AFiD-Darcy: A finite difference solver for numerical simulations of convective porous media flows

We present an efficient solver for massively-parallel simulations of convective, wall-bounded and incompressible porous media flows. The algorithm consists of a second-order finite-difference pressure-correction scheme, allowing the use of an efficient FFT-based solver in problems with different boundary conditions. The parallelization method is implemented in a two-dimensional pencil-like domain decomposition, which enables efficient parallel large-scale simulations. The original version of the code presented by van der Poel et al. (2015) [35] has been modified to solve the Darcy equation for the momentum transport, representative of porous media flows driven by buoyancy. Two schemes are implemented to treat the diffusive term of the advection-diffusion equation, namely a fully implicit and semi-implicit formulation. Despite exhibiting a higher computational cost per time step, the fully implicit scheme allows an efficient simulation of transient flows, leading to a smaller time-to-solution compared to the semi-implicit scheme. The implementation was verified against different canonical flows, and the computational performance was examined. To show the code's capabilities, the maximal driving strength explored has been doubled as compared to state-of-art simulations, corresponding to an increase of the associated computational effort of about 8 to 16 times. Excellent strong scaling performance is demonstrated for both schemes developed and for domains with more than 10^10 spatial degrees of freedom.我们提出了一种适用于对流、固壁约束不可压缩多孔介质流动大规模并行模拟的高效求解器。该算法采用二阶有限差分压力修正格式，可在不同边界条件下结合基于快速傅里叶变换（FFT）的高效求解器。并行化方案采用二维类笔式区域分解实现，可支撑高效的大规模并行模拟。本代码基于van der Poel等人（2015）[35]的原始版本进行修改，以求解表征浮力驱动多孔介质流动的动量输运达西方程。程序实现了两种用于处理对流扩散方程扩散项的格式，即全隐式格式与半隐式格式。尽管单时间步的计算成本更高，但全隐式格式可高效模拟瞬态流动，相较半隐式格式拥有更短的求解耗时。我们通过多种典型流动对该代码实现进行了验证，并测试了其计算性能。为展示该代码的性能上限，本次研究探索的最大驱动强度较现有前沿模拟提升了一倍，对应计算开销提升约8至16倍。针对所提出的两种格式，以及拥有超过10^10个空间自由度的计算域，本研究均验证了优异的强缩放性能。