[Yuby]

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??

[FMDenaro]

Originally Posted by Yuby

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??

in principle, you have always a system of equations, actually in explicit methods you have only a diagonal matrix so the system is decoupled.

[Yuby]

Originally Posted by FMDenaro

in principle, you have always a system of equations, actually in explicit methods you have only a diagonal matrix so the system is decoupled.

Thank you for your answer Filippo!

So, why do we implement an iterative solver in that case?

We could solve every equation separatelly in an exact way couldn't we?

[FMDenaro]

Originally Posted by Yuby

Thank you for your answer Filippo!

So, why do we implement an iterative solver in that case?

We could solve every equation separatelly in an exact way couldn't we?

what explicit method are you using where an interative solver is required?

[Yuby]

Originally Posted by FMDenaro

what explicit method are you using where an interative solver is required?

I am not talking about an explicit method in concrete terms...

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.

[FMDenaro]

Originally Posted by Yuby

I am not talking about an explicit method in concrete terms...

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.

the iterative procedure in due to the non-linear 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.

[Yuby]

Originally Posted by FMDenaro

the iterative procedure in due to the non-linear 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.

I think I am not explaining my question in a correct way.

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.

[FMDenaro]

Originally Posted by Yuby

I think I am not explaining my question in a correct way.

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.

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.

[Alisha]

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!

[shahrooz.omd]

Iterative methods are being used because we have used an approximation to make the non-linear 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.

[Yuby]

Thank you everybody for your help!!

It's clear to me now! I'm extremely hapyy!