Transport Equation in 2D

The following is the simulation of the following non-diffusive transport equation in 2d :

(d/d_t)F+(d/d_x)*F+2*(d/d_y)*F = 0

on the square -1<=x<=1, -1<=y<=1, for 0<=t<=1. The exact solution is specified along the sides with y=0 and x=0. The extrapolation conditions v(n+1,L,m)=v(n,L-1,m) and v(n+1,l,M)=v(n,l,M-1) have been applied along the sides x_L=1 and y_M=1, respectively. The exact solution is :

u(t,x,y)=u₀(x-t, y-2t)

with :

u₀(x,y) = (1-2|x|)(1-2|y|) if |x|<=0.5 and |y|<=0.5 ; 0 otherwise

The explicit method have been used.

Last modified 22/12/99 by Juan de Lara ( Juan.Lara@ii.uam.es, http://www.ii.uam.es/~jlara) need help for using this courses?.