步长和差分格式对一维非稳态导热数值计算的影响

Effects of Step Lengths and Finite Difference Schemes on One Dimensional Unsteady Heat Conduction Computation

以一个一维非稳态导热问题为例 ,研究了不同的步长和差分格式对计算结果的影响。研究表明 :空间步长不能选得过大 ,否则会使得网格数较少 ,计算误差增加 ;空间步长一定时 ,计算结果随傅立叶数变化而波动 ,且波动幅度因空间步长的增加而加剧 ;空间步长较大时 ,从显式格式、Crank-N icolson格式到全隐格式的计算精确度逐渐变差。另外 ,显式格式计算结果的合理性较强依赖于傅立叶数的取值 ;Crank-Nicolson格式只在空间步长较大时 ,才显示出这种依赖性 ;

A problem about one dimensional unsteady heat conduction is numerically studied with different space and time steps,and three different finite difference schemes.The effects of them on the numerical computation are analyzed in details.It is shown that the space step(Δx)shouldnt be too large,otherwise errors will be caused and the computation results will fluctuate increasingly with Fourier Number(Fo).In addition,the results accuracy of explicit schemes depends greatly on the value of Fo,while for the Crank Nicolson schemes,it is available only with greater space steps.And nothing for the fully implicit schemes.