# Implicit versus Explicit

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 August 8, 2006, 23:00 Implicit versus Explicit #1 Deepak Guest   Posts: n/a Hi pals, Yesterday i had a big discussion on implicit vs explicit with my Senior.but we r not able to conclude and distinguish it completely.My understanding in this is all that Anderson has explained in his book "CFD-Basic with applications".. I want u people to Give me some basic ideas in this regard.Like whats special abt implicit and explicit schemes,which have what advantages,which can be used wher?.Numerical problems in each of the schemes...like that Any help will be well appreciated... Thanks in advance, Deepak Student..

 August 9, 2006, 05:53 Re: Implicit versus Explicit #3 Deepak Guest   Posts: n/a Thanks a lot rajesh for this nice enlighting article on this topic.Its really gave me a basic idea. Can we clearly distinguish that explicit method is used for these kinda problems and implicit for some other category.Or all problems can be solved by both the methods... Then if iam not wrong,explicit methods r more suitable for transient simulations,right?....

 August 9, 2006, 06:21 Re: Implicit versus Explicit #4 Tom Guest   Posts: n/a "However, for unsteady solvers, the implicit schemes cannot be used as such. Implicit schemes actuallt exploit the ideas of ``inconsistent linearisation" and does not bother about the temporal accuracy, as steady state problem is not time-dependent." This is generally untrue - a correctly implemented implicit scheme such as Crank-Nicolson is time accurate (2nd Order). Basically you just need to ensure that your iterative scheme converges to a solution of the nonlinear difference equations at each timestep. You also need to account for the type of pde you are solving. For parabolic equations such as the the heat equation and unsteady Navier-Stokes equations implicit methods treat the single characteristic direction (time) consistently while explicit schemes do not (this is why explicit schemes have stability constraints when applied to diffusion problems). A simple problem that highlights a problem with explicit methods is to use a forward Euler step to solve the heat equation with a prescribed time dependent wall condition - in this case you can step the solution forward a single time step without knowing the wall value at the end of the step! That is to say the solution one grid point from the wall does not know the wall temperature has changed. This is inconsistent with the continuous form of the equations. o_mars_2010 likes this.

 August 9, 2006, 07:16 Re: Implicit versus Explicit #5 Mani Guest   Posts: n/a >explicit methods r more suitable for transient simulations,right You got the general idea, but that statement should not be regarded as generally true. To put it in simple terms: There are two considerations that determine the maximum allowable time step: a) stability, b) solution accuracy. Explicit methods are more efficient if b) dominates over a), i.e. if the solution accuracy requires such a small time step that stability will never be an issue and an implicit method is simply not necessary. Implicit methods are more efficient in cases when the time step can be increased beyond the explicit stability method because the important time scales of the flow are so large that even large time steps give you a good solution (steady state is the extreme). DaveyBaby likes this.

 August 9, 2006, 08:20 Re: Implicit versus Explicit #6 Renato. Guest   Posts: n/a Just to put some other possibilities in this thread. You can have a tradeoff between the good properties of both worlds (implicit/explicit). For further details, I suggest you take a look in the following articles: Souza DAF, Martins MAD, Coutinho ALGA, Edge-based adaptive implicit/explicit finite element procedures for three-dimensional transport problems, Communications in Numerical Methods in Engineering, 2005 21(10): 545-552 Hughes TJR, LIU WK, Implicit-explicit finite elements in transient analysis: stability theory. Journal of Applied Mechanics 1978 (45):371-374 Hughes TJR, Liu WK, Implicit-explicit finite elements in transient analysis: implementation and numerical examples. Journal of Applied Mechanics 1978 (45):375-378 Tezduyar TE, Liou J. Adaptive implicit-explicit finite element algorithms for fluid mechanics problems. Computer Methods in Applied Mechanics and Engineering 1992, 95(8):397-440 DaveyBaby likes this.

 August 10, 2006, 03:50 Re: Implicit versus Explicit #8 Tom Guest   Posts: n/a "It is therefore necessary to make use of some suitable idea, such as Dual Time Stepping which constructs a pseudo-steady problem in dual time,..." Just a comment - Not all steady state/implicit solvers use psuedo-time stepping. Two common iterative methods as taught in maths courses those of Newton and Picard. Neither of these are psuedo-time stepping methods (you could try to reformulate them as such but that would be missing the point of the method). As an example when you solve a linear elliptic problem (which arises as the steady state of a parabolic equation) do you consider solution methods such as BiCG, GCR(k), etc as psuedo-time marching schemes? I know I don't.

 August 10, 2006, 05:23 Re: Implicit versus Explicit *NM* #10 jj Guest   Posts: n/a

 August 17, 2006, 21:42 Re: Implicit versus Explicit #11 Sneha Raj Guest   Posts: n/a Hi all, They say even in implicit we can give time based load similar to explicit, then where exactly the difference lies? We usually think that explicit is time based n implicit is not, but what is the exact definitions for these two, can anyone pls help me out. I have carried out both Linear static as well as crash as of now.But I get confused about it when ever we have a discussion about it. regards, Sneha

 August 17, 2006, 22:53 Re: Implicit versus Explicit #12 Deepak Guest   Posts: n/a hi The difference lies in the factors of time step we can give for quick convergence.U can give any time step in implicit,but it ll affect ur convergence after a certain extent. thats why its always better to be in a safer side and give it as a multiple of explicits time step.But in explicit the time step is limited.U cant go beyond that otherwise u have to compromise with the stability of the particular scheme.. The main difference is the post no 4 by mani..a nice explanation of the application of both the schemes. i thk this ll help u,otherwise let us no, with regards, Deepak

 September 6, 2006, 21:12 Re: Implicit versus Explicit #13 Sneha Raj Guest   Posts: n/a Hi Deepak, Thanks for the response. I do understand that there is an empherical formula for calculating the time step for explicit analysis. How do u go about it in implicit for an example. I also wanted to know about implicit and explicit applications. Like, to which domain does contact analysis belong to? Some guys speak about contact analysis in Nastran, where as its suppose to be implicit, right? I get confused with these sort of questions. Is it that in implicit, Mass matrices and K matrices are calulated for only 1 time and in explicit for every incriment of time step we have specified. Hope u got what my doubt is? I am very new to this forum. Will try to search the link u specified. (Post 4 by Mani). Regards, Sneha

 September 9, 2006, 09:42 Re: Implicit versus Explicit #14 Deepak Guest   Posts: n/a Dear Sneha, I ll soon come with more descriptive answers to your questions.By that time i ll suggest you to go thro the previous posts one implicit and explicit method. Thanks and with regards, Deepak Thirumurthy

 September 10, 2006, 21:43 Re: Implicit versus Explicit #15 Sneha Raj Guest   Posts: n/a Sure. Will be waiting for your reply. Thanks

 September 12, 2014, 00:27 implicite vs explicite #16 New Member   VIJAY BHENDWADE Join Date: Sep 2014 Posts: 1 Rep Power: 0 is alternate direction implicite approach (ADI) unconditionally stable or not? -VIJAY BHENDWADE (student)

 November 29, 2014, 20:54 #17 Member   Join Date: Mar 2013 Posts: 42 Rep Power: 13 well this was quite the in depth explanation...

 November 7, 2015, 13:14 #18 New Member   izzudinshah Join Date: Feb 2015 Posts: 1 Rep Power: 0 sorry guys, the chatters in years 2006 have passed away