Next:Resolution with a constant Up:The 2-D Burgers Equation Previous:Introduction   Contents

# The physical problem

We solve 2-D Burgers equation in a square field integration limited by . The u velocity depends of time because we consider an unsteady problem with two space variables : u=u(x,y,t)

2-D Burgers equation :

 (2.1)
with  the transversal velocity :

In order to trigger the shock, we take an initial condition sinus type in the x direction. We choose to deaden this sinus by an exponential term in the y direction. Thus, we will be able to see the propagation of the wave front in this direction :

Initial condition :

 (2.2)
In order to pose well the problem, we must define some boundary conditions. Those are four because this is a second order problem with two space dimensions.

The boundary conditions in x=0 and x=1 are fixed at zero, and these  in y=0 always corresponds to a sinus in order to cause the steepening of the wave front. On the other hand, to be compatible with the initial condition, the boundary condition in y=1 follows an exponential decreasing law of the sinus :

Boundary conditions :

 (2.3)

Initial condition on u velocity

(We can see this initial condition in his original size in clicking here)

The problem thus proposed is however not completely well posed because the advection v velocity is not defined. Precisely, one proposes in this study to test several cases for this transversal velocity.

Subsections

Next:Resolution with a constant Up:The 2-D Burgers Equation Previous:IntroductionContents

Alban Depoutre
2000-11-21