Abstract In this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) limiters, for the RungeKutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [32]. Both limiters use information ...

Weighted essentially non-oscillatory (WENO) methods have been developed to simultaneously provide robust shockcapturing in compressible fluid flow and avoid excessive damping of fine-scale flow features such as turbulence. Under certain conditions in compressible turbulence, however, numerical dissipation remains unacceptably high even after optimization of the linear component that dominates i...

We describe a newly developed cosmological hydrodynamics code based on the weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. High order finite difference WENO schemes are designed for problems with piecewise smooth solutions containing discontinuities, and have been successful in applications for problems involving both shocks and complicated smooth solution ...

Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of first-order, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill–Whitham–Richards traffic model and a model for the sedimentation of polydisperse suspensions. T...

In this paper, we develop an efficient moving mesh weighted essentially nonoscillatory (WENO) method for one-dimensional hyperbolic conservation laws. The method is based on the quasi-Lagrange approach of the moving mesh strategy in which the mesh is considered to move continuously in time. Several issues arising from the implementation of the scheme, including mesh smoothness, mesh movement re...

The weighted essentially non-oscillatory (WENO) methods are a popular high-order spatial discretization for hyperbolic partial differential equations. Typical treatments of WENO methods assume a uniform mesh. In this paper we give explicit formulas for the finite-volume, fifth-orderWENO (WENO5) method on non-uniform meshes in a way that is amenable to efficient implementation. We then compare t...

A double-GPU code is developed to accelerate WENO schemes. The test problem is a compressible viscous flow. The convective terms are discretized using third- to ninth-order WENO schemes and the viscous terms are discretized by the standard fourth-order central scheme. The code written in CUDA programming language is developed by modifying a single-GPU code. The OpenMP library is used for parall...

Abstract In this paper, we propose a new conservative semi-Lagrangian (SL) finite difference (FD) WENO scheme for linear advection equations, which can serve as a base scheme for the Vlasov equation by Strang splitting [4]. The reconstruction procedure in the proposed SL FD scheme is the same as the one used in the SL finite volume (FV) WENO scheme [3]. However, instead of inputting cell averag...

In this article, we analyze the fifth-order weighted essentially non-oscillatory(WENO-5) scheme and show that, at a transition point from smooth region to a discontinuity point or vice versa, the accuracy order of WENO-5 is decreased. A new method is proposed to overcome this drawback by introducing 4th-order fluxes combined with high order smoothness indicator. Numerical examples show that the...

ABSTRACT High order nite di erence WENO methods have the advantage of simpler coding and smaller computational cost for multi-dimensional problems, compared with nite volume WENO methods of the same order of accuracy. However a main restriction is that conservative nite di erence methods of third and higher order of accuracy can only be used on uniform rectangular or smooth curvilinear meshes. ...