An approximation of incompressible miscible displacement in porous media by mixed finite element method and characteristics-mixed finite element method
An approximation of incompressible miscible displacement in porous media by mixed finite element method and characteristics-mixed finite element method
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DOI：
10.1016/j.cam.2008.09.029
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发表时间：
2009-06
影响因子：
2.4
通讯作者：
T. Sun;Yirang Yuan
中科院分区：
文献类型：
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作者：
T. Sun;Yirang Yuan
定义了多孔介质中不可压缩混溶驱动问题的一种近似格式。该方案是通过使用两种方法构造的。达西速度方程采用标准混合有限元。提出了一种求解浓度方程的特征混合有限元方法。浓度方程的对流部分采用特征近似，扩散部分采用最低阶混合有限元空间近似。因此，标量未知浓度和扩散通量可以同时近似。为了得到最优的L2范数误差估计，后处理步骤包括在标量未知浓度的近似中。该方案在整体上保持了质量守恒;事实上，在离散水平上，流体沿着近似特征进行传输。最后通过数值实验验证了理论分析的正确性。
An approximation scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by using two methods. Standard mixed finite element is used for the Darcy velocity equation. A characteristics-mixed finite element method is presented for the concentration equation. Characteristic approximation is applied to handle the convection part of the concentration equation, and a lowest-order mixed finite element spatial approximation is adopted to deal with the diffusion part. Thus, the scalar unknown concentration and the diffusive flux can be approximated simultaneously. In order to derive the optimal L2-norm error estimates, a post-processing step is included in the approximation to the scalar unknown concentration. This scheme conserves mass globally; in fact, on the discrete level, fluid is transported along the approximate characteristics. Numerical experiments are presented finally to validate the theoretical analysis.