Can any body here experienced in solving lid-driven flow in a square cavity (just for viscous incompressible N-S equations) help me on setting the pressure boundary and initial conditions in detail, or details of the corresponding refferences? thank you very much.

If you were a student, you should ask your professor for such a simple question.

If you have a answer to his question you could respond..otherwise it is completely uncalled for you to suggest what he needs to do to get an answer to his question..and least of all who wants your opinion on whether the question is simple or hard!!!

thanks Magesh for your great reply.

well done

Well, I certainly know the answer for this basic and simple question. Do you know that?

The original Navier-Stokes equations only need a reference pressure datum.

thank every body. I know what non-slip condition means to pressure. and I suppose pressure at the left bottom node to be zero. and with pressure correction method, I let all the pressure to be zero at all nodes at the right begining. I am writing my own code. I began with this simple and basic example. I know the pressre correction process is the key one in such a method. My results of pressure distribution is not precision enough. if anybody have experience in making ones own code, please give me more detail suggestions and please do not like someone just laughing. thank again.

which formulation u r using, r u using primitive variable formulation or r u using vorticity-stream function formulation?

for pressure boundary u dont need to do anything i guess, on the boundaries the gredient will be zero.I mean the pressure on the boundary node shd be equal to the first node near the boundary. Read Anderson's book or Versteeg / Malasekera for this.

J-

JG, you are an expert who should participate only in an advanced level forum. we don't need your answers and your harsh comments.

Lets have a round of applause for JG.....The likes of you is not, in my opinion, welcome around here. This is a forum where simple ---> extremly hard questions can be posted. Respect all questions, you were at the beginning stage once.

J.

there is a very good reference for your problem the refrence is computantional methods for fluid dynamics by joe freizer good luck

Why I ask the question is that I used pressure correction method in my code making. And I let dp/dn=0 at all boundaries for the non-slip condition, and all p=0 at the right begining of my cal, and I fix p of the left bottom to be zero (or the mid point). For solving the problem efficiently, I began with an example of elleptic partial differential equations in a square domain with unit length. I compared my results of the problem with that of an existed difference code. although my results have the same trend with that of the difference method, there are errors of 15% at each point. and with the refinement of my element, the whole errors become smaller but the center point. I feel strange here. I think that is because it is a problem with one gaven stress point

(d/dx(du/dx)+d/dy(du/dy)=f(x,y); f(x,y)=0,or 2*JMAX**2(only at the mid point of the square domain,and JMAX means the total number divided in each direction), u(x,y)=0,at all bonudary).

Can any body help me with the problem or show me your answer of my example.

Maybe you can give us some more information?

Where are your variables located on your mesh? Velocities & pressure at the same points, velocities on cell edges, pressure in the center, or what?

What sort of algorithm are you using to solve the difference equations?

Patankar's famous techniques (and those from Imperial College - and earlier, from the Los Alamos Lab), use an iterative technique that solves the velocities, then determines the pressure correction from a Poisson equation derived from the continuity equation. Fixing the continuity throws the velocities out of balance, so the cycle is repeated until everything is balanced within an 'acceptable' tolerance. These are usually based on velocities located at cell edges, pressures in cell centers.

Good Luck!

Dear Park: I used Cholesky defracterization to solve the pressure poisson equations formed in the process of standard Galerkin process (FEM). My poisson equations were deduced from continuity equation. I plan to set the three on the same point(nodes). for solving the pressure poisson equations efficiently, I began with the example I mentioned. As the pressure solving is the key part of the whole solving process, I think if it can provide precise correction to velocity at each time step, the answer will be right, for I plan to set all the u,v,p at the right begining to be zero. Am I right? thank again

A. "Am I right?"

Can't say for sure. I've not done any FEM. It is encouraging that your solutions show the correct trends. Perhaps there is still a small bug someplace in the code?

B. " ... dp/dn=0 at all boundaries for the non-slip condition ... "

Perhaps you mean to say "no-flow"? Continuity is about fluxes across boundaries. I think the no-slip condition is set by u = 0 on the top or bottom (u = Uo on the moving boundary) boundaries, v= 0 on the left and right in the appropriate momentum equations. But, regardless of the word (slip or flow), the condition dp/dn = 0 that you've applied for the pressure is the correct one.

setting dp/dn=0 at the boundaries, I mean as the velocity are gaven, there is no need to modify u and v here and the pressure on the boundary equal its neighbour node at the normal direction. If you can, please give me more suggestions. Thank you from my heart.

I have no ways to access the books mentioned here. and I am a poor one.If anyone can help, please give me suggestions in details.thank alot

Helle,tommewang,

What do you mean ' and I fix p of the left bottom to be zero (or the mid point) ' ? Do you mean keep p fix at these places all the time during the iteration?

dp/dn = 0 is enough to determine the pressure at the boundaries. The fixing of pressure at some points will lead to pressure drifting in the field.

pressure BC is still in confusion even in the most respected literature of J. of Computational Physics.

for example, the pressure BC on wall is not a vanishing Neumann at all, which is a good approximation in when Re is high but wrongk for low Re. I derived this case, and found P.M.Gresho's 1987's article supports the same view.

pressure BC on non-walls are not fully determined.

I even doubt all appraoches, that applying normal component of mometum equation on boundary is sort of incorrect, I mean, they are all just approximate BC.