求解Kuramoto-Sivashinsky方程的有限体积一次元方法  

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

作　　者：卢付强 姜婷婷 丁凯孟 LU Fu-qiang;JIANG Ting-ting;DING Kai-meng(Changzhou Institute of Technology,Changzhou 213022,China;Keppel Communication(Nanjing)Co.,Ltd.,Nanjing 211189,China;Jinling Institute of Technology,Nanjing 211169,China)

机构地区：[1]常州工学院计算机信息工程学院,江苏常州213022 [2]吉宝通讯(南京)有限公司,江苏南京211189 [3]金陵科技学院网络与通信工程学院,江苏南京211169

出　　处：《金陵科技学院学报》2019年第4期66-70,共5页Journal of Jinling Institute of Technology

基　　金：国家自然科学基金(41801303);江苏省自然科学基金(BK200170116);金陵科技学院孵化项目(jit-fhxm-201604);常州工学院基金项目(YN1712);2019年度江苏省高校“青蓝工程”项目

摘　　要：Kuramoto-Sivashinsky(K-S)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。首先引入一个新变量,将方程转化为一个低阶的方程组,然后采用有限体积一次元方法对其空间变量进行离散近似,时间积分采用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(K-S)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 was introduced and then the K-S equation could be converted into low-order equations.Then the finite volume linear element method was used to approximate the space derivatives of the equations.As for the time integration,two-order explicit Runge-Kutta scheme was utilized,numerical experiments,including two travelling shock waves,a chaotic phenomenon 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 有限体积一次元方法 Runge-Kutta格式 

分 类 号：O241.8[理学—计算数学]