I’m trying to run external flow simulations at very low Reynold’s numbers (i.e. Re<<1) where fluid momentum is completely unimportant and I know the Navier-Stokes equations are linear. The default solver/interpolation settings in Simscale have fairly low convergence rates. I was wondering if anyone knew which settings would best to change if I know the equations of motion are linear (and likely free from instabilities).
Hi there,
When dealing with simulations at very low Reynolds numbers where the flow is predominantly laminar and linear, there are specific adjustments and considerations you might want to make in your simulation settings to optimize convergence and accuracy.
You are right, the convergence settings (under-relaxation factors etc) have to be adjusted accordingly. Also, it is important to have a look at the mesh, the solver settings and the numerics (along with the tolerances).
Can you please share your project? It might be helpful to have a look 
Hello, thank you for the reply.
This is a link to the project: Low Re Aerodynamics
A bit of context: I’m a professor at the University of Delaware, developing a fluid mechanics assignment for our 3rd years students (optimize drag for low Re external flow). Right now, I’m just debugging it using a sphere as the aerodynamic object, designed to a low Re of about 0.0001 (mu = 1 Pa-s, sphere volume = 1m^3, rho = 0.0001 kg/m3, V = 1 m/s). There is known analytic result D = 6PimuVR which in this case works out to be 11.69 N. I’m also cutting the sphere into either 1/4 or 1/5 to exploit the axisymmetry (so I’m expecting Drag = 11.69N/4 = 2.9N (for 90deg wedge) or 2.3N (for 72deg wedge).
At this point, I’m not expecting to replicate that number, but I would like the simulations to converge with respect to a number in a reasonable number of iterations. I’ve tried a number of different meshes, all of which have good quality elements, and some which are quite fine. The residuals generally converge quite well, but the Result Control (i.e. Drag = Total Force in Y) doesn’t not.
I guess what I was thinking is that since I know this is a linear problem (mu*laplacian u - grad p = 0), there should be some way to coax the solver into solving in an almost direct manner and avoid a large number of iterations)
Hello,
I was able to get the default under-relaxation factors for velocity and pressure a bit higher (0.4 and 0.8). Also, I remeshed the geometry with near wall prism layers, a coarser overall level and a refinement on the sphere itself. The overall convergence is still pretty slow, but it is quicker than it was before. There may be some other solver settings that have a pronounced effect on this specific very low Re case, but I did not try playing with anything else.
Thanks,
–Nolan
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