Mixed finite volume element-upwind mixed volume element of compressible two-phase displacement and its numerical analysis
 作者： Yirang Yuan,  Changfeng Li,  Huailing Song 作者单位： 1Institute of Mathematics, Shandong University, Jinan, 250100, PR China2School of Economics, Shandong University, Jinan, 250100, PR China3College of Mathematics and Econometrics, Hunan University, Changsha, 410082, PR China 刊名： Journal of Computational and Applied Mathematics, 2020, Vol.370 来源数据库： Elsevier Journal DOI： 10.1016/j.cam.2019.112637 关键词： Three-dimensional compressible displacement;  Conservation of mass;  Mixed volume element-upwind mixed volume element;  Convergence analysis;  Numerical experiment; 原始语种摘要： Abstract(#br)A fundamental topic in numerical simulation of two-phase displacement is discussed in this paper. The mathematical model for the compressible problem is defined mainly by two nonlinear partial differential equations: a parabolic equation for the pressure and a convection–diffusion equation for the saturation. The Darcy velocity is determined by the pressure, and affects the whole physical process. The system is solved by a composite numerical scheme. The conservative mixed volume element is used for the first equation. The computational accuracy is improved for the Darcy velocity. The second equation is solved by a conservative upwind mixed volume element, where the mixed volume element and upwind approximation treat the diffusion and convection, respectively. The upwind... method preserves the high computational accuracy, and numerical dispersion and nonphysical oscillation are eliminated. The saturation and its adjoint vector function are obtained simultaneously. An important feature in numerical scheme, the conservation of mass, is proved. By the traditional theoretical work of numerical analysis such as a priori estimates of differential equations, the optimal order error estimate is obtained. Finally, numerical tests show the effectiveness and practicability, then the present method possibly solves the challenging problems as a powerful tool.

• compressible　可压缩性的
• upwind　上升风
• displacement　迁移
• mixed　混合的
• numerical　数字的
• element　元素
• volume　体积
• analysis　分析
• convection　对流
• scheme　略图