Designing large-scale geological carbon capture and storage projects and ensuring safe long-term CO2 containment - as a climate change mitigation strategy - requires fast and accurate numerical simulations. These simulations involve solving complex PDEs governing subsurface fluid flow using implicit finite-volume schemes widely based on Two-Point Flux Approximation (TPFA). This task is computationally and memory expensive, especially when performed on highly detailed geomodels. In most current HPC architectures, memory hierarchy and data management mechanism are insufficient to overcome the challenges of large scale numerical simulations. Therefore, it is crucial to design algorithms that can exploit alternative and more balanced paradigms, such as dataflow and in-memory computing. This work introduces an algorithm for TPFA computations that leverages effectively a dataflow architecture, such as Cerebras CS2, which helps to significantly minimize memory bottlenecks. Our implementation achieves two orders of magnitude speedup compared to multiple reference implementations running on NVIDIA A100 GPUs.

翻译：设计大规模地质碳捕集与封存项目并确保长期安全二氧化碳封存——作为减缓气候变化的一项策略——需要快速且精确的数值模拟。这些模拟涉及使用基于两点通量近似（TPFA）的隐式有限体积格式，求解控制地下流体流动的复杂偏微分方程。该任务在计算和内存方面成本高昂，尤其是在对高度精细的地质模型进行模拟时。在当前大多数高性能计算（HPC）架构中，内存层级结构和数据管理机制不足以应对大规模数值模拟的挑战。因此，设计能够利用数据流和内存计算等替代性且更均衡范式的算法至关重要。本文提出了一种用于TPFA计算的算法，该算法有效利用了数据流架构（例如Cerebras CS2），从而显著减轻了内存瓶颈。与在NVIDIA A100 GPU上运行的多个参考实现相比，我们的实现实现了两个数量级的加速。