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

小行星9407008 该项目涉及多孔介质中的流动和分散的研究，特别是多孔介质的物理性质，如渗透率和溶质的流体动力学分散系数的估计。 已经有相当大的努力致力于探索之间的相关性，如扩散弛豫时间，电导率和声速，以及流体动力学渗透率和分散系数等物理性质。 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类似方程而产生的。 我们将构造边界和估计的渗透率和弥散系数的基础上更容易测量的属性的知识。 这个问题已经被研究了一段时间，并由斯伦贝谢科学家在工作中率先提出。 溶质在多孔介质中的输运和分散将通过不同微观结构的分析和数值计算来分析，例如毛细管网络或颗粒间空间。 我们将进行理论和数值研究，其中我们将集中在以下问题：i）建立有效的数值算法，模拟多孔介质中的三维运输，ii）模拟多孔介质是双周期或包含两个或更多的特征尺度，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.