Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic response of geo-materials have been developed, but require the repeated solution of the small-scale problem and provide the motivation for this work. We present an efficient computational method to study fluid flow and solute transport problems in periodic porous media. Fluid flow is governed by the Stokes equation, and the solute transport is governed by the advection–diffusion equation. We follow the accelerated computational micromechanics approach that leads to an iterative computational method where each step is either local or the solution of a Poisson’s equation. This enables us to implement these methods on accelerators like graphics processing units (GPUs) and exploit their massively parallel architecture. We verify the approach by comparing the results against established computational methods and then demonstrate the accuracy, efficacy, and performance by studying various examples. This method efficiently calculates the effective transport properties for complex pore geometries.

中文翻译：

---

多孔介质中溶质传输的加速计算微观力学

可渗透多孔介质中的反应输运与多种应用相关，但由于长度和时间尺度的范围而提出了重大挑战。旨在将微观结构与地质材料的宏观响应联系起来的多尺度方法已经被开发出来，但需要重复解决小尺度问题，并为这项工作提供了动力。我们提出了一种有效的计算方法来研究周期性多孔介质中的流体流动和溶质传输问题。流体流动由斯托克斯方程控制，溶质输送由平流扩散方程控制。我们遵循加速计算微观力学方法，该方法产生迭代计算方法，其中每个步骤要么是局部的，要么是泊松方程的解。这使我们能够在图形处理单元 (GPU) 等加速器上实现这些方法，并利用其大规模并行架构。我们通过将结果与已建立的计算方法进行比较来验证该方法，然后通过研究各种示例来证明其准确性、有效性和性能。该方法有效计算复杂孔隙几何形状的有效传输特性。