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

 September 5, 2006, 14:27 Need your help! #1 hawk Guest   Posts: n/a Hi! All. I am quite confuesed by the argument from the following link. http://www.flow3d.com/Cfd-101/impvexp.htm It is on the accuracy of Implicit and Explicit Methods. In my opinion, if both are the first order Euler scheme, either implicit or explicit will have the error of the same order. But from the statement in the above webpage, it seems that implicit is more inaccuracy even with the same time step, which, of course, satisfies the stable condition for explicit method. Could you give me more explanation? Thank you very much.

 September 5, 2006, 22:42 Re: Need your help! #2 deepak Guest   Posts: n/a hi, a very crude idea reg this,we can take explicit method as direct method for solving eqns resulting in exact solution like solving system of eqns using some analytical method. And implicit method as an iterative process,which as a result of convergence, results to solution nearer to exact soln. (pls correct me if my intuition is wrong).. But implicit has its own advantages compared to explicit..u can refer to our previous discussions reg the same. hope this will help u.. thanks and with regards, Deepak Thirumurthy

 September 6, 2006, 02:34 Re: Need your help! #3 Ahmed Guest   Posts: n/a Accuracy, is not only a function of the order of the scheme but it depends also on the number of mathematical operations needed to arrive to a solution. each operation adds a rounding error (unavoidable), I leave thr rest of the sentence to you

 September 6, 2006, 07:37 Re: Need your help! #4 Mani Guest   Posts: n/a The argument rests on the supposedly necessary under-relaxation in the implicit method. I cannot comment on that as I have never used the first order Euler scheme (and I don't know who would). There are some other arguments in this article that make me question the experience of the author. For example: "Another general rule is that the time-step sizes for explicit stability and accuracy are usually equivalent." This is complete nonsense. I can imagine cases like that but it's certainly not a "general rule" and I wouldn't say it's "usually" the case. There are plenty of unsteady flows where the time scales of interest are way larger than the explicit stability limit. Explicit methods as useless for those cases.

 September 9, 2006, 14:57 Re: Need your help! #5 Jitendra Guest   Posts: n/a Mani, I believe what the Author is trying to say that "If Explicit Scheme is stable for a particular time step, its usually accurate too... " This is not the case with Implicit case, as you rightly said due to under-relaxation paramter. It makes pretty much sense to me, with my limited experience with these schemes. As far as unsteady flows are concerned if we have time step for which explicit scheme is stable (and is small as compare to time scale of interest) you can still use the scheme. In fact for a Vortex Shedding case I solved both with explicit and implicit schemes. I found explicit scheme to give better accuracy although at the compromise of CPU time reqd. Regards, Jitendra

 September 11, 2006, 08:47 Re: Need your help! #6 Mani Guest   Posts: n/a The author is saying that the requirements for accuracy and explicit stability are equivalent, and that's not generally the case. In cases like your vortex shedding example, the time steps required for accuracy are much larger (somewhat depending on Reynolds number, laminar versus turbulent flow) than the time step required for explicit stability on the very fine grid used for this type of flow. Of course, it's possible to use an explicit scheme. The question is: Is it efficient? If you could use a time step of 1 with an implicit scheme, because that's all you need for accuracy, but you have to go down to 1e-3 with your explicit scheme, your explicit approach is likely less efficient than the implicit one (that's what I meant by 'useless' in such cases). I cannot say why you got different accuracy using the explicit vs implicit scheme. That depends on a lot of parameters such as type and order of the scheme, size of time step, convergence, grid resolution, a.s.o. The proper way to compare both is to a) compare the computational runtimes of both methods required to get to the same level of accuracy b) compare the accuracies of both methods running the same amount of clock-time per vortex shedding period

 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

All times are GMT -4. The time now is 10:02.