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

该程序的目标是研究、发展和分析超材料中的电磁学守恒数值方法和环境中的输运流动问题。 最近，建模被认为是电磁学中的一项关键技术。超材料因其超常的电磁特性，在许多应用中扮演着非常重要的角色。由于电磁响应时间长，尺度结构复杂，超材料的电磁学计算面临着巨大的挑战。多组分输运问题的计算在大气环境和地下水污染模拟中具有重要意义。描述这一复杂过程的数学模型是非线性偏微分方程组，它具有输运占优势、锋面或界面运动陡峭、湍流、非线性、多尺度、场尺度巨大、预报时间长等特点。这些问题的解决一直是环境中大规模输运流动和超材料中电磁学的高效数值方法和计算工具的发展动力，其中三维高阶保守数值方法的发展引起了人们的极大兴趣。 该程序包括(1)发展和分析三维超材料电磁问题的高阶能量守恒方法；(2)发展和分析三维气溶胶输运问题的高阶质量守恒特征方法；(3)发展和分析环境中多组分气溶胶输运问题的质量守恒分裂区域分解方法；(4)发展和分析控制多组分污染在多孔介质中的流动。

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.