广义对流扩散方程的隐式特征线混合元方法

MIXED FINITE ELEMENT METHOD FOR GENERALIZED CONVECTION-DIFFUSION EQUATIONS BASED ON IMPLICIT CHARACTERISTIC-BASED ALGORITHM

提出了一个广义对流扩散方程的混合有限元方法,方程的基本变量及其空间梯度和流量在单元内均作为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理结合特征线法给出了控制方程的单元弱形式．混合元方法采用基于一点积分方案并结合可以滤掉虚假的数值震荡的隐式特征线法．数值结果证明了所提出的方法可以提供和四点积分同样的数值计算结果,并能够提高计算效率．

A mixed finite element method for generalized convection-diffusion equations is proposed. The primitive variable with its spatial gradient and the diffusion flux are interpolated as independent variables. The variational （weak） form of the governing equations is given on the basis of the extended Hu-Washizu three-field variational principle. The mixed element is formulated with stabilized one point quadrature scheme and par- ticularly implicit characteristic-based algorithm for eliminating spurious numerical oscillations. The numerical results show good performances in accuracy and efficiency of the proposed mixed element in comparison with a standard finite element.