基于Darcy-Stokes耦合模型的水污染问题数值模拟方法

项目名称： 基于Darcy-Stokes耦合模型的水污染问题数值模拟方法

项目编号： No.11501335

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 尹哲

作者单位： 山东师范大学

项目金额： 18万元

中文摘要： 带交界面的Darcy-Stokes耦合系统结合关于浓度的对流扩散方程刻画了污染物在具有自由流动地表水和渗流地下水实际运移过程，发展其准确高效的数值模拟方案，对深刻揭示实际流动和渗流的运动机理、指导科学工程实践具有重要的理论价值与应用前景。本项目针对耦合Darcy-Stokes系统, 研究Darcy方程混合元方法以及Stokes方程的间断有限体积方法，利用各单元函数间断的性质处理流动区域和渗流区域的交界面问题。针对浓度方程中含有对流项的特点，采用迎风或特征线法结合间断有限体积方法进行数值模拟，得到污染物的浓度分布,进而结合求得的流速和压力，动态模拟污染物在两种介质中的运移规律。在进行严格的收敛性和稳定性分析的基础上，将通过算法程序实现对污染物运移的时间预报和浓度预报，为水资源保护特别是应对水污染突发性事件提供快速、直观的决策依据。

中文关键词： 有限体积方法；Darcy-Stokes耦合系统；对流扩散方程；误差估计；数值试验

英文摘要： The combination of the Stokes-Darcy coupling equation with the interface boundary and convection-diffusion equation about concentration describes the actual migration of contaminant between the free-flowing surface water and seepage ground water incisively. Developing acute and efficient numerical simulation method about this combination could reveal the actual flowing and seepage movement mechanism, which means important theory value and application prospect to guide scientific engineering practice, improving theory of value analysis could as well. .Concerned to the Darcy-Stokes coupling equation, this project is built up to research on the mixed finite element method of the Darcy equation and discontinuous finite volume method of the Stokes equation. We would solve the problem of interface between flow regions and seepage regions, utilizing the discontinuity of respective functions. Concerned to the convection term in the concentration equation, we could use the upwind or characteristics methods which combine discontinuous finite volume method to make numerical simulation，then we would get the concentration distribution of the contaminant. Combining it with obtained flow velocity and compression，we could make the dynamic simulation of the contaminant migration between the two medium. . On the basis of the Convergence and stability analysis, the mathematics model would forecast the time and distribution of the contaminant migration, which would provide quick and straightforward decision reference about the water resources protection, especially in the environmental emergencies.

英文关键词： Finite volume method;Coupled Darcy-Stokes system;Convection-Diffusion equation ;Error estimates;Numerical experiment