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

• 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

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.

该计划的目标是研究，开发和分析多孔介质和环境中流体流动以及计算电磁学的有效和准确的数值方法。 流体流动建模在地下水建模、储层模拟和环境预测中发挥着越来越重要的作用。石油储层中的三次采油和含水层中的污染物运移激发了多孔介质中多组分混相驱替问题模拟的研究。由于气溶胶对气候变化和人类健康的重要影响，气溶胶模拟在环境预测中具有重要意义。偏微分方程组的数学模型具有非线性、对流占优、移动的陡峭锋或界面、巨大的场尺度和长时间的预测等特点。解决这些问题已经成为开发和分析大规模应用的有效数值方法和计算工具的驱动力。数值模拟在电磁科学的许多应用中也已成为一种关键技术，其中对求解高维麦克斯韦方程组的有效和精确的数值方法的研究引起了极大的兴趣。 该方案包括：（1）发展和分析多孔介质中可压缩多组分流动的有效质量守恒分裂区域分解方法;（2）发展和分析多孔介质中输运问题的ELLAM分裂区域分解方法;（3）发展和分析气溶胶动力学空间输运问题的有效特征和自适应小波方法;（4）发展并分析了求解高维麦克斯韦方程组的高阶能量守恒S-FDTD方法。