# exact solution of burger's equation

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

 February 28, 2004, 20:03 exact solution of burger's equation #1 sajar Guest   Posts: n/a Sponsored Links 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 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

 February 29, 2004, 21:03 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.

 March 1, 2004, 06:12 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.

 March 1, 2004, 10:07 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.

 March 1, 2004, 10:32 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.

 March 2, 2004, 00:52 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

 March 2, 2004, 00:57 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

 March 3, 2004, 22:47 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.

 March 4, 2004, 05:55 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.

 Thread Tools Display Modes Linear Mode

 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 OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Phiper Main CFD Forum 4 December 10, 2010 02:58 Sas CFX 15 July 13, 2010 08:56 santiagomarquezd OpenFOAM Running, Solving & CFD 0 March 26, 2010 08:52 Tian Baolin Main CFD Forum 3 May 13, 2003 04:34 pran Main CFD Forum 0 February 14, 2002 03:46