Since 2004, supercomputer growth hasbeen constrained by energy efficiency rather than raw hardware speeds. Tomaintain exponential growth of overall computing power, a massive growth inparallelization is under way. To keep up with these changes, computationalfluid dynamics (CFD) must improve its strong scalability – its ability tohandle lower cells-per-core ratios and achieve finer-grain parallelization. Amaritime-focused, unstructured, finite-volume code (ReFRESCO) is used toinvestigate the scalability problems for incompressible, viscous CFD using two classicaltest-cases. Existing research suggests that the linear equation-system solveris the main bottleneck to incompressible codes, due to the stiff Poisson pressure equation. Here, these results are expandedby analysing the reasons for this poor scalability. In particular, a number ofalternative linear solvers and preconditioners are tested to determine if thescalability problem can be circumvented, including GMRES, Pipelined-GMRES,Flexible-GMRES and BCGS. Conventional block-wise preconditioners are tested,along with multi-grid preconditioners and smoothers in various configurations.Memory-bandwidth constraints and global communication patterns are found to bethe main bottleneck, and no state-of-the-art solution techniques which solve thestrong-scalability problem satisfactorily could be found. There is significantincentive for more research and development in this area.