I really want to contact you in private even Skype chat or anything you want please. I want to hit a wall with my confused head.

Why stam uses the normal derivative equals zero and Bridson uses the normal derivative of pressure to be different in page 83 in his book

Where can I read more about this? I don't find any paper say something clear about what is a boundary condition!!!

I still don't understand everything. Why can't I use set_bnd in staggered grids? What's the tangential component and how can I code some function like set_bnd to enforce the slip boundary? (yes or no) Does the velocity boundary condition whether it's slip or no slip affects the normal derivative of pressure? I mean that if slip, the normal derivative will be like Bridson stated and in no slip, it will be just zero?

Another thing please, Stam says that the normal derivative of pressure should be zero in stick condition but Bridson says a difference thing in equ in the secondary edition book you told me about. Is the normal derivative of pressure different in the two cases? I would like to add you on Facebook or something

Also there is no code implementing the slip boundaries of velocity like the code of stam is implementing the no slip. I added this in an answer by mistake lol

Now I understand how stam realizes the velocity boundary condition on an allocation grid. Can we use his implementation in a staggered grid? I still don't understand the relation between forcing the normal derivative to be zero in the way stam is doing and the equation that Bridson derives of the pressure at boundaries. Bridson says that when we subtract the pressure gradient with the velocity of the slip boundary conditions it will just enforce the pressure boundary but he didn't explain why. One time I asked someone and he told me that it's prescribed in the momentum and I didn't understand

Sorry, Bridson changes the equations so that they fit the boundary conditions for the pressure and the velocity. Now i understand this. But how can we implement the free slip boundaries?

Actually stam doesn't imply the boundaries in the matrix of the pcg like the math. He just finds the values of the pressure and the velocity that applies the boundaries and put them in the matrix. Actually I see not the code of the no slip of Stam which I will try to understand (the set_bnd and how it works according to the paper of cpu gems) but I didn't find a way for the free slip or no stick condition in which the fluid moves freely in the tangential direction. Thanks for your answers again and again. I would like to chat with you at any time.

If you see Stam code, you will see that he applied the boundaries as mentioned here in GPU GEMS Equation 17 and 18. developer.download.nvidia.com/books/HTML/gpugems/…. But Bridson derives a formula to calculate the pressure of the boundary cells dependant on the velocity which is in the SIGGRAPH paper i mentioned above in chapter 4 equation number 4.10

Firstly, thank you for your detailed answer. Stam applies a no slip boundary condition for the velocity and Bridson applies slip boundary condition. I don't have a problem with the velocity right now. I am sorry I didn't put the code because i thought it's in the paper. The problem is at the pressure boundary condition which is indeed a neuman (the normal derivative of p is just zero) and it's applied in the projection step but stam applies it in a different way from Bridson. If you see the code of stam (I will modify the question to add it), TBC in the next comment

Why can't I use the same technique in the PCG Method? I mean the set_bnd

Really thanks for this detailed answer. Can you read Bridson paper who has a different way of boundaries from Stam's one and I can't relate them. Another thing, can we just evaluate the values of the velocity and pressure at the boundaries then put the values directly in the matrix?