# bifurcation of numerical solution

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

 June 26, 2002, 12:46 bifurcation of numerical solution #1 yfyap Guest   Posts: n/a hi there, what is bifurcation and why it happens? i came across this term in curved duct flow studies, where it is used to explain the formation of two and more vortex solutions when the Dean number (similarity parameter) exceeds certain critical value. any information would be greatly appreaciated. thanks. regards, yfyap

 June 26, 2002, 16:00 Re: bifurcation of numerical solution #2 Peter Attar Guest   Posts: n/a A bifurcating solution is one which does not exist over a range of parameter values(in this case the Dean number) but does exist when the parameter reaches a certain value. The point of bifurcation can usually be discerned by looking at the stability of the linearized problem. An example in structural dynamics is buckling..another in aeroelasticity is flutter.

 June 26, 2002, 21:04 Re: bifurcation of numerical solution #3 yfyap Guest   Posts: n/a Peter Attar, isn't it that there should be a unique solution when the Dean number is smaller than the critical value, and beyond that there are more than one solution? thanks. regards, yfyap

 June 26, 2002, 22:22 Re: bifurcation of numerical solution #4 Peter Attar Guest   Posts: n/a In the way I'm familiar with when the critical parameter value is reached there are a family of solutions of which some are stable and some aren't..numericallly you won't be able to see the unstable solution(s) though. I am not familiar with the case you are speaking of though. Perhaps you can point out the article which you are referring to.

 June 27, 2002, 04:51 Re: bifurcation of numerical solution #5 yfyap Guest   Posts: n/a hi peter, do you mean that when the critical parameter value is reached, there will be two or more distinct solutions for a given problem? if this is the case then, how do we decide which one is the solution for the physical problem that is modeled? or all the solutions are valid ? What will happen if beyond the critical parameter value? Actually, why bifurcation happens? i have two papers on bifurcation study of laminar flow in curved square ducts: Winters, K. (1987). "A bifurcation study of laminar flow in curved tube of rectangular cross section." J. of Fluid Mechanics, Vol. 180, pp. 343-369. Daskopoulos, P. and Lenhoff, .M. (1989). "Flow in curved ducts: bifurcation structure for stationary ducts." J. of Fluid Mechanics, Vol. 203, pp. 125-148. thank you. regards, yfyap

 June 27, 2002, 08:29 Re: bifurcation of numerical solution #6 Peter Attar Guest   Posts: n/a You should take a look at a text which deals with nonlinear ordinary ODE's..most will go over bifurcation theory in detail. Like I said there are a family of solutions but usually only one is stable..ie only one will persist with time. I'm only speaking from my personal experience in dealing with Limit Cycle Oscillations in aeroelasticity where at certain flow speeds a Hopf bifurcation will appear. I will take a look at those articles today and see what they are speaking of.

 June 28, 2002, 03:21 Re: bifurcation of numerical solution #7 versi Guest   Posts: n/a The bifurcation of solution is a characteristic of nonlinear dynamic system. When some parameters, say, Re or Dean number, exceeds a critical value, there may be multiple solutions of the system (Euler, N-S or other equations). There are may be more than one stable states in supercritical regime. Typical examples of flow bifurcation are cylindrical and spherical Couette flows. There much literatures on "flow bifurcation". A discretzied equation also forms a dynamic system. If it is good approximation to Euler or N-S, it will produces the same bifurcation. However, it may produce erroneous bifurcations of itself, or can not reproduce the bifurcation of original equation.

 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 makaveli_lcf OpenFOAM Running, Solving & CFD 3 September 11, 2013 12:44 chriswatt Main CFD Forum 0 February 15, 2011 22:32 msrinath80 OpenFOAM Running, Solving & CFD 9 July 22, 2007 02:58 liugx212 OpenFOAM Running, Solving & CFD 3 January 4, 2006 19:07 Paresh Main CFD Forum 0 September 17, 2003 16:03

All times are GMT -4. The time now is 05:51.