基于待定系数法的改进迎风格式  

Up-wind scheme based on the undetermined coefficient method

作　　者：吴腾[1] 张红武[1] 钟德钰[1] 申晓东[1] 

机构地区：[1]清华大学水利水电工程系,水沙科学与水利水电工程国家重点实验室,北京100084

出　　处：《清华大学学报（自然科学版）》2009年第12期1954-1957,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金委员会、水利部黄委会黄河联合研究基金项目(50339020)

摘　　要：为了提高求解对流方程的计算精度,对传统迎风格式进行了改进。运用待定系数法,引入量纲一的参数来抑制格式的频散和耗散。将该格式应用于经典的矩形波算例和Gauss波算例,结果表明:对于Gauss波,将该格式与L-W格式、Fromm格式和FTCS格式均具有较高的精度;对于矩形波,与其他格式(L-W、Fromm和FTCS格式)相比,该格式具有较高的精度。因此,该算法能比传统迎风格式更好反映波形的传播。An up-wind difference scheme was developed for the advection-diffusion equations with the dimensionless parameters determined using the undetermined coefficient method to reduce the numerical diffusion.The scheme was applied to classical case studies such as a rectangular wave and a Gaussian wave.The results show that the scheme and the other classical schemes,such as the L-W scheme,the Fromm scheme,and the forward time-centered space（FTCS） scheme,all agree well with the exact solution for pure convection of a Gauss wave.The scheme has better accuracy than the other schemes for the rectangular wave.Thus,the scheme accurately reflects the wave propagation and performs better than the conventional schemes.

关 键 词：对流方程 数值格式 待定系数法 迎风格式 

分 类 号：TV131.4[水利工程—水力学及河流动力学]