五阶WENO有限差分法在线性双曲守恒律方程中的应用  

Application of fifth-order WENO finite difference method in linear hyperbolic partial differential equation

作　　者：汤淑芳[1] 林贤坤[1] 覃柏英[1] 秦文东[1] 

机构地区：[1]广西科技大学汽车与交通学院,广西柳州545006

出　　处：《广西科技大学学报》2015年第1期90-95,共6页Journal of Guangxi University of Science and Technology

基　　金：国家自然科学基金项目(51209042;11272057)资助

摘　　要：利用五阶WENO格式离散空间导数,三阶Runge-kutta法离散时间导数,探讨了五阶WENO有限差分法在线性双曲守恒律方程中的应用.经过经典数值算例的验证,结果表明五阶WENO有限差分法可实现线性双曲守恒律方程高精度、高分辨率和本质无振荡的求解,也可实现流体力学中运动界面高精度、高分辨率的追踪.Coupling with third-order Runge-Kutta, the fifth-order WENO （WENO5） scheme was used to discuss numerical calculation of the linear hyperbolic conservation equation. Third-order Runge-Kutta method was applied to discrete its time derivative, and WENO5 finite difference method was applied to discrete its spatial derivative. The accuracy and reliability of the method was verified with the classical numerical examples. From the results of numerical examples, it indicates that this method has high oscillatory, thus can achieve high resolution and high accuracy resolution, high precision, and is essentially non- interface tracking in the fluid mechanics.

关 键 词：WENO 数值计算 双曲守恒律方程 界面追踪 

分 类 号：O241[理学—计算数学] O354[理学—数学]