[amin144]

Originally Posted by FMDenaro

the issue is not simple to explain in few words ... you need to distinguish if you are using an exact projection method or an approximate projection method. In the latter case you do not satisfy exactly div V =0 but only up to the magnitude of the local truncation error.
Try to read:

F.M. Denaro, On the application of the Helmholtz-Hodge decomposition in projection methods for the numerical solution of the incompressible Navier-Stokes equations with general boundary conditions, Int. J. Num. Methods in Fluids, 43, 2003

F.M. Denaro, A 3D second-order accurate projection-based Finite Volume code on non-staggered, non-uniform structured grids with continuity preserving properties: application to buoyancy-driven flows,Int. J. Num. Meth. Fluids, 52, 4, 393-432, 2006.

Also it's not simple to understand
I think transient flows are not easy to understand

Thanks Very Very much

[FMDenaro]

Originally Posted by amin144

Also it's not simple to understand
I think transient flows are not easy to understand

Thanks Very Very much

as a matter of fact, there is not much difference between steady or unsteady flows, the continuity equation is a constraint that does not have an unsteady term. I hope that the reading of those papers can help you

[amin144]

Originally Posted by FMDenaro

as a matter of fact, there is not much difference between steady or unsteady flows, the continuity equation is a constraint that does not have an unsteady term. I hope that the reading of those papers can help you

Thanks very very much Dear Filippo
A basically maybe very simple question:
If I discretize my equation like this:
(U_n+1 - U_n)/dt = f( U_n+1 )
And solve my equation with a iterative equation system solver, in first iterate I calculate a U that named U_n+1 but it’s not actually U_n+1
And in next iteration I replace U_n with U_n+1 and continue to solving problem,
Which means marching in TIME !!!!! and is not suitable because I don’t want to march in time till my iteration reach a true answer for U_n+1
This is a conceptual subject which confusing me. I think the problem is in discretizing and I should change it.

Is my question foolish and I’m wrong in a simple thing or it is a usual question?
What is the solution of this problem in CFD?

[FMDenaro]

As you can see, your way to integrate needs to face with the continuity constraint. I think you need to clarify the ideas about the existing methods such as simple,simplec, piso, fractional, etc. You will find some help starting the reading in the book of Ferziger & Peric. Once assessed the method you want to explore you can go more indeep the topic.

[sbaffini]

Dear amin,

i really reccomend to follow the suggestions from Filippo (Hi Filippo). However,to quote you, "you are wrong in a simple thing".

That is, when you need to iterate at FIXED time in:

U_n+1 = U_n + dt * f(U_n+1)

because of the implicitness of f (and probably the non linearity), you don't have to touch U_n, the first term in the second member or, as you said, you would be advancing in time (which is not what you want).

At the end of the iterations your U_n+1 will satisfy the above relation with respect to U_n, which is what you want to achieve in a single time step dt. This is general and even apply to linear parabolic equations.

[FMDenaro]

Originally Posted by sbaffini

Dear amin,

i really reccomend to follow the suggestions from Filippo (Hi Filippo). However,to quote you, "you are wrong in a simple thing".

That is, when you need to iterate at FIXED time in:

U_n+1 = U_n + dt * f(U_n+1)

because of the implicitness of f (and probably the non linearity), you don't have to touch U_n, the first term in the second member or, as you said, you would be advancing in time (which is not what you want).

At the end of the iterations your U_n+1 will satisfy the above relation with respect to U_n, which is what you want to achieve in a single time step dt. This is general and even apply to linear parabolic equations.

Ciao ....

[amin144]

Originally Posted by sbaffini

Dear amin,

i really reccomend to follow the suggestions from Filippo (Hi Filippo). However,to quote you, "you are wrong in a simple thing".

That is, when you need to iterate at FIXED time in:

U_n+1 = U_n + dt * f(U_n+1)

because of the implicitness of f (and probably the non linearity), you don't have to touch U_n, the first term in the second member or, as you said, you would be advancing in time (which is not what you want).

At the end of the iterations your U_n+1 will satisfy the above relation with respect to U_n, which is what you want to achieve in a single time step dt. This is general and even apply to linear parabolic equations.

Hi Dear Paolo
You would be a good teacher
you are the first one that understood what i'm saying
my mistake was too simple as you said
I found it after reading Ferziger CFD book and I became sure after reading your post
Thanks very very much guys