  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.
