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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.

Alban Depoutre