1. Mathematical model of a compressible or incompressible fluid

Depending on the physical context of the applications studied, these flows are not of the same nature, and before tackling the solution of the Navier-Stokes equations, it is necessary to define a certain number of notions commonly used in fluid mechanics.

A fluid is a material medium that is perfectly deformable when subjected to a force, i.e. it can take on the shape of the container in which it is located. Fluids include liquids, gases and plasmas. Gases and plasmas are highly compressible, i.e. they can be pressurized to change their volume; in other words, they can be compressed into a smaller space by exerting pressure on the fluid. Liquids, on the other hand, are not very compressible, only slightly more so than solids; they are said to be incompressible, i.e. their occupied volumes cannot be changed by exerting pressure on them; in other words, they cannot...