Enforcing global constraints for the dispersion closure problem: τ2-SIMPLE algorithm

IF 4 2区 环境科学与生态学 Q1 WATER RESOURCES
Ross M. Weber, Bowen Ling , Ilenia Battiato
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Abstract

Permeability and effective dispersion tensors are critical parameters to characterize flow and transport in porous media at the continuum scale. Homogenization theory defines a framework in which such effective properties are first computed from solving a closure problem in a repeating unit cell of the periodic microstructure and then used in a macroscopic formulation for efficient computation. The closure problem is formulated as a local boundary value problem subjected to global constraints, which guarantee the uniqueness of the solution and can be difficult to satisfy for complex geometries and at high flow conditions. These constraints also ensure that pore-scale pressure, velocity, and concentration fields can be accurately reconstructed from the closure variable. Building on previous work, here we present a framework that allows to satisfy global constraints associated to both the permeability and the dispersion closure problems by introducing two artificial time scales. The algorithm, called τ2-SIMPLE, computes both permeability and effective dispersion given an arbitrarily complex geometry and flow condition. This algorithm is demonstrated to be accurate for both 2D and 3D geometries across varying flow conditions, and thus it can be used to quickly characterize effective properties from porous media images in many applications.

强制执行分散闭合问题的全局约束:τ2-SIMPLE 算法
渗透性和有效弥散张量是表征多孔介质连续尺度流动和传输的关键参数。均质化理论定义了一个框架,在这个框架中,首先通过求解周期性微结构重复单元格中的闭合问题来计算此类有效特性,然后将其用于宏观表述以实现高效计算。闭合问题被表述为一个局部边界值问题,受到全局约束条件的限制,这些约束条件保证了解的唯一性,但在复杂几何形状和高流动条件下可能难以满足。这些约束条件还能确保孔隙尺度的压力场、速度场和浓度场能够从封闭变量中准确重建。在之前工作的基础上,我们在此提出一个框架,通过引入两个人工时间尺度,满足与渗透率和弥散闭合问题相关的全局约束。该算法被称为 τ2-SIMPLE 算法,可在任意复杂的几何形状和流动条件下计算渗透率和有效弥散。实验证明,该算法在不同流动条件下对二维和三维几何形状都能准确计算,因此可用于在许多应用中快速描述多孔介质图像的有效特性。
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来源期刊
Advances in Water Resources
Advances in Water Resources 环境科学-水资源
CiteScore
9.40
自引率
6.40%
发文量
171
审稿时长
36 days
期刊介绍: Advances in Water Resources provides a forum for the presentation of fundamental scientific advances in the understanding of water resources systems. The scope of Advances in Water Resources includes any combination of theoretical, computational, and experimental approaches used to advance fundamental understanding of surface or subsurface water resources systems or the interaction of these systems with the atmosphere, geosphere, biosphere, and human societies. Manuscripts involving case studies that do not attempt to reach broader conclusions, research on engineering design, applied hydraulics, or water quality and treatment, as well as applications of existing knowledge that do not advance fundamental understanding of hydrological processes, are not appropriate for Advances in Water Resources. Examples of appropriate topical areas that will be considered include the following: • Surface and subsurface hydrology • Hydrometeorology • Environmental fluid dynamics • Ecohydrology and ecohydrodynamics • Multiphase transport phenomena in porous media • Fluid flow and species transport and reaction processes
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