics recently proposed by Peshkov and Romenski [110] …

Computational fluid dynamics (CFD) studies the flow motion in a discretized space. Its basic
scale resolved is the mesh size and time step. The CFD algorithm can be constructed …

In this paper we develop a novel two-stage fourth order time-accurate discretization for time-
dependent flow problems, particularly for hyperbolic conservation laws. Different from the …

We present the first high order one-step ADER-WENO finite volume scheme with adaptive
mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is …

In this paper we first review the development of high order ADER finite volume and ADER
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …

For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver
and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function …

With increasing engineering demands, there need high order accurate schemes embedded
with precise physical information in order to capture delicate small scale structures and …

Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs,
coastal areas, and other situations in which the water depth is much smaller than the …