Mixed volume element combined with characteristic mixed finite volume element method for oil–water two phase displacement problem
 作者： Yirang Yuan,  Tongjun Sun,  Changfeng Li,  Yunxin Liu,  Qing Yang 作者单位： 1Institute of Mathematics, Shandong University, Jinan, 250100, PR China2School of Economics, Shandong University, Jinan, 250100, PR China3School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, PR China 刊名： Journal of Computational and Applied Mathematics, 2018, Vol.340 , pp.404-419 来源数据库： Elsevier Journal DOI： 10.1016/j.cam.2018.02.038 关键词： Three-dimensional incompressible miscible displacement;  Mixed volume element-characteristic mixed volume element;  Local conservation of mass;  Second order L 2 estimates;  Numerical experiments; 原始语种摘要： Abstract(#br)As the basic of numerical simulation of energy science, the displacement of three-dimensional oil–water two phase in porous media is discussed in this paper. For incompressible miscible displacement, the pressure is described by a flow equation in an elliptic mathematical formulation and the saturation is defined by a convection–diffusion equation. The pressure exists in the saturation equation by Darcy velocity, and controls the whole flow. We develop and improve substantially the work of Arbogast and Wheeler, then put forward a mixed volume element combined with characteristic mixed finite volume element method for two-phase displacement problem. The flow equation is discretized by the conservative mixed volume element method, which could improve the accuracy of an order... for computing Darcy velocity. The saturation equation is solved by a characteristic mixed volume element method, where mixed volume element method is used to compute the diffusion term and the method of characteristics is adopted to discretize the convection term. The method of characteristics can confirm high stability of numerical simulation at the fronts, avoid numerical dispersion and nonphysical oscillation, and can adopt large time steps, obtain smaller time truncation error and improve the computation accuracy. Mixed volume element can solve the convection term, confirm conservation of mass at each element and approximate the saturation and the adjoint vector meanwhile. It is most important in numerical computation of seepage mechanics. Optimal second order estimates in L 2 norm are derived by theory and special techniques of priori estimates. Finally, numerical experiments are shown to illustrate the efficiency and practicability and to solve the international problem successfully.

• method　方法
• element　元素
• volume　体积
• numerical　数字的
• equation　方程
• mixed　混合的
• velocity　速度
• displacement　迁移
• saturation　饱和
• problem　题目