Transport Equation in 2D

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

(d/dt)F+(d/dx)*F+2*(d/dy)*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 xL=1 and yM=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.

Theory pages:
Main page
FEM (i)
FEM (ii)
FDM (i)
Example pages:
1-d Heat Equation
2-d steady state Heat Equation
2-d Heat Equation
1-d non diffusive transport equation
1-d diffusive transport equation
2-d Non diffusive transport equation
Mesh generation with OOCSMP
Moving grids
Application pages:
Heating of two beams
Heating of two moving beams
Solving the equation Ut+Uxx+Uxy+Uyx=0
Solving the equation Ut+Uxx+Uxy+Uyx=0 using MGEN
Heat 1d using several outputs
Solving the Heat equation with a CA
Comparing a CA with the FEM
Gordon's sine equation

Other courses
Other pages

Last modified 22/12/99 by Juan de Lara (, need help for using this courses?.

The OOCSMP code - The SODA code