Development of High-Order Conservative Numerical Methods for Electromagnetics in Metamaterials and Transport Flows in Environment

超材料电磁学和环境传输流高阶保守数值方法的发展

• 批准号: RGPIN-2017-05666
• 负责人: Liang, Dong
• 金额: $ 1.46万
• 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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711351
• 关键词: Development; Order; Conservative; Numerical; Methods

The objective of the proposed program is to study, develop and analyze the conservative numerical methods for electromagnetics in metamaterials and transport flow problems in environment. Modelling has been recently recognized as a crucial technique in electromagnetics. For their supernormal electromagnetic features, metamaterials play a very important role in many applications. Due to the long-time electromagnetic responses and the complicated scale structures, computations for electromagnetics in metamaterials are confronted with great challenges. Computing multi-component transport problems is of significant importance in the atmospheric environment and groundwater contamination modelling. The mathematical models describing the complex processes are the nonlinear partial differential equations, which are characterized by transport dominance, moving steep front or interface, turbulence, nonlinearity, multi-scales, enormous size of field scale and long time prediction. Solving these problems has been a driving force in developing efficient numerical methods and computational tools for large scale transport flows in environment and for electromagnetics in metamaterials, in which there are great interests in the development of high-order conservative numerical methods in three dimensions. The program includes (1) Develop and analyze high-order energy conservative methods for electromagnetics in three dimensional metamaterials; (2) Develop and analyze high-order mass-preserving characteristic methods for aerosol transport problems in three dimensions; (3) Develop and analyze the mass conservative splitting domain decomposition method for multi-component aerosol transports in environment; (4) Development of controlling multicomponent pollution flows in porous media.

该项目的目标是研究、开发和分析超材料电磁学和环境中传输流问题的保守数值方法。 建模最近被认为是电磁学中的一项关键技术。由于超常电磁特性，超材料在许多应用中发挥着非常重要的作用。由于长时间的电磁响应和复杂的尺度结构，超材料中的电磁学计算面临着巨大的挑战。计算多组分传输问题在大气环境和地下水污染建模中具有重要意义。描述复杂过程的数学模型是非线性偏微分方程，其特点是输运主导、移动陡峭前沿或界面、湍流、非线性、多尺度、场尺度巨大和长时间预测。解决这些问题一直是开发环境中大规模输运流和超材料电磁学的有效数值方法和计算工具的驱动力，其中三维高阶保守数值方法的发展引起了极大的兴趣。 该项目包括（1）开发和分析三维超材料电磁学高阶能量守恒方法； （2）开发并分析三维气溶胶输运问题的高阶质量守恒特征方法； (3) 开发并分析环境中多组分气溶胶输送的质量守恒分裂域分解方法； (4)多孔介质中多组分污染流控制技术的发展。