[amin144]

Hi to everyOne

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

TNX very Much

[amin144]

No any answer?

[cfdnewbie]

Originally Posted by amin144

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!

[FMDenaro]

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

[amin144]

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

[amin144]

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

[FMDenaro]

Originally Posted by amin144

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?

[amin144]

Absolutly yes

[amin144]

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

[cfdnewbie]

Originally Posted by FMDenaro

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

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

[FMDenaro]

Originally Posted by amin144

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

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.

[FMDenaro]

Originally Posted by cfdnewbie

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

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

[amin144]

Originally Posted by FMDenaro

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.

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

[cfdnewbie]

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?

[FMDenaro]

Originally Posted by cfdnewbie

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

[FMDenaro]

Originally Posted by amin144

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

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

[amin144]

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

[FMDenaro]

Originally Posted by amin144

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

[amin144]

Originally Posted by FMDenaro

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

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?

[FMDenaro]

Originally Posted by amin144

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.