Hi team,

I have a question about the Rayleigh number that the basic statistics postprocessor returns. To demonstrate the question I’ve run the shell_simple_3d.prm cookbook with slight modification (I’m pasting the content of the parameter file below since as a ‘new user’ of the form I don’t seem to be allowed to add attachments). Following the equation in the manual, the material model should result in a Rayleigh number of 0.910e+07.

However, when running the parameter file it returns a Rayleigh number of 1.00e+07 (see log file). The reason for this is that the Reference density is returned as 3458.4 instead of 3300, which is the value of the material model. Looking at the simple material model, the reference density is returned as an average:

out.densities[i] = MaterialUtilities::average_value(volume_fractions, eos_outputs.densities, MaterialUtilities::arithmetic);

Given that the reference temperature is 1600, a density of 3458.4 is obtained at T = 0. I’m not really sure how this can be the average over any part of the model domain and is not reflective of the total average density. I don’t know the averaging function too well so wanted to check with you all if you see what’s going wrong. Why is the reference density not closer to 3300?

The difference in reference density also propagates into a reference thermal diffusivity that differs between what the log prints vs. what would be calculated based on the parameter file.

Thank you for your help!! The relevant part of the log file and the parameter file are pasted below.

Best,

Jacky

## relevant part of log file

## – This is ASPECT, the Advanced Solver for Problems in Earth’s ConvecTion.

– . version 2.2.0-pre (master, 729c918e1)

– . using deal.II 9.0.0

– . with 32 bit indices and vectorization level 1 (128 bits)

– . using Trilinos 12.12.1

– . using p4est 2.0.0

– . running in DEBUG mode

– . running with 1 MPI process

Number of active cells: 768 (on 2 levels)

Number of degrees of freedom: 28,690 (20,790+970+6,930)

*** Timestep 0: t=0 years

Solving temperature system… 0 iterations.

Rebuilding Stokes preconditioner…

Solving Stokes system… 118+0 iterations.

Postprocessing:

```
Model domain depth (m): 2.89e+06
Temperature contrast across model domain (K): 3000
Reference depth (m): 0
Reference temperature (K): 0
Reference pressure (Pa): 0
Reference gravity (m/s^2): 9.81
Reference density (kg/m^3): 3458.4
Reference thermal expansion coefficient (1/K): 3e-05
Reference specific heat capacity (J/(K*kg)): 1250
Reference thermal conductivity (W/(m*K)): 4.125
Reference viscosity (Pa*s): 7.72399e+21
Reference thermal diffusivity (m^2/s): 9.54198e-07
Rayleigh number: 1e+07
```

[…]

## Parameter file

# A simple setup for convection in a 3d shell. See the

# manual for more information.

set Dimension = 3

set Use years in output instead of seconds = true

set End time = 0

set Output directory = output-shell_simple_3d

subsection Material model

set Model name = simple

subsection Simple model

set Reference density = 3300

set Viscosity = 7.72399e21

set Thermal expansion coefficient = 3e-5

set Reference temperature = 1600

set Thermal conductivity = 4.125

set Reference specific heat = 1250

end

end

subsection Geometry model

set Model name = spherical shell

subsection Spherical shell

set Inner radius = 3481000

set Outer radius = 6371000

end

end

subsection Boundary velocity model

set Zero velocity boundary indicators = bottom

set Tangential velocity boundary indicators = top

end

subsection Boundary temperature model

set Fixed temperature boundary indicators = top, bottom

set List of model names = spherical constant

subsection Spherical constant

set Inner temperature = 3300

set Outer temperature = 300

end

end

subsection Initial temperature model

set Model name = function

subsection Function

set Function expression = 1.473e3

end

end

subsection Gravity model

set Model name = radial constant

subsection Radial constant

set Magnitude = 9.81

end

end

subsection Mesh refinement

set Initial global refinement = 1

set Initial adaptive refinement = 0

set Strategy = temperature

set Time steps between mesh refinement = 15

end

subsection Postprocess

set List of postprocessors = basic statistics

end