Mathematical modelling and computational methods in porous media flow and biology

该项目的目标是研究、分析和发展多孔介质中流体流动和生物种群增长的数学建模和计算方法。石油和天然气是当今世界不可替代的重要能源。有效开采石油储备最可行的方法是使用提高采收率(EOR)工艺。多孔介质渗流的数学模拟在提高采收率和油藏模拟中发挥着越来越重要的作用，它为理解复杂的化学、物理和流体流动过程，优化油藏油气开采提供了有效的工具。在地下水污染的修复中也是非常重要的。这些数学模型具有非线性、对流占优势、运动陡峭的锋面或界面、介质的非均质性、多孔介质中的多尺度等特点。这些特点导致了多孔介质中系统的数值模拟非常困难。计算生物学在研究物种与环境之间的关系方面也发挥着重要作用。在生物学中研究大规模高维空间场和人口增长的长期预测，以及在大空间范围内(在多个城市或多个国家之间)模拟和控制流感流行是特别有兴趣的。建立和分析了自适应ELLAM与小波相结合的多孔介质渗流计算方法；发展和分析了可压缩流体在多孔介质中流动的分裂区域分解方法；强非均质多孔介质中混相流动的放大；(4)生物学中种群增长的建模与分析及其应用

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