非定常对流占优扩散方程的龙格库塔伽辽金有限元方法  

Rung-Kutta Galerkin FEM Method for Unsteady Convection Dominated Diffusion Equation

作　　者：冯立伟 席伟 FENG Li-wei;XI Wei(College of Science,Shenyang University of Chemical Technology,Shenyang 110142,China;School of Computer Science and Technology,Shenyang University of Chemical Technology,Shenyang 110142,China)

机构地区：[1]沈阳化工大学数理系,辽宁沈阳110142 [2]沈阳化工大学计算机科学与技术学院,辽宁沈阳110142

出　　处：《沈阳化工大学学报》2020年第1期91-96,共6页Journal of Shenyang University of Chemical Technology

摘　　要：为了消除伽辽金有限元方法在求解非定常对流占优扩散方程时的伪数值振荡,通过在扩散项上添加指数型拟合因子,并采用三角形剖分上的线性伽辽金有限元将方程化为半离散化常微分方程;再采用四阶四级龙格库塔方法求解常微分方程.指数型拟合因子有效抑制了伪数值振荡的产生,实现了非定常对流占优扩散方程的求解.对方法进行了理论分析,并阐述了详细计算过程.使用数值实例和天然气管道泄漏模拟实验,验证了方法的有效性.In order to eliminate the pseudo numerical oscillation of Galerkin finite element method in solving unsteady convection-dominated diffusion equation, the exponential fitting factor is added to the diffusion term, then the linear Galerkin finite element method on triangular subdivision is used to transform the equation into semi-discrete ordinary differential equation, then the fourth-order Runge-Kutta method is used to solve ordinary differential equation. The exponential fitting factor can effectively suppress the pseudo numerical oscillation and solve the unsteady convection dominated diffusion equation.The method is theoretically analyzed and the detailed calculation process is described. The effectiveness of the method is verified by numerical examples and leakage simulation experiments of natural gas pipeline.

关 键 词：对流占优扩散方程 有限元 龙格库塔方法 拟合因子 

分 类 号：O241[理学—计算数学]