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 

机构地区：[1]School of Economics,Shandong University,Jinan 250100,China [2]Institute of Mathematics,Shandong University,Jinan 250100,China [3]College of Mathematics and Econometrics,Hunan University,Changsha 410082,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第4期808-829,共22页应用数学学报（英文版）

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

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.

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

分 类 号：X771[环境科学与工程—环境工程] O241.82[理学—计算数学]