Adaptive mixed-hybrid and penalty discontinuous Galerkin method for two-phase flow in heterogeneous media

作者：Hou, Jiangyong; Chen, Jie^*; Sun, Shuyu; Chen, Zhangxin

来源：Journal of Computational and Applied Mathematics, 2016, 307: 262-283.

DOI：10.1016/j.cam.2016.01.050

• Brezzi-Douglas-marini
• Raviart-Thomas
• Mixed-hybrid
• Penalty discontinuous Galerkin
• Discontinuous nonlinear interface condition
• Centroidal Voronoi-Delaunay triangulation

In this paper, we present a hybrid method, which consists of a mixed-hybrid finite element method and a penalty discontinuous Galerkin method, for the approximation of a fractional flow formulation of a two-phase flow problem in heterogeneous media with discontinuous capillary pressure. The fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity. and the saturation affected coefficients. For the wetting phase pressure equation, the continuous mixed-hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous. While it can reduce the computational cost by using less degrees of freedom arid avoiding the post-processing of velocity reconstruction, this method can also keep several good properties of the discontinuous Galerkin method, which are important to the fractional flow formulation, such as the local mass balance, continuous normal flux and capability of handling the discontinuous capillary pressure. For the wetting phase saturation equation, the penalty discontinuous Galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation. Furthermore, an adaptive algorithm for the hybrid method together with the centroidal Voronoi-Delaunay triangulation technique is proposed. Five numerical examples are presented to illustrate the features of proposed numerical method, such as the optimal convergence order, the accurate and efficient velocity approximation, and the applicability to the simulation of water flooding in oil field and the oil-trapping or barrier effect phenomena.

• 出版日期2016-12-1
• 单位KAUST; 西安交通大学