High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

被引:700
作者
Shu, Chi-Wang [1 ]
机构
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
关键词
weighted essentially nonoscillatory (WENO) scheme; hyperbolic partial differential equations; convection dominated problems; computational fluid dynamics; computational astronomy and astrophysics; semiconductor device simulation; traffic flow models; computational biology; DIFFERENCE WENO SCHEMES; DISCONTINUOUS GALERKIN METHODS; HAMILTON-JACOBI EQUATIONS; FINITE-VOLUME SCHEMES; EXACT CONSERVATION PROPERTY; DIRECT NUMERICAL-SIMULATION; HIGH-RESOLUTION SCHEMES; ALPHA TRANSMITTED FLUX; STEADY-STATE PROBLEMS; ENO SCHEMES;
D O I
10.1137/070679065
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
High order accurate Weighted essentially nonoscillatory (WENO) schemes are relatively new but have gained rapid popularity in numerical solutions of hyperbolic partial differential equations (PDEs) and other convection dominated problems. The main advantage of such schemes is their capability to achieve arbitrarily high order formal accuracy in smooth regions while maintaining stable, nonoscillatory, and sharp discontinuity transitions. The schemes are thus especially suitable for problems containing both strong discontinuities and complex smooth solution features. WENO schemes are robust and do not require the user to tune parameters. At the heart of the WENO schemes is actually an approximation procedure not directly related to PDEs, hence the WENO procedure can also be used in many non-PDE applications. In this paper we review the history and basic formulation of WENO schemes, outline the main ideas in using WENO schemes to solve various hyperbolic PDEs and other convection dominated problems, and present a collection of applications in areas including computational fluid dynamics, computational astronomy and astrophysics, semiconductor device simulation, traffic flow models, computational biology, and some non-PDE applications. Finally, we mention a few topics concerning WENO schemes that are currently under investigation.
引用
收藏
页码:82 / 126
页数:45
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