A cross-platform, high-performance SPH toolkit for image-based flow simulations on the pore scale of porous media

Efficient numerical simulations of fluid flow on the pore scale allow for the numerical estimation of effective material properties of porous media like effective permeability or tortuosity, among others. In contrast to time-consuming and often expensive laboratory tests, pore scale-resolved numerical simulations further enable the computational quantification of anisotropy of inherent material properties and the estimation of representative sample domains. Numerically calculated quantities are valuable in several fields, such as carbon dioxide sequestration, geothermal energy production and groundwater contamination remediation. Our specific pore scale-resolved simulation method directly based on images obtained from Micro X-Ray Computed Tomography (μXRCT) is based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) approach. SPH is a meshless Lagrangian method, highly suitable for modeling complex geometries and flow at moderate Reynolds numbers. Low Reynolds number flow, also denoted as creeping flow, is a typical scenario present in the above mentioned applications. However, SPH is computationally demanding, especially in simulations of large domains. To overcome these difficulties, we have designed a specific SPH module for the highly optimized HOOMD-blue Molecular Dynamics software. Our implementation supports single-phase flow, and targets both CPU and GPU clusters. Due to the high computational demands, scalability is essential to make the software practically usable, and our tests indicate that our implementation can scale almost ideally. We study a wide variety of test cases, which are not only representative for XRCT-based geometries, but for pore scale-resolved flow simulations in general. Additionally, we present a large-scale simulation investigating an unconventional high porous volcanic rock sample (Reticulite).

孔隙尺度流体流动的高效数值模拟，可对多孔介质的有效材料特性（如有效渗透率、迂曲度等）进行数值估算。相较于耗时且通常成本高昂的实验室测试，孔隙尺度解析数值模拟还可实现固有材料特性各向异性的计算量化，以及代表性样本区域的估算。数值计算得到的参数在诸多领域具有重要应用价值，例如二氧化碳封存、地热能开发与地下水污染修复。
我们所提出的专属孔隙尺度解析模拟方法，直接基于微X射线计算机断层扫描（Micro X-Ray Computed Tomography, μXRCT）获取的图像，以弱可压缩光滑粒子流体动力学（Smoothed Particle Hydrodynamics, SPH）方法为基础。SPH是一种无网格拉格朗日方法，非常适用于中等雷诺数下的复杂几何建模与流动模拟。低雷诺数流动（又称蠕动流）正是上述应用场景中的典型工况。
然而SPH的计算开销极大，尤其是在大区域模拟中。为解决此类难题，我们针对高度优化的HOOMD-blue分子动力学软件，设计了专属SPH模块。本实现支持单相流，可适配CPU与GPU集群。
鉴于计算需求高昂，可扩展性是保障该软件具备实际可用性的核心要素，我们的测试表明，该实现的可扩展性近乎理想。
我们测试了多种工况，这些工况不仅可代表基于XRCT的几何模型，也普遍适用于各类孔隙尺度解析流动模拟。
此外，我们还开展了针对非常规高孔隙火山岩样品（Reticulite，火山浮石）的大规模模拟研究。