基于通量分裂的一阶迎风差分格式在传输线分析中的应用  

Application of first-order upwind difference scheme based on flux splitting method in transmission line analysis

作　　者：高印寒[1] 王天皓[1] 杨开宇[1] 张俊东[1] 金宇[2] 赵竟园 

机构地区：[1]吉林大学汽车仿真与控制国家重点实验室,长春130022 [2]吉林大学仪器科学与电气工程学院,长春130061

出　　处：《吉林大学学报（工学版）》2014年第4期1031-1036,共6页Journal of Jilin University:Engineering and Technology Edition

基　　金：高等学校博士学科点专项科研基金项目(20110061110059);吉林省科技发展计划重点项目(20110326)

摘　　要：利用一阶偏微分方程组将属于一阶双曲型偏微分方程组的多导体传输线方程变换为一阶线性常系数方程组,应用偏微分方程的特征线构造该方程组的一阶迎风格式,将一阶线性方程组的系数矩阵进行通量分裂,结合阻性负载的边界条件,计算出传输线的瞬态响应。最后通过仿真将本文计算结果与利用具有二阶精度的传统时域有限差分(FDTD)格式和LaxWendroff格式计算出的结果进行比较。结果表明:本文算法克服了传统FDTD格式和LaxWendroff格式在间断解处的非物理振荡,同时还具有简单稳定,适用范围广的特点。Multi-conductor transmission line equations belong to the first order hyperbolic partial differential equations, which are converted into first-order linear constant coefficient equations by means of the first-order partial differential equations. It applies the characteristic line of the partial differential equations to construct its first-order upwind scheme, conducts a flux splitting of the coefficient matrix of the linear equations and combines the boundary conditions of resistive load to calculate the transient response of the transmission line. Finally, by simulation, the calculation results of this work are compared with that of the traditional PDTD format and Lax-Weng off format with second order accuracy. It is demonstrated that the proposed calculation method overcomes the non-physical oscillation of traditional PDTD format and Lax-Wndroff format at the discontinuous solutions. At the same time the new method has the characteristics of simple and stable, wide range ofapplication and similar efficiency to those two calculation methods.

关 键 词：仪器仪表技术 通量分裂法 一阶迎风差分格式 传输线方程 数值解 

分 类 号：TH89[机械工程—仪器科学与技术]