
[Sponsors] 
February 28, 2004, 20:03 
exact solution of burger's equation

#1 
Guest
Posts: n/a

can anyone help me getting exact solution of inviscid burger's equation?


February 29, 2004, 01:05 
Re: exact solution of burger's equation

#2 
Guest
Posts: n/a

For u_t + u u_x =0
we get u(x,t)=f(x  u(x,t)t) for any f(x). which gives us an implicit solution for u(x,t) but this solution can be used to obtain a slope in order to check the change of u wrt "x". Hope this helps 

February 29, 2004, 21:03 
Re: exact solution of burger's equation

#3 
Guest
Posts: n/a

hey rvndr i did not get exactly what you write. can u plz elaborate.


March 1, 2004, 06:12 
Re: exact solution of burger's equation

#4 
Guest
Posts: n/a

The characteristics of the Burger equation satisfy
dt/ds = 1, dx/ds = u, du/ds = 0 where s is a parameter along the characteristic. Initially (s=0) set t = 0, x= z, u=f(z), then we have (t=s) u=f(z), x = z + tf(z) Tom. 

March 1, 2004, 10:07 
Re: exact solution of burger's equation

#5 
Guest
Posts: n/a

You can also solve it using a ColeHopf transformation. Try doing a search on google for ColeHopf and burger's equation.


March 1, 2004, 10:32 
Re: exact solution of burger's equation

#6 
Guest
Posts: n/a

The HopfCole transformation is for the viscous problem and doesn't work in the inviscid case  unless you are suggesting solving the viscous problem exactly and then taking the limit of zero viscosity.


March 2, 2004, 00:52 
Re: exact solution of burger's equation

#7 
Guest
Posts: n/a

hi sajar,
Tom explained it nicely. Still if you have doubt post that PDE and let me solve that euation for you if I can. rvndr 

March 2, 2004, 00:57 
Re: exact solution of burger's equation

#8 
Guest
Posts: n/a

hi sajar,
Tom explained it nicely. Still if you have doubt post that PDE for which you want to know the exact solution and let me solve that euation for you if I can. rvndr 

March 3, 2004, 22:47 
Re: exact solution of burger's equation

#9 
Guest
Posts: n/a

The viscous and inviscid Burger's equations display markedly different dynamics in the shock region  are you sure that you can get to the inviscid solution with such a limiting process? I would guess not, but I haven't actually done it.


March 4, 2004, 05:55 
Re: exact solution of burger's equation

#10 
Guest
Posts: n/a

Yes you can  it's simple matched asymptotic expansions (see the book by Kevorkian and Cole and also Whitham's book on linear and nonlinear waves). Basically this is how shock capturing methods work in numerical models.


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Iterative solution to Poissons Equation  Phiper  Main CFD Forum  4  December 10, 2010 02:58 
Constant velocity of the material  Sas  CFX  15  July 13, 2010 08:56 
Does FOAM converge to exact solution in Laplace equation?  santiagomarquezd  OpenFOAM Running, Solving & CFD  0  March 26, 2010 08:52 
to find the exact solution of 1D Burges Equation  Tian Baolin  Main CFD Forum  3  May 13, 2003 04:34 
exact solution of acoustic equations  pran  Main CFD Forum  0  February 14, 2002 03:46 