摘要
In this paper,we use trigonometric polynomial reconstruction,instead of algebraic polynomial reconstruction,as building blocks for the weighted essentially non-oscillatory(WENO)finite difference schemes to solve hyperbolic conservation laws and highly oscillatory problems.The goal is to obtain robust and high order accurate solutions in smooth regions,and sharp and non-oscillatory shock transitions.Numerical results are provided to illustrate the behavior of the proposed schemes.
基金
supported by NSFC grants 10671091,10811120283
the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simulations
Additional support was provided by USA NSF DMS-0820348 while J.Qiu was in residence at Department of Mathematical Sciences,Rensselaer Polytechnic Institute.
