  Fast and accurate numerical simulations are crucial for designing large-scale
geological carbon storage projects ensuring safe long-term CO2 containment as a
climate change mitigation strategy. These simulations involve solving numerous
large and complex linear systems arising from the implicit Finite Volume (FV)
discretization of PDEs governing subsurface fluid flow. Compounded with highly
detailed geomodels, solving linear systems is computationally and memory
expensive, and accounts for the majority of the simulation time. Modern memory
hierarchies are insufficient to meet the latency and bandwidth needs of
large-scale numerical simulations. Therefore, exploring algorithms that can
leverage alternative and balanced paradigms, such as dataflow and in-memory
computing is crucial. This work introduces a matrix-free algorithm to solve
FV-based linear systems using a dataflow architecture to significantly minimize
memory latency and bandwidth bottlenecks. Our implementation achieves two
orders of magnitude speedup compared to a GPGPU-based reference implementation,
and up to 1.2 PFlops on a single dataflow device.
