[aspect-devel] Far different velocity magnitudes & timestep sizes of the same Ra

[Shangxin Liu]

Hi;

Recently I'm trying the new Boussinesq approximation formulation of ASPECT
to test the 3D spherical shell time-dependent convection. I tried running
the non-dimensional cases and set the start time to 0 and end time to
1. Through a series of tests, I found that the same Ra but different
gravity and alpha have far different results of velocity magnitude and the
tilmestep size. For example, I fixed the Ra to 7000 and run three cases:

Case1: gravity 7000, alpha 1
Case2: gravity 70000, alpha 0.1
Case3:  gravity 700000, alpha 0.01
(All other parameters of these three cases in prm file are the same:
constant viscosity, CFL number=1, same solver tolerance, same spherical
shell geometry,etc..)

Case1 takes only 13 timesteps to reach the end time and the end RMS/Max
velocity is 0.00182/0.0055;
Case2 takes 20 timesteps to reach the end time and the end RMS/Max velocity
is 0.00558/0.0352;
Case3 takes 141 timesteps to reach the end time and the end RMS/Max
velocity is 0.0479/0.305.

They all ran on one node of our cluster but the running time is also
different:
case1: 999s
case2: 1.48e03 s
case3: 3.86e03 s

The end min/avg/max temperature and heat flux of upper/lower boundary of
the three cases are all the same.

>From ASPECT manual, I noticed that the time step size is inversely
proportional to the max velocity of the cell so such a huge difference of
tilmestep size must be caused by the difference of the velocity magnitude.
But in the non-dimemsioanl problem, the same Ra should have the same
magnitude of velocity. Why in ASPECT, the same Ra can have such different
velocity magnitude? I've realized that ASPECT uses the total pressure and
total density in its momentum equation, so larger value of gravity can
introduce a larger rho_0*g_0 term in the momentum equation. I'm not sure
whether this will cause the solver matrix of momentum equation going crazy.
Did anyone else run into this similar confusion? Wolfgang, Timo, Rene,
Juliane, any insight on this?

Best,
Shangxin
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