Refrences about transient flow
 

Hi to everyOne

Can anybody introduce me some good refrences about simulation of transient flows?

TNX very Much

No any answer?

I guess your request is just too wide/general, there's so much literature about that out there, I guess it would be easier to help if you were more specific!

if you need a test-case, it exists an analytical benchmark of a 3d incompressible flow on periodic box

Thanks Dear cfdnewbie
I have some problem for undarstanding what should I do with Neuman B.C. in flow
for example in flow between 2 plates
in each step after solving we see continuity is not satisfied
I can't realize how should I correct Continuity without changing transient answer

Dear Filippo
Thanks for your reply
As I said I can,t understand some basic concept
I solve first step
and I see continuty is not satisfied
now what should I do?
my BC is Neumann and I have a fix value to itterate and reach it
I don't know how itterate to doesn,t going forward in time

are you using a fractional-step/projection method?

Absolutly yes

my BC is Neumann and I have a fix value to itterate and reach it
sorry:
my BC is Neumann and I DONT have a fix value to itterate and reach it

Oh, I would be interested in that one as well...could you provide more details, please? thank you!

well, after the prediction step for solving the non-solenoidal velocity V*, you use the Hodge decomposition of the vector field:

V* = Vn+1 + grad phi

Taking the divergence of both sides you get the "pressure equation", the BCs are obtained by projecting the decomposition along the normal unit vector.
The problem is well posed and has a unique solution a part a constant.

If you verify that the divergence-free constraint is not verified at the end of the steps, you probabily have fixed wrong BCs.

C. Ross Ethier and D.A. Steinman, ‘Exact fully 3D Navier–Stokes solutions for benchmarking’, Int. J. Numer.Methods Fluids, 19, 369 (1994).

Thanks for your complete reply
my problem I want know this basically
can you introduce me a refrence to study much more in detail?

thank you very much, I don't have access to the paper from home, but will check it out tomorrow. From the first page it looks like what they are doing might be a manufactured solution method (adding a forcing source term), is that asssumption correct?

you will see that the solution is unsteady and divergence-free in such a way that the time derivative, convection, pressure gradient and diffusion in the momentum equation balance each others

you need to start studyng some basical book such as that of Ferziger and Peric. However, you can take as the reference the well know paper of Kim & Moin on JCP http://chainarong.me.engr.tu.ac.th/d...CFD/59-308.pdf.

There are many recent papers on this topic you can read after you have basic knowledge of the projection method

Thanks Dear Filippo
Unfortunately some question haven't answered in any book and the key is finding someOne that have some works in this fields

the work of Kim & Moin is the starting point to understand the method, I think is useful for you...

I have also some of my papers discussing the property of the Hodge decomposition in the projection method, you can find them on the IJNMF

I studied the method and I am not very amateur
I saw in papers that neumann BC cause problem in continuty but I cant remember that paper unfortunately

if I understood good you are saying if everything be ok continuty should be satisfied even in case with neumann BC?

Have you any paper using this method in a simulation case?

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

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. :confused:

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?

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.

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 .... ;)

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