This paper presents a combined stabilized mixed finite element and discontinuous Galerkin method for coupled Stokes-Darcy flows model with transport, where the fluid viscosity depends on the concentration. We use nonconforming piecewise linear Crouzeix-Raviart (C-R) element to approximate velocity, piecewise constant function to approximate pressure and the symmetric interior penalty Galerkin (SIPG) method to solve concentration equation. A “cut-off” operator is introduced into SIPG scheme to avoid the assumption on the boundness of infinity norms of approximate velocity in convergence analysis. Optimal a priori error estimates for the full discrete scheme are obtained. Finally, some numerical examples are presented to verify the theoretical analysis, and a water injection oil production process is simulated to illustrate the practicability of our method.

本文提出了一种组合稳定混合有限元和间断 Galerkin 方法，用于耦合斯托克斯-达西流动模型，其中流体粘度取决于浓度。我们使用非一致性分段线性Crouzeix-Raviart（CR）单元来近似速度，分段常数函数来近似压力和对称内部惩罚Galerkin（SIPG）方法来求解浓度方程。SIPG方案中引入了一个“截止”算子，以避免在收敛分析中假设近似速度的无穷范数有界。最优先验获得了全离散方案的误差估计。最后，通过数值算例验证了理论分析，并模拟了注水采油过​​程，说明了该方法的实用性。