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

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.