Claude-Louis Navier (1785–1836) and George Gabriel Stokes (1819–1903). Flow past a cylinder in a channel.
Inlet →Outlet →2U0
This is the incompressible case. The infographic labels its top equation “compressible”, but that form is the incompressible one. A true compressible flow also needs the density equation ∂ρ/∂t + ∇·(ρv) = 0, an extra term (ζ + μ/3)∇(∇·v), and an equation of state. Incompressible is accurate for water, blood, and air well below the speed of sound (Mach under about 0.3).
Name check: the mathematician is Claude-Louis Navier. “Jean Léonard Marie” is the name of Poiseuille, who studied blood flow in pipes.
2D slice. Real flow at high Reynolds number is 3D and turbulent. This sim shows the smooth (laminar) kind. Above about Re 200 treat it as a picture, not a prediction.
Grid limits. 160×64 cells. The solver adds a little extra numerical viscosity, so swirls can appear at a higher Re than in theory. The walls squeeze the flow (cylinder blocks up to 38% of the channel), which also shifts the Re where swirls start.
Open problem: nobody has proved that smooth 3D solutions always exist. That is a Millennium Prize problem. Computers still solve it well in practice.