For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …

There have been growing research interests in high-order discontinuous schemes over
recent years. With established theoretical basis and framework, more efforts have recently …

CFD (computational fluid dynamics) 在航空航天中的应用发展迅速, 成效斐然,
成为飞行器研制和空气动力学研究的重要手段. 但另一方面, CFD 在物理模型和计算方法等核心 …

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 …

A shock capturing strategy for higher order Discontinuous Galerkin approximations of scalar
conservation laws is presented. We show how the original explicit artificial viscosity methods …

Emerging as the mathematical expression of principles of conservation, conservation laws
have proven themselves to provide effective and accurate predictive models of our physical …

A high-order, conservative, yet efficient method named the spectral volume (SV) method is
developed for conservation laws on unstructured grids. The concept of a “spectral volume” is …

In this paper, a class of fifth-order weighted essentially non-oscillatory (WENO) schemes
based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one …

The Runge--Kutta discontinuous Galerkin (RKDG) method is a high order finite element
method for solving hyperbolic conservation laws. It uses ideas from high resolution finite …