Treat this as a "what do I need to do to make fluid flow that looks okayish in graphics" post rather than "how do I implement physics accurate CFD for industrial/scientific purposes" post.

Lots of points in there like

> "Air is an example of a compressible fluid; you squish it and it gets smaller. Water is an example of an incompressible fluid; you squish it and it pushes back, and doesn't get any smaller" (this only really depends on the Mach number, Ma>~0.3 and you are in compressible territory for any fluid. Incompressibility usually means we assume the divergence of velocity of zero)

> "Incompressible fluids are simpler to simulate because their density and pressure is always constant." (This is only true if you choose to adopt a grad P = 0 approximation)

are incorrect from a physics perspective.

If you look at what real incompressible Navier-Stokes solvers do [1], it's mathematically totally different from what this post shows. In fact, the part that this post omits (handle the pressure gradient term by first approximate time stepping the velocity term by ignoring the pressure term and then correct by solving a Poisson equation for the pressure residual, and then correct the velocity) is the most expensive step in incompressible solvers by far.

[1] https://en.wikipedia.org/wiki/Projection_method_(fluid_dynam...

Hate it when incompressible fluids are mentioned like it’s literally true with any qualification or explanation.

Iiuc water might compress ~50% at the right place in the Earth’s mantle, maybe just not looking much like liquid.