Mathematical modelling and computational methods in porous media flow and biology

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The objective of the proposed project is to study, analyze and develop mathematical modeling and computational methods for fluid flows in porous media and population growth in biology.Oil and gas, which currently cannot be replaced, are important energy resources in the modern world. The most viable way to efficiently exploit petroleum reserves is the use of enhanced oil recovery (EOR) processes. Mathematical modeling of flows in porous media is playing an increasingly important role in EOR and reservoir simulations, which provides an efficient tool for understanding the complex chemical, physical, and fluid flow processes in order to optimize the recovery of hydrocarbon in reservoirs. It is also very important in the remediation of the contamination in groundwater. The mathematical models are characterized by nonlinearities, convection dominance, moving steep fronts or interfaces, heterogeneities of media, multiple scales in porous media. These features lead to the numerical simulations of the systems in porous media to be severely difficult. Computational biology is also playing an important role in the study of the relation between species and their environment. There are particular interests in studying the large-scale high-dimensional spatial field and long time predictions of the population growth in biology, and in modelling and controlling the epidemics of influenza in a large spatial range (among multi-cities or multi-countries).The project includes: (1). Developing and Analyzing the adaptive ELLAM combining with wavelets for fluid flows in porous media; (2). Developing and analyzing the splitting domain decomposition methods for compressible fluid flows in porous media; (3). Upscaling for miscible flows in strongly heterogeneous porous media; (4). Modelling and analysis of population growth in biology and applications