Mathematical Sciences: Courant - Schlumberger Postdoctoral Research Associateship in the Mathematical Sciences

9407008 Avellaneda这个项目涉及研究多孔介质中的流动和弥散，特别是估计多孔介质的物理性质，如渗透率和溶质的流体动力弥散系数。已有相当多的工作致力于探索扩散弛豫时间、电导率和声速等物理性质与流体动力渗透率和弥散系数之间的相关性。这些宏观常数是联系在一起的，因为它们是通过求解相同微观结构上的相似方程而产生的。我们将根据更容易测量的特性的知识来构建渗透率和弥散系数的界限和估计值。这个问题已经研究了一段时间，斯伦贝谢的科学家在工作中率先提出了这个问题。溶质在多孔介质中的运移和弥散将通过对不同微观结构的分析和数值计算来进行，例如毛细管网络或晶间空间。我们将进行理论和数值研究，其中我们将集中于以下问题：i)建立有效的数值算法来模拟多孔介质中的三维输运；ii)模拟双周期或包含两个或两个以上特征尺度的多孔介质；iii)研究部分饱和多孔介质中的流动和弥散。

9407008 AVELLANEDA This project concerns the study of flow and dispersion in porous media, in particular the estimation of the physical properties of porous media such as permeability and the hydrodynamic dispersion coefficient of solutes. There has been considerable effort devoted to exploring correlations between such physical properties as diffusional relaxation times, conductivity and sound velocity, and the hydrodynamic permeability and dispersion coefficient. These macroscopic constants are linked because they arise by solving similar equations on the same microstructure. We will construct bounds and estimators of permeability and dispersion coefficient based on knowledge of more easily measured properties. This problem has been studied for some time, and was pioneered in work by Schlumberger scientists. The transport and dispersion of solutes in porous media will be analyzed through analysis and numerical calculation of different microstructures, e.g. networks of capillaries or intergranular space. We will perform theoretical and numerical studies in which we will concentrate on the following issues: i) building efficient numerical algorithms for modelling 3D transport in porous media, ii) modelling porous media which are bi-periodic or contain two or more characteristic scales, iii) studying flow and dispersion in partially saturated porous media.