1a. Maybe I am confused with the term “scaled”. What exactly do you mean? By scaling, I assume non-dimensionalise, which I understand for the current problem, therefore I cannot see why we cannot write the system with the Reynolds number term.
1b. So do you mean just scale the lengths?
2. To create the mesh (as I said in a different post), I use the generate_mesh function as
# Define geometries
domain = Rectangle(Point(0,0),Point(L,H))
#circle = Circle(Point(-0.5,0.5),r)
circles = [[r,x0, y0]]; circles = np.array(circles)
for circle in circles:
circleD = Circle(Point(circle[1:]), circle[0], 60)
# Set subdomains
domain.set_subdomain(1,circleD)
# Create mesh
mesh=generate_mesh(domain,60)
So N=60, but does that mean that I have 60 points across H and L? As I said in the post above, when L is larger than H, there are less and less points between 0 and H, and I can end up with points only on the boundaries. Also, I can’t tell if the mesh is uniform or not. I definitely not have a unit square since L will be larger than H.
So using CFL for N=60, u=0.05 and H=0.001 I get a \Delta=3\times 10^{-4} which I think is very small? And I tried that too (just have increasing the number of time steps) with no luck, meaning the maximum velocity (printed at every time step) is not stable (alternates between 0.2 and 9e-5).