CFD Online URL
[Sponsors]
Home > Forums > Main CFD Forum

exact solution of burger's equation

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   February 28, 2004, 20:03
Default exact solution of burger's equation
  #1
sajar
Guest
 
Posts: n/a
can anyone help me getting exact solution of inviscid burger's equation?
  Reply With Quote

Old   February 29, 2004, 01:05
Default Re: exact solution of burger's equation
  #2
rvndr
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
  Reply With Quote

Old   February 29, 2004, 21:03
Default Re: exact solution of burger's equation
  #3
sajr
Guest
 
Posts: n/a
hey rvndr i did not get exactly what you write. can u plz elaborate.
  Reply With Quote

Old   March 1, 2004, 06:12
Default Re: exact solution of burger's equation
  #4
Tom
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.
  Reply With Quote

Old   March 1, 2004, 10:07
Default Re: exact solution of burger's equation
  #5
ag
Guest
 
Posts: n/a
You can also solve it using a Cole-Hopf transformation. Try doing a search on google for Cole-Hopf and burger's equation.
  Reply With Quote

Old   March 1, 2004, 10:32
Default Re: exact solution of burger's equation
  #6
Tom
Guest
 
Posts: n/a
The Hopf-Cole 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.
  Reply With Quote

Old   March 2, 2004, 00:52
Default Re: exact solution of burger's equation
  #7
rvndr
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
  Reply With Quote

Old   March 2, 2004, 00:57
Default Re: exact solution of burger's equation
  #8
rvndr
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
  Reply With Quote

Old   March 3, 2004, 22:47
Default Re: exact solution of burger's equation
  #9
Saverio
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.
  Reply With Quote

Old   March 4, 2004, 05:55
Default Re: exact solution of burger's equation
  #10
Tom
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.
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


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 09:56
Does FOAM converge to exact solution in Laplace equation? santiagomarquezd OpenFOAM Running, Solving & CFD 0 March 26, 2010 09:52
to find the exact solution of 1D Burges Equation Tian Baolin Main CFD Forum 3 May 13, 2003 05:34
exact solution of acoustic equations pran Main CFD Forum 0 February 14, 2002 03:46


All times are GMT -4. The time now is 00:42.