[aspect-devel] Aspect-devel Digest, Vol 12, Issue 3

Wolfgang Bangerth bangerth at math.tamu.edu
Mon Nov 19 12:27:46 PST 2012

I know it's terrible -- I don't recall who exactly sent me this input 
file (attached) and whether I modified it, but in any case I ran it over 
the weekend to see what happens to the boundary fluxes in the shell 
geometry. Attached is what I get from simply running this on 16 
processors for a *very* long time.

The two heat fluxes never reach a steady state -- rather, the jump up 
and down every time a plume detaches from the inner or outer boundaries. 
Looking at the solution picture (also attached), I'm not surprised that 
the heat fluxes don't coincide: it looks like the boundary layers are 
less than one cell width, and so we can not expect to resolve them 
accurately. Rather, the heat flux given by these numerical 
approximations is determined by the smallest length scale that can be 
resolved by the mesh -- and because this length scale is different for 
the inner and outer boundaries, the heat fluxes is different. (Of 
course, had we chosen a mesh where the radial resolution is the same at 
the two boundaries, we may have gotten results where the two heat fluxes 
match -- but are both completely wrong.)


Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/

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set CFL number                             = 1.0
set End time                               = 1e12
set Output directory                       = output
set Resume computation                     = false
set Start time                             = 0
set Use years in output instead of seconds = true
set Dimension = 2

subsection Boundary temperature model
  set Model name = spherical constant
  subsection Spherical constant
    set Inner temperature = 5000
    set Outer temperature = 1

subsection Discretization
  set Stokes velocity polynomial degree       = 2
  set Temperature polynomial degree           = 2
  set Use locally conservative discretization = true
  subsection Stabilization parameters
    set alpha = 2
    set beta  = 0.078
    set cR    = 0.11

subsection Geometry model
  set Model name = spherical shell
  subsection Spherical shell
    set Inner radius  = 3481000
    set Outer radius  = 6371000

subsection Gravity model
  set Model name = radial constant
  subsection Radial constant
    set Magnitude = 9.81

subsection Initial conditions
  set Model name = spherical hexagonal perturbation

subsection Material model
  set Model name = simple
  subsection Simple model
    set Reference density             = 3300
    set Reference temperature         = 273
    set Thermal conductivity          = 4.1
    set Thermal expansion coefficient = 4e-5
    set Viscosity                     = 1e22
    set Composition viscosity prefactor = 1.
    set Density differential for compositional field 1 = 1000.

subsection Mesh refinement
  set Additional refinement times        = 
  set Initial adaptive refinement        = 0
  set Initial global refinement          = 5
  set Refinement fraction                = 0.0
  set Coarsening fraction                = 0.00
  set Strategy                           = Temperature
  set Time steps between mesh refinement = 1000000

subsection Model settings
  set Fixed temperature boundary indicators   = 0,1
  set Include shear heating                   = false
  set Include adiabatic heating               = false
  set Prescribed velocity boundary indicators = 
  set Radiogenic heating rate                 = 0e0
  set Tangential velocity boundary indicators = 1
  set Zero velocity boundary indicators       = 0

subsection Compositional fields
  set Number of fields = 0

subsection Postprocess
  set List of postprocessors = visualization, heat flux statistics
  subsection Visualization
    set Number of grouped files       = 1
    set Output format                 = vtu
    set Time between graphical output = 1e7
    set List of output variables = density,partition,viscosity

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