A mixed volume element with upwind multistep mixed volume element and convergence analysis for numerical simulation of nuclear waste contaminant disposal
 作者： Changfeng Li,  Yirang Yuan,  Huailing Song 作者单位： 1Institute of Mathematics, Shandong University, Jinan 250100, China2School of Economics, Shandong University, Jinan 250100, China3College of Mathematics and Econometrics, Hunan University, Changsha 410082, China 刊名： Journal of Computational and Applied Mathematics, 2019, Vol.356 , pp.164-181 来源数据库： Elsevier Journal DOI： 10.1016/j.cam.2019.01.035 关键词： Nuclear waste contamination in porous media;  Mixed volume element with upwind multistep mixed volume element;  Conservation of mass and energy;  Convergence analysis;  Numerical computation; 原始语种摘要： Abstract(#br)In this paper the authors discuss a numerical simulation problem of three-dimensional contamination treatment from nuclear waste. The mathematical model is defined by a nonlinear system of an initial–boundary problem of four partial differential equations: an elliptic equation for the fluid pressure, three convection–diffusion equations for the brine, radionuclides and heat. The pressure appears within the concentration equations and heat conduction equation, and the Darcy velocity controls the concentrations and the temperature. The pressure is solved by the conservative mixed volume element method, and the order of accuracy is improved by the Darcy velocity. The concentrations and temperature are treated by a combination of a multistep method, the upwind approximation and a... mixed volume element. The partial derivatives to time variable are approximated by a multistep method. A mixed volume element and an upwind scheme are used to discretize the diffusion and the convection, respectively. The composite method can solve the convection-dominated diffusion problems well because it eliminates numerical dispersion and nonphysical oscillation and has high order computational accuracy. The mixed volume element has the local conservation of mass and energy, and it can obtain the concentrations and temperature and their adjoint vector functions simultaneously. The conservation nature plays an important role in numerical simulation of underground fluid. By the technique of a priori estimates of differential equations, we derive an optimal second order result in L 2 norm. Numerical examples are given to show the effectiveness and practicability of our approach and the composite method is testified as a powerful tool for solving the challenging benchmark problem.

• waste　岩屑
• mixed　混合的
• disposal　处理
• multistep　多步的
• contaminant　沾染物质
• element　元素
• volume　体积
• upwind　上升风
• concentrations　浓聚物
• numerical　数字的