  In this article, I present recent methods for the numerical simulation of
fluid dynamics and the associated computational algorithms. The goal of this
article is to explain how to model an incompressible fluid, and how to write a
computer program that simulates it. I will start from Newton laws "$F = ma$"
applied to a bunch of particles, then show how Euler's equation can be deduced
from them by "taking a step backward" and seeing the fluid as a continuum. Then
I will show how to make a computer program. Incompressibility is one of the
main difficulties to write a computer program that simulates a fluid. I will
explain how recent advances in computational mathematics result in a computer
object that can be used to represent a fluid and that naturally satisfies the
incompressibility constraint. Equipped with this representation, the algorithm
that simulates the fluid becomes extremely simple, and has been proved to
converge to the solution of the equation (by Gallouet and Merigot).
