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.

翻译：可渗透多孔介质中的反应输运与多种应用相关，但由于涉及多尺度时空范围而面临重大挑战。旨在关联微观结构与地质材料宏观响应的多尺度方法虽已得到发展，但需要反复求解小尺度问题，这构成了本工作的动机。我们提出了一种高效的计算方法，用于研究周期多孔介质中的流体流动与溶质输运问题。流体流动由斯托克斯方程控制，溶质输运由对流-扩散方程控制。我们采用加速计算微观力学方法，形成了一种迭代计算策略，其中每一步要么是局部操作，要么是泊松方程的求解。这使得我们能够在图形处理器（GPU）等加速器上实现这些方法，并充分利用其大规模并行架构。通过与现有计算方法的对比结果验证了该方法的有效性，进而通过多种算例展示了其精度、效率与性能。该方法可高效计算复杂孔隙结构的有效输运特性。