饱和多孔介质中水力-力学-传质耦合过程的混合有限元法

Mixed finite element method for coupled hydro-mechanical-mass transfer process in saturated porous media

对饱和多孔介质提出了一个含溶混污染物输运(传质)过程的混合元方法,其中污染物输运过程数学模型包含了对流、机械逸散、分子弥散和吸附等机制。固相位移、应变和有效应力,孔隙水压力、压力空间梯度和Darcy速度,污染物浓度、浓度空间梯度和浓度流量在单元内均为独立变量分别插值。基于胡海昌-Washizu三变量广义变分原理,结合可以滤掉虚假振荡的特征线方法,推导出饱和土中水力-力学-传质耦合问题控制方程的单元弱形式,并导出了混合元计算公式。数值模拟证明了所提出的方法可以提供与传统4点积分方案同样精度,同时能够提高计算效率。

A mixed finite element method for miscible contaminant transport （mass transfer） process in saturated porous media is presented. The governing mechanisms in contaminant transport model contain convection, mechanical dispersion, molecular diffusion and adsorption. The displacement, strain and effective stress in solid phase; pressure, pressure gradient and Darcy velocity in liquid phase; contaminant concentration, concentration gradient and its flux are treated 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 with particular consideration of the characteristic-based algorithm in eliminating spurious numerical oscillations in solving mass transfer process. The numerical results illustrate good accuracy and efficiency in comparisons with the existing standard four-point quadrature.