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

基本信息

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：
2018
资助国家：
加拿大
起止时间：
2018-01-01 至 2019-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=657562
关键词：
Development Order Conservative Numerical Methods

项目摘要

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.

该计划的目的是研究，开发和分析超材料和环境中传输流量问题的保守数值方法。对于它们的超常电磁特征，超材料在许多应用中起着非常重要的作用。由于长期电磁响应和复杂的尺度结构，超材料中电磁学的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至关重要。描述复杂过程的数学模型是非线性偏微分方程，其特征在于运输优势，移动陡峭的前面或界面，湍流，非线性，多尺度，巨大的场尺度和长时间预测。解决这些问题一直是开发有效的数值方法和计算工具的驱动力（2）在三个维度上开发和分析用于气溶胶传输问题的高阶质量保护特征方法；（3）开发和分析用于多组分气溶胶在环境中的多组分气溶胶运输的质量保守分裂域的分解方法；（4）在多孔介质中控制多组分污染流的发展。