基于SUPG稳定有限元技术的纯对流耦合管涌模型  

Pure convection coupled piping model based on stabilized finite element SUPG

作　　者：罗玉龙[1] 彭华[2] 张晋[2] 

机构地区：[1]河海大学水利水电学院,江苏南京210098 [2]武汉大学土木建筑工程学院,湖北武汉430072

出　　处：《岩土工程学报》2010年第7期1072-1078,共7页Chinese Journal of Geotechnical Engineering

基　　金：河海大学自然科学基金项目(2009421611);河海大学中央高校基本科研业务费项目(2009B01914)

摘　　要：标准Galerkin法求解纯对流耦合管涌模型时易出现剧烈的数值振荡,严重影响计算质量及效率。从模型控制方程和标准Galerkin法的适用性两方面分析,指出模型控制方程中非线性对流项的出现使得方程具有非自伴随特征,导致总体矩阵非对称,破坏了标准Galerkin法的最佳近似特性,是产生剧烈数值振荡的本质原因。为消除振荡,采用稳定有限元技术Streamline Upwind Petrov/Galerkin(SUPG)对耦合管涌模型进行改进。研究表明:SUPG法能够有效抑制纯对流耦合管涌模型产生的剧烈数值振荡,并可以在较少单元的情况下获得比标准Galerkin法更满意的结果。Numerical oscillation always occurs when the standard Galerkin method is applied to the pure convection coupled piping model,and it affects the calculation quality and efficiency seriously.The characteristics of piping governing differential equations and the applicability of the standard Galerkin method are analyzed,with the results showing that the nonlinear convection item in the governing differential equations induces the non-self-adjoint equations and unsymmetrical total matrix,and that the optimal approximation character of the standard Galerkin method is destroyed,resulting in the numerical oscillation.The stabilized finite element technique,Streamline Upwind Petrov/Galerkin（SUPG）,is employed to improve the coupled piping mathematical model.The results indicate that the SUPG method can eliminate numerical oscillation of pure convection equations effectively,and gain more satisfactory results under the condition of fewer elements compared with the standard Galerkin method.

关 键 词：管涌 数值振荡 SUPG 纯对流 

分 类 号：TV139.1[水利工程—水力学及河流动力学]