高精度WENO格式的发展与展望
Development and prospect of high-order WENO schemes
朱君 1舒其望 2邱建贤3
作者信息
- 1. 南京航空航天大学数学学院,南京 211106
- 2. Division of Applied Mathematics,Brown University,Providence,RI 02912,USA
- 3. 厦门大学数学科学学院,厦门 361005
- 折叠
摘要
加权本质无振荡(weighted essentially non-oscillatory,WENO)格式是用于求解双曲守恒律方程和对流占优问题的一类高精度数值方法.WENO格式设计的思想是在解的光滑区域中获得高阶数值精度,而在解的间断附近保持本质无振荡的性质.以这种思想设计的有限差分和有限体积高精度WENO格式在计算流体力学等领域中得到了广泛应用.本文首先回顾WENO格式设计的基本思想和性质,简要介绍近年来WENO格式研究方面的一些进展,并阐述US-WENO(unequal-sized WENO)格式、MR-WENO(multi-resolution WENO)格式和 HWENO(Hermite WENO)格式的构造策略.此外,本文还介绍高精度WENO格式在结构网格和非结构网格上的一些进展,展望这些高精度格式在多个领域中的应用以及未来的发展趋势.
Abstract
The weighted essentially non-oscillatory(WENO)schemes are high-precision numerical methods for solving hyperbolic conservation laws and convection-diffusion equations.The design idea of such WENO schemes is to obtain arbitrary high-order numerical accuracy in smooth regions while maintaining essentially non-oscillatory(ENO)properties near the discontinuities of the solution.The finite difference and finite volume WENO schemes designed with this idea have been widely used in computational fluid dynamics and other fields.In this paper,we first review the basic idea and nature of WENO schemes,briefly introduce some progress of WENO schemes in recent years,and elaborate on the US-WENO(unequal-sized WENO)schemes,MR-WENO(multi-resolution WENO)schemes,and HWENO(Hermite WENO)schemes,respectively.Finally,the research progress of high-order WENO schemes is introduced on structured and unstructured meshes.The application of these high-order WENO schemes in many fields and the development trend in the future are proposed.
关键词
计算流体力学/本质无振荡格式/加权本质无振荡格式/US-WENO格式/MR-WENO格式/HWENO格式Key words
computational fluid dynamics/ENO scheme/WENO scheme/US-WENO scheme/MR-WENO scheme/HWENO scheme引用本文复制引用
基金项目
国家自然科学基金(11872210)
国家自然科学基金(12071392)
出版年
2024
NETL
NSTL
万方数据