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

For a two/three-phase flow: http://petroleum.berkeley.edu/papers/patzek/riemsol.pdf

For a two-phase flow: the excellent book by Randall J. Leveque (P 48): "Numerical Methods for Conservation Laws"

in 'Lecture in Mathematics' ETH Zurich

ed: Birkauser

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

Well I am not an expert at all on multi-phase 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.

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 non-linear TVD scheme for the non-linear hyperbolic conservation laws. I have implimented it on 1-D invisid Burger's equation and on Buckley-Leverett problem as test cases. Now in order to compare numerical results with the exact solution I need to know the exact solution of Buckley-Leverett 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 non-linear 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 non-linear scheme. Can you help me about it.

regards Ritesh

I am having a look on the Buckley-Leverett equation. Can you tell me what you did so far as numerical experiments regarding the Burger's equation.

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.

It seems that building up analitically the rarefaction fan (self-similar solutions) for the Buckley-Leverett equation is not that easy. Actually I had a look on the way of finding out self-similar 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.

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

[mj2286]

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 Buckley-Leverett problem ?

[mj2286]

Originally Posted by Rits
;37833

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.

my Gmail is: mehdi.jamei59@gmail.com