Corner no slip B.C
I am confused baout setting the noslip boundary condition at corners. For a wall between control volumes cells 1 (adjacent to the wall) and 2 (within the wall) I am using
u(1) = 0
v(1) = 0
P(1) = P(2)
rho(1) = rho(2)
But what if I have a corner at (3,3) would it be rewritten as
u(3,3) = 0
v(3, 3) = 0
P(3, 3) = P(4,4)?
Any comment is appreciated
My 5 cents: Corners generally creat singularity. However, in primitive variable formultion, the singularity fades away as the resolution of the grid increase. In my code I don't set a separate b.c. for the corners. In the early days, I used to worry like you and once come up with a formulation for the corners. The performance of the code didnt improve. In fortan vectorized format, for instance I set v(1,:,:)=0 if the velocity at the left is zero.
I have benchmarked my code with differnt flow and heat difusion benchmarks and it works fine.
Saying that, however if you use vorticity streamfunction formulation, the corner is a big issue, in which a lot has been written about. Infact many claim this is the drawback of this formulation as opposed to primitive variable formualtion. If needed I will cite the references that claim this.
But if you are not convinced yet, maybe extrapolate the values from the interior nodes, everytime afetr updaing (relaxing) the quantities. for instance v(1,:,:,)=2*v(2,:,:,)-v(3,:,:,), assuming uniform grid and Neuman condition, (but might work also for non uniform grid)
Yeah I get massive values for vorticity near the nozzle wall corners when I am simulating supersonic jets. Culd you provide me with some references that discusses this. That would be great!
Numerical Solutions of 2-D Steady Incompressible Flow in a Driven Skewed Cavity, E. Erturk, B. Dursun
ZAMM - Journal of Applied Mathematics and Mechanics 2007, Vol 87, pp 377-392
The above article gives references on the treatment of corner vortices for a driven lid cavity problem.
Hope it helps.
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