Problems obtaining the correct contours for Lid driven cavity
 

Hi

I am solving the problem of lid driven cavity in C++. I have used the Finite volume discretization and I have used the Semi Explicit method for solving the problem. However, I am obtaining results that do not match with that of the ones already existing.

The results I plotted are about symmetric about the central vertical line where in that should not be the case. I tried running the code for a finer mesh and higher reynolds number only to encounter the same problem.

I checked my boundary conditions and they are as follows.

u, v = 0 at all the walls except at the top where u = 1
dp/dn = 0 at all the walls
dp'/dn = 0 at all the walls
p' = pressure correction


I have attached the U and V velocity contours and also the pressure contours that I have obtained.

Can someone help me figure out the problem? Any help will be appreciated

what about the Re number? what main differences you found from the Ghia & Ghia benchmark?

I carried out this simulation at reynolds number 100. I tried for various reynolds number but still got similar plots for all the cases.

I have attached the correct solution of the problem which is also the same as that given by Ghia.

I am unable to figure out the problem causing the u velocity contours to be symmetric about the central vertical line. As compared to the existing result, the nature is same only that the contours are not inclined towards the corner in my solution.

if your solution is at Re=100, I see that the contour pattern is too specular as respect with the centerline x=L/2. That seems the convective does not enter into the solution. Are you sure you are gettin a steady state solution?

Yes, this is the steady state solution that I have obtained. I checked my convection flux equation a lot of times and couldn't find any error in that.

I also compared the magnitudes of the convection and diffusion fluxes and found that the diffusion flux was comparatively larger than the convection flux. But I can't figure out any solution to this since the error could be anywhere (even in my pressure correction equations or somewhere else)

I cross-checked all my equations and formulas and couldn't get the correct results yet.

I think I am missing out on something but I can't figure out what

Yes, this is the steady state solution that I have obtained. I checked my convection flux equation a lot of times and couldn't find any error in that.

I also compared the magnitudes of the convection and diffusion fluxes and found that the diffusion flux was comparatively larger than the convection flux. But I can't figure out any solution to this since the error could be anywhere (even in my pressure correction equations or somewhere else)

I cross-checked all my equations and formulas and couldn't get the correct results yet.

I think I am missing out on something but I can't figure out what

Using non-dimensional equations, the convective flux should be O(1), compared to the O(10^-2) of the diffusive one, irrespective of the pressare term.

That is exactly what I have not been able to solve. My convective flux is O(10^-3) of the diffusive one. Hence, the convective flux doesn't contribute much to the equations.

I'd really appreciate if anyone could help me with this problem. I want to know what could be the possible errors so that I can work on them.

As I previously wrote, the symmetry could be due to an error in the discretization of the convective terms