求解Kuramoto-Sivashinsky方程的有限体积二次元方法  

Quadratic Finite Volume Element Method for the Solution of the Kuramoto-Sivashinsky Equation

作　　者：卢付强 史永 王甜 余晓栋 LU Fuqiang;SHI Yong;WANG Tian;YU Xiaodong(School of Computer Information Engineering, Changzhou Institute of Technology, Changzhou 213032;Key Laboratory of Changzhou Software Technology Research and Application, Changzhou 213032)

机构地区：[1]常州工学院计算机信息工程学院,江苏常州213032 [2]常州市软件技术研究与应用重点实验室,江苏常州213032

出　　处：《常州工学院学报》2020年第1期25-31,共7页Journal of Changzhou Institute of Technology

基　　金：国家自然科学基金(41901323);江苏省高等学校自然科学研究项目(18KJB520004);常州市科技项目应用基础研究计划(CJ20180038)。

摘　　要：Kuramoto-Sivashinsky方程是一个非线性四阶偏微分方程,常被用于反应扩散系统的动力过程建模。在文章中,首先引入一个新变量,将方程转化为一个低阶的方程组,然后采用有限体积二次元方法对其空间变量进行离散近似,时间积分采用显式2阶Runge-Kutta格式,在数值实验中采用所提出的方法分别对激波解以及混沌现象进行数值模拟。结果表明提出的有限体积元方法能够对以上各种现象进行有效模拟。The Kuramoto-Sivashinsky equation belongs to nonlinear four-order partial differential equations(PDEs),which is commonly used for the modelling of dynamics in reaction-diffusion systems.In this paper,a new variable is introduced and the K-S equation can be converted into low-order equations.The finite volume quadratic element method is used to approximate the space derivatives of the equations.As for the time integration,explicit two-order Runge-Kutta scheme was utilized,Numerical experiments,including two travelling shock waves,a chaotic would be simulated by the proposed method respectively.The results demonstrate that our method could simulate all the above experiments successfully.

关 键 词：KURAMOTO-SIVASHINSKY方程 数值近似 有限体积二次元方法 Runge-Kutta格式 

分 类 号：O175.29[理学—数学] TP399[理学—基础数学]