Let us consider the case of a an unsteady and bidimensional flow of incompressible
Newtonian fluid not undergoing by any voluminal forces and any compressive
forces. Physically, no flow is at the base of such hypothesis, those being
too strong. But under these hypothesis, the Navier-Stokes equations, bases
of all problems in fluid mechanics, are simplified largely until obtaining
only one equation : the 2-D Burgers equation. The studied problem is a
model, but it makes us understand in a simple way phenomenons which can
arrived in reality in a complex form and are not always desirable : the
shocks. Those, under certain particular conditions, are due to the nolinear
terms intervening in the equations and in particular in the Burgers equation.
This is why we propose in this study to try to trigger the shock and then
to visualize it. For that, numerical methods will be used, based on finite-difference
schemes. The objectives are not to study a physical flow issue to the 2-D
Burgers equation, but just to study the impact of certain parameters (Reynolds
number) on the shock. Also, we will study the effect of the transversal
velocity on the propagation of the shock inside the field.