Efficient Conservative High-Order Solution-Flux Domain Decomposition Methods and Local Refinements for Flows in Porous Media and Electromagnetics

多孔介质和电磁学中流动的高效保守高阶解-通量域分解方法和局部细化

• 批准号: RGPIN-2022-04571
• 负责人: Liang, Dong
• 金额: $ 1.31万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759038
• 关键词: Efficient; Conservative; Order; Solution; Flux

Modeling contamination flow in porous media plays a crucial role in understanding and predicting complex physical, chemical and flow processes, as well as in preventing and controlling pollution in groundwater modeling and environmental protection. Modeling the propagation of electromagnetic waves is also critically important for many applications of electromagnetic science. Recent rapid growth in the use of electromagnetics in materials and metamaterials includes biomedical imaging and processing, radio-frequency identification (RFID), wireless power transmission, holographic processing, nanolithography, and cloaking devices, etc. The mathematical models describing these processes are complex and there are challenges in the development of accurate methods that preserve the important natural physical properties.  When modeling contamination flows in porous media, mathematical models are nonlinear systems of coupled partial differential equations (PDEs) that involve challenging features such as transport dominance, moving steep fronts, nonlinearity, adsorption, interface and heterogeneity. Solving these problems is driving the development and analysis of efficient, accurate, and conservative domain decomposition methods for long-term, large-scale field prediction problems in parallel computing.  Since modeling faces with the challenges of micro-scale, local solution behavior, complex and refined structure, and long-time response, it is of utmost importance to develop efficient and conservative local mesh-refined methods for electromagnetics. The proposed research program includes: (1) Develop time second-order conservative characteristic domain decomposition methods for contamination porous media flows; (2) Develop conservative fourth-order block-centered compact-difference solution-flux domain decomposition method for contamination flows; (3) Develop energy-preserving local mesh-refined fourth-order S-FDTD schemes for Maxwell's equations; (4) Develop energy-preserving curvilinear-coordinated local mesh-refined S-FDTD schemes for electromagnetics; and (5) Develop global energy-preserving local mesh-refined S-FDTD schemes for metamaterial electromagnetics. The research program will benefit Canada through the establishment of methods, theories, algorithms and applications of conservative domain decomposition and local refinement techniques for computational fluid dynamics in porous media and computational electromagnetics. It will also train students and postdocs to meet the growing demand for highly qualified personnel in the environmental and electromagnetic industries and in the computing technology.

在多孔介质中建模污染流在理解和预测复杂的物理，化学和流动过程以及预防和控制地下水建模和环境保护中的污染方面起着至关重要的作用。对电子波的传播建模对于电子科学的许多应用也至关重要。材料和超材料中电子产品使用的近期快速增长包括生物医学成像和处理，射频识别（RFID），无线功率传输，全息处理，纳米现象和掩盖设备等。描述这些过程的数学模型是复杂的，并且描述了这些过程中的挑战是具有准确性的物理性质的挑战。当对多孔介质中的污染流进行建模时，数学模型是耦合的部分微分方程（PDE）的非线性系统，涉及挑战特征，例如运输优势，解决这些问题的移动是推动对长期，大规模的现场预测问题的高效，准确和保守的领域分解方法的开发和分析，大规模的现场预测问题。由于建模面对微型，局部解决方案行为，复杂和精致的结构以及长期响应的挑战，因此开发有效且保守的局部网格精制方法至关重要。拟议的研究计划包括：（1）为污染多孔培养基流的时间开发时间二阶保守特征域分解方法； （2）为污染流提供保守的四阶紧凑型解决方案 - 液液溶液分解方法； （3）为Maxwell的方程开发提供能源的本地网状固定的四阶S-FDTD方案； （4）开发用于电子设备的曲线曲线曲线协调的局部网状固定的S-FDTD方案； （5）开发用于超材料电子设备的全球固定局部网状固定的S-FDTD方案。该研究计划将通过建立保守域分解的方法，理论，算法和应用来使加拿大受益，并在多孔媒体和计算电子产品中用于计算流体动力学的局部改进技术。它还将培训学生和博士后，以满足对环境和电磁工业和计算技术中高素质人员的需求不断增长的需求。