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

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Chang-feng Li, Yi-rang Yuan, Huai-ling Song
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引用次数: 0

Abstract

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 L2 norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.

核废料三维可压缩污染处理的迎风混合有限体积元-分步法及收敛分析
本文讨论了核废料三维可压缩污染处理的数值模拟问题。该数学模型是一个由四个偏微分方程组成的非线性对流-扩散系统,确定了四个主要的物理未知数:压力、盐水和放射性核素的浓度以及温度。采用保守混合有限体积元法求解压力,提高了达西速度的计算精度。其他未知量采用逆风近似和混合有限体积元的组合格式进行计算。消除了数值色散和非物理振荡,很好地解决了对流主导的扩散问题,具有高阶计算精度。混合有限体积元具有局部保守性,同时得到目标函数及其伴随向量函数。守恒性质是地下流体数值模拟的一个重要特征。引入分数阶差来求解放射性核素因子的浓度,并将三维问题分解为三个连续的一维问题,大大缩短了计算时间。利用微分方程的先验估计理论和技术,导出了L2范数下的最优阶估计。最后,通过算例说明了对一些实际问题的有效性和实用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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