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?

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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 testcase, 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 
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are you using a fractionalstep/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 
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Oh, I would be interested in that one as well...could you provide more details, please? thank you! 
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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 divergencefree constraint is not verified at the end of the steps, you probabily have fixed wrong BCs. 
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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?

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you will see that the solution is unsteady and divergencefree in such a way that the time derivative, convection, pressure gradient and diffusion in the momentum equation balance each others 
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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 
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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 
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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? 
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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 HelmholtzHodge decomposition in projection methods for the numerical solution of the incompressible NavierStokes equations with general boundary conditions, Int. J. Num. Methods in Fluids, 43, 2003 F.M. Denaro, A 3D secondorder accurate projectionbased Finite Volume code on nonstaggered, nonuniform structured grids with continuity preserving properties: application to buoyancydriven flows,Int. J. Num. Meth. Fluids, 52, 4, 393432, 2006. 
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