Required solution of Buckley Leverett problem
Hi all, I am in need of the exact solution of Buckley Leverett problem. Thanks, Ritesh

Re: Required solution of Buckley Leverett problem
For a two/threephase flow: http://petroleum.berkeley.edu/papers/patzek/riemsol.pdf
For a twophase flow: the excellent book by Randall J. Leveque (P 48): "Numerical Methods for Conservation Laws" in 'Lecture in Mathematics' ETH Zurich ed: Birkauser 
Re: Required solution of Buckley Leverett problem
Thanks jessy for the references. I would like to discuss it with you, if you don't mind. Can we discuss it here on this forum or over mail <riteshkd@iitk.ac.in>. Thanks once again regards Ritesh

Re: Required solution of Buckley Leverett problem
Well I am not an expert at all on multiphase flows. Regarding hyperbolic systems however, if I can be of any help. It depends how much you know about these topics. Just tell me.
Regards. 
Re: Required solution of Buckley Leverett problem
Thanks for your reply, I also don't know much about multi phase fluid flow. In fact I am working on Numerical methods for hyperbolic conservation laws. I have desined a nonlinear TVD scheme for the nonlinear hyperbolic conservation laws. I have implimented it on 1D invisid Burger's equation and on BuckleyLeverett problem as test cases. Now in order to compare numerical results with the exact solution I need to know the exact solution of BuckleyLeverett problem. Meanwhile I have arranged the Leveque's book and started looking into it. I also don't have much idea about "what I have to show mathematically for my nonlinear scheme in order to show that it converges to the correct physically relevent solution ( Weak Solutions)". Till now I have done some work on linear schems and relaxation schemes. This is for the first time I am trying for nonlinear scheme. Can you help me about it.
regards Ritesh :) 
Re: Required solution of Buckley Leverett problem
I am having a look on the BuckleyLeverett equation. Can you tell me what you did so far as numerical experiments regarding the Burger's equation.

Re: Required solution of Buckley Leverett problem
I picked up the test problems on invisid Burger eq. given in the book Computational Gas Dynamics by Culbert B. Laney, Cambrdge University press (chapter 17). These test problems involves Shocks, rarefaction wave and contact discontinuty. So these problem can be considered as standared test problems as for as scalar conservation laws is concern. I have implimented TVD and several other schemes on these test problems and compared the results with exact soltuion of these problem obtained by method of lines.

Re: Required solution of Buckley Leverett problem
It seems that building up analitically the rarefaction fan (selfsimilar solutions) for the BuckleyLeverett equation is not that easy. Actually I had a look on the way of finding out selfsimilar solutions. The equation for a such a solution is non linear. And the first references I gave you do not help that much in solving this problem. As far as I see, some authors indicate algorithms for first solving numerically the Riemann problem for the exact equation. I got a couple of references (including a PhD dealing exactly with what you try to do). If you could give me your email address.

Re: Required solution of Buckley Leverett problem
Thanks Jessy for everything, My email id is riteshkd@iitk.ac.in. It will be very nice of you, if you could mail some references mentined in your previous posting.
Thanks once again Ritesh 
Hi. i am a Ph.D student and develop a code about multiphase flow with DG method.but my result in saturation equation are wrong.would you please a sample code about BuckleyLeverett problem ?

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