Dear Will,
Thanks for your message. We have applied the ACM solver to any internal flows, so it is interesting see your progress.
“What is the meaning of ma = 0.2? Do you mean the max velocity/ac-zeta? I think for ideal incompressible flow, ma = 0.”
I meant the Mach number of the real life application that your are trying to simulate. The pressure residual (div u), which is more stiff to converge than velocity residuals, is kind of an indicator how far the pseudo waves which distribute the pressure have travelled. For truly incompressible flows (elliptic p, residual = 0), the information from an arbitrary point would have to propagate everywhere in the domain within every physical time-step. However, since the physical problems are never incompressible, but low-Mach, it may not be necessary to drive the pressure residual all the way to zero as long as the information has propagated over important length scales. I understand if you want to reproduce an incompressible test case you want to be as incompressible as possible, but for low-Mach industrial applications this is not necessarily the case.
The residuals in your cases are still quite high and they would benefit from multip and BDF2. Just to give you some tips, I tend to keep constant number of iterations, set the dt/dtau ratio between 5 and 10, and aim for u,v,w < 1e-4 pressure typically < 1e-3 . For example, for a Taylor-Green vortex Re=1,600, the level of convergence after 3 multigrid cycles
[solver-dual-time-integrator-multip]
pseudo-dt-fact = 1.7
cycle = [(4, 1), (3, 1), (2, 1), (1, 1), (0, 2), (1, 1), (2, 1), (3, 1), (4, 3)]
is
1254,10.002000000000095,3,0.00244778059095,0.000476855091426,0.000476823492017,0.00043626471224.
Using the same cycle and again 3 cycles per time step, the convergence of turbulent Jet at Re=10,000 is
240000,1799.9950000010913,3,0.00204563896311,0.000209207025143,0.000196374204824,0.000183716409294.
I used dt/dtau = ~7 in both cases.
Please also note that it can take considerable amount of time to dissipate initial transient waves. I’m expecting this phenomenon to be highlighted with internal flows because the waves are trapped inside the domain. I would suggest developing the flow with P=1 and restart with higher P after the flow has transitioned to turbulent.
Cheers,
Niki