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

[407008 . AVELLANEDA]该项目涉及多孔介质中流动和分散的研究，特别是多孔介质的物理性质的估计，如渗透率和溶质的流体动力分散系数。在探索诸如扩散弛豫时间、电导率和声速等物理性质与流体动力渗透率和色散系数之间的相关性方面，已经付出了相当大的努力。这些宏观常数是相互联系的，因为它们是通过在相同的微观结构上求解相似的方程而产生的。我们将根据更容易测量的性质的知识构造渗透率和色散系数的界限和估计。这个问题已经研究了一段时间，并由斯伦贝谢的科学家率先提出。通过对不同微观结构（如毛细血管网络或粒间空间）的分析和数值计算，分析溶质在多孔介质中的迁移和分散。我们将进行理论和数值研究，其中我们将专注于以下问题：i)建立有效的数值算法来模拟多孔介质中的3D输运，ii)模拟双周期或包含两个或更多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分散。

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.