Development of Efficient Numerical Methods for Fluid Flows and Electromagnetics

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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.