Non-Iterative Multi-Physics Domain Decomposition Method for the Navier-Stokes-Darcy Model

纳维-斯托克斯-达西模型的非迭代多物理域分解方法

• 批准号: 1418624
• 负责人: Xiaoming He
• 金额: $ 9万
• 依托单位: Missouri University of Science and Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1418624&HistoricalAwards=false
• 关键词: Non; Iterative; Multi; Physics; Domain

The Navier-Stokes-Darcy model is crucial to accurately describe many important real world problems, such as the flow problems in vuggy/fractured porous media, groundwater systems in karst aquifers, interaction between surface and subsurface flows, and industrial filtrations. The efficiency of the numerical methods to solve this model is very important for the large-scale applications. But most of the related published works focus on a simpler model, which is not accurate for many applications since it does not consider several crucial realistic factors. This project is to study a more realistic Navier-Stokes-Darcy model and design an efficient numerical method to solve it in parallel. The completion of this project will provide large advances in the study of the coupled fluid flow and porous media flow. The basic idea and framework of this project have potential to be applied to other interesting multi-physics coupling problems. This project provides undergraduate and graduate students many valuable training opportunities in the development of new methods and packages, mathematical analysis, and engineering applications. The methods under development will be applied to simulate the flow in vuggy/fractured porous media. The investigators plan to disseminate the methods and software packages to more engineers and scientists by presenting the work in professional conferences and colloquia and organizing special sessions. The goal of this project is to carry out a systematic research on the development, analysis, and application of a non-iterative multi-physics domain decomposition method for the Navier-Stokes-Darcy model with the Beavers-Joseph (BJ) interface condition and defective boundary conditions. The proposed non-iterative multi-physics domain decomposition method enables us to efficiently and simultaneously deal with the significant difficulties arising from the interaction among the aforementioned crucial realistic factors. The key ideas include a non-iterative algorithm with a direct prediction on the interface, a multi-physics decomposition with Robin conditions arising from the three physical interface conditions which include the BJ condition, and the Lagrange multiplier method to deal with the defective boundary condition. The major difficulty is the inherent interaction of the nonlinear advection, BJ condition, parameters in the Robin-Robin decomposition, and the saddle point problem arising from the Lagrange multiplier method.

纳维-斯托克斯-达西模型对于准确描述许多重要的现实世界问题至关重要，例如孔隙/裂隙多孔介质中的流动问题、岩溶含水层中的地下水系统、地表和地下流之间的相互作用以及工业过滤。求解该模型的数值方法的效率对于大规模应用非常重要。但大多数相关已发表的作品都关注于更简单的模型，这对于许多应用来说并不准确，因为它没有考虑几个关键的现实因素。该项目旨在研究更真实的纳维-斯托克斯-达西模型，并设计一种高效的数值方法来并行求解。该项目的完成将为耦合流体流动和多孔介质流动的研究带来巨大进展。该项目的基本思想和框架有潜力应用于其他有趣的多物理场耦合问题。该项目为本科生和研究生提供了许多宝贵的培训机会，涉及新方法和软件包的开发、数学分析和工程应用。正在开发的方法将用于模拟孔隙/破裂多孔介质中的流动。研究人员计划通过在专业会议和座谈会上展示研究成果以及组织特别会议，向更多工程师和科学家传播这些方法和软件包。本项目的目标是对具有 Beavers-Joseph (BJ) 界面条件和缺陷边界条件的 Navier-Stokes-Darcy 模型的非迭代多物理域分解方法的开发、分析和应用进行系统研究。所提出的非迭代多物理域分解方法使我们能够有效地同时处理上述关键现实因素之间相互作用所产生的重大困难。其关键思想包括直接预测界面的非迭代算法、由包括BJ条件在内的三个物理界面条件产生的Robin条件的多物理分解，以及处理缺陷边界条件的拉格朗日乘子法。主要困难在于非线性平流、BJ条件、Robin-Robin分解中参数的内在相互作用以及拉格朗日乘子法产生的鞍点问题。

项目成果

A DUAL-POROSITY-STOKES MODEL AND FINITE ELEMENT METHOD FOR COUPLING DUAL-POROSITY FLOW AND FREE FLOW

• DOI: 10.1137/15m1044072
• 发表时间: 2016-01-01
• 期刊: SIAM JOURNAL ON SCIENTIFIC COMPUTING
• 影响因子: 3.1
• 作者: Hou, Jiangyong;Qiu, Meilan;Bai, Baojun
• 通讯作者: Bai, Baojun