2D convection solutions

prapanj

hi I am trying to solve a @D convection equation(circular convection)....

Ut+yUx-xUy=0 in [-1,1]x[0,1] with boundary U(x,0)=0 for x<-.65

=1 for -.65<x<-.35

=0 for x>-.35

The charactersitcs must be circular. I use finite volume flux splitting scheme. First order.

And i got a contour plot in which the left half of the image had circular solution(one quarter of a circle). In the right half of the solution, the lines became straight and horizontal. and they ran upto the right boundary.

Do you think the problem was with my code? or is it the method. What second order methods can i use? thank you.