二维扩散方程的9点格式有限近似解法  

Finite approximate method with 9 points scheme for two-dimensional diffusion equation

作　　者：李泰儒[1] 赵明登[2] 彭晓春[1] 槐文信[2] 

机构地区：[1]环境保护部华南环境科学研究所,广东广州510655 [2]武汉大学水资源与水电工程科学国家重点实验室,湖北武汉430072

出　　处：《水利水运工程学报》2011年第2期20-25,共6页Hydro-Science and Engineering

摘　　要：通过假设在曲线网格局部单元内满足二维扩散方程的近似解,并对计算区域进行离散,推导出中心点函数值和周边8点函数值之间的关系式,从而建立求解二维扩散方程的新方法,即基于曲线网格下的有限近似解法9点迭代格式.该格式用于非规则区域定常扩散方程和规则区域非定常扩散方程的计算,并与精确解等进行比较,结果表明该方法在计算简便性、精度和适用性等方面具有良好的特性,且比5点格式的有限近似解在精度方面有明显改善.最后计算了典型的坝基渗流流场,计算结果与试验结果吻合较好.The finite approximate solution for two-dimensional diffusion equation in the local unit of curvilinear grid is hypothesized,and the calculation region is discrete to deduce the relational expression between center function value and 8 points function value around.A finite approximate method with 9 points scheme of the curvilinear grid is proposed to solve the two-dimensional diffusion equation thereby.The comparison of the calculated and exact values for both the steady diffusion equation with the irregular region and the unsteady diffusion equation with regular region indicates that the method has the properties of simple process,high precision and strong adaptability.Compared with FPM（5 points scheme）,the method is improved in precision.Then the typical seepage flow field of the bottom for spillway dam is calculated and the calculated results are in good agreement with the measured results by electrical analogue method.

关 键 词：扩散方程 有限近似法 渗流 

分 类 号：TV139.1[水利工程—水力学及河流动力学]