求解三维对流扩散方程的高精度隐式紧致差分方法  

Compact Difference Method Based on High-Order Implicit Scheme for Solving the 3D Steady Convection-Diffusion Equation

作　　者：魏剑英[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《西南大学学报（自然科学版）》2012年第11期27-32,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11061025);教育部科学技术研究重点项目(210239);霍英东教育基金会高等院校青年教师基金资助项目(121105);宁夏自然科学基金资助项目(NZ12123)

摘　　要：首先利用一阶和二阶导数的Padé型四阶紧致差分格式,并结合原方程本身,构造了三维定常对流扩散方程的四阶隐式紧致差分格式;然后采用Richardson外推技术外推一次,得到了三维定常对流扩散方程具有六阶精度的数值解;最后通过数值实验验证了该方法的高阶精度及有效性.Based on the Pad6 schemes of first-and second-order partial derivatives and combined with the original differential equation, a fourth-order implicit compact difference method is proposed for solving the 3D steady convection-diffusion equation. Then, the Richardson extrapolation method is used to further im prove the computational accuracy and a sixth-order accurate solution is obtained. Lastly, numerical experi ments are conducted to demonstrate the high accuracy and validity of this method.

关 键 词：定常对流扩散方程 高精度 隐式紧致格式 RICHARDSON外推法 

分 类 号：O241.82[理学—计算数学]