Development of Efficient Numerical Methods for Fluid Flows and Electromagnetics

流体流动和电磁学的有效数值方法的开发

基本信息

批准号：
238471-2012
负责人：
Liang, Dong
金额：
$ 1.82万
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：
2015
资助国家：
加拿大
起止时间：
2015-01-01 至 2016-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570429
关键词：
Development Efficient Numerical Methods Fluid

项目摘要

The objective of the proposed program is to study, develop and analyze efficient and accurate numerical methods for fluid flows in porous media and environment as well as for computational electromagnetics. Modeling of fluid flows is playing an increasingly important role in groundwater modeling, reservoir simulation and environmental prediction. Tertiary recovery in petroleum reservoirs and contaminant transport in aquifers have motivated research for the simulation of multi-component miscible displacement problems in porous media. Aerosol modeling is of significant importance in environmental prediction due to the major impacts of aerosols on climate change and human health. The mathematical models of systems of partial differential equations are characterized by nonlinearities, convection dominances, moving steep fronts or interfaces, enormous sizes of field scale and long time predictions. Solving these problems has been a driving force in developing and analyzing efficient numerical methods and computational tools for large scale applications. Numerical modeling has also emerged as a crucial technique in many applications in electromagnetic science, in which there are great interests in the study of efficient and accurate numerical methods for solving Maxwell's equations in high dimensions. The program includes: (1) Develop and analyze efficient mass-conserved splitting domain decomposition methods for compressible multi-component flows in porous media; (2) Develop and analyze the ELLAM splitting domain decomposition method for transport problems in porous media; (3) Develop and analyze efficient characteristic and adaptive wavelet methods for spatial transport problems of aerosol dynamics; (4) Develop and analyze high-order energy-conserved S-FDTD schemes for Maxwell's equations in high dimensions.

该计划的目的是研究，开发和分析多孔媒体和环境中流体流以及计算电磁学中流体流的有效，准确的数值方法。流体流的建模在地下水建模，储层模拟和环境预测中起着越来越重要的作用。含水层中石油储层和污染物运输的三级恢复激发了多孔介质中多组分可混杂的位移问题的仿真研究。由于气溶胶对气候变化和人类健康的重大影响，气溶胶建模在环境预测中至关重要。部分微分方程系统的数学模型的特征是非线性，对流主导地位，移动陡峭的前部或接口，巨大的场尺度和长时间的预测。解决这些问题一直是开发和分析用于大规模应用的有效数值方法和计算工具的推动力。在电磁科学的许多应用中，数值建模也已成为一种至关重要的技术，在该技术中，在高维度中求解麦克斯韦方程的有效，准确的数值方法的研究中，人们对高维度的有效和准确的数值方法有很大的兴趣。该程序包括：（1）开发和分析多孔介质中可压缩多组分流的有效质量保存的分裂域分解方法；（2）开发和分析多孔培养基中传输问题的Ellam分裂域分解方法；（3）为气溶胶动力学的空间传输问题开发和分析有效的特征和自适应小波方法；（4）在高维度中为麦克斯韦方程开发和分析高阶能量保存的S-FDTD方案。