An Upwind Mixed Finite Volume Element-fractional Step Method and Convergence Analysis for Three-dimensional Compressible Contamination Treatment from Nuclear Waste

作     者：Chang-feng LI Yi-rang YUAN Huai-ling SONG Chang-feng LI;Yi-rang YUAN;Huai-ling SONG

作者机构：School of EconomicsShandong UniversityJinan 250100China Institute of MathematicsShandong UniversityJinan 250100China College of Mathematics and EconometricsHunan UniversityChangsha 410082China 

出 版 物：《应用数学学报:英文版》 (Acta Mathematicae Applicatae Sinica)

年 卷 期：2023年第39卷第4期

页      面：808-829页

核心收录：

学科分类：083002[工学-环境工程] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 07[理学] 08[工学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the Natural Science Foundation of Shangdong Province (Grant No.ZR2021MA019) Natural Science Foundation of Hunan Province (Grant No.2018JJ2028) 

主　　题：compressible nuclear waste contamination in porous media upwind mixed finite volume elementfractional step conservation of mass and energy convergence analysis numerical example 

摘      要：In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in L2norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.