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Newbie question about explicit and implicit methods 

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May 13, 2015, 12:36 
Newbie question about explicit and implicit methods

#1 
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Rubén
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Hi! How are you?
I have a question about implicit and explicit methods. As far as I know, CFD solvers get a equation system and it is resolved iteratively. So, when we use an implicit approach, we have more than one values unknown, as we don't know anything about the next iteration step. But, if we use an explicit approach, we just don't know one value of our equation, doesn't we? We know the variables of our current iteration, and we calculate the value of the next iteration in our node using them. So, in explicit method we don't get a equation system. Is that true? CFD software which uses explicit methods doesn't solve equation system?? 

May 13, 2015, 15:25 

#2  
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Filippo Maria Denaro
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Quote:
in principle, you have always a system of equations, actually in explicit methods you have only a diagonal matrix so the system is decoupled. 

May 16, 2015, 09:56 

#3  
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Rubén
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So, why do we implement an iterative solver in that case? We could solve every equation separatelly in an exact way couldn't we? 

May 16, 2015, 18:01 

#4 
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Filippo Maria Denaro
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May 16, 2015, 18:50 

#5  
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Rubén
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Every book I have read about CFD talks about iterative solvers, not another ones. So, I came to the conclusion that CFD softwares only uses iterative methods in explicit and implicit methods. For example, in "The OpenFOAM Technology Primer" it is said that OpenFOAM implements iterative methods in order to solve the CFD problems. 

May 17, 2015, 03:29 

#6  
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Filippo Maria Denaro
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the iterative procedure in due to the nonlinear nature of the NS system... to understand better, start from simple test problem in which explicit and implicit methods can be tested, for example the parabolic heat equation. 

May 17, 2015, 10:12 

#7  
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Rubén
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As I understand, an incompressible problem is solved with iterations until it converges. But, every of this iterations contains an equation system which is solved with another iterative method with matrixes. It is an iteration method for solving equation systems in every iteration step of the problem, isn't it? So,I am talking about the iteration method used to solve this matrix equation system . As far as for explicit methods we obtain a diagonal matrix with every equation decoupled, we could solve every of them in an exact way, instead of dealing with matrices and their solving methods. What books say to me is that we solve this matrix iterating, no matter if we are dealing with an explicit or implicit method. 

May 17, 2015, 14:46 

#8  
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Filippo Maria Denaro
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I suppose you have to go deeper in studying the problem for incompressible flow... the pressure equation drives to a linear algebric system that is part of the problem, independently if you use explicit or implicit methods for solving the momentum equation. 

May 19, 2015, 07:14 
hi Yuby

#9 
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Biswajit Ghosh
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Look, in literature, by a implicit or explicit solver they mean whether the momentum equation is implicit or explicit.
For example, in SIMPLE the momentum is solved implicitly (to be more precise semi implicitly) where in MAC the momentum equation is being solved explicitly. But no matter whether your momentum equation is implicit or explicit, the pressure correction equation you solve is always of implicit type (because of the fact that it is a poisson equation). I guess by now you must have understand why you need to learn how to solve system of equation! BEST WISHES! 

May 20, 2015, 05:13 

#10 
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shahrooz
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Iterative methods are being used because we have used an approximation to make the nonlinear equations linear and then solve the linearized system of equations. That's why we use iterations in CFD and it has nothing to do with an scheme being IMPLICIT or EXPLICIT.


May 29, 2015, 13:16 

#11 
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Rubén
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Thank you everybody for your help!!
It's clear to me now! I'm extremely hapyy! 

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