Tags: category:benchmark feature:2d feature:spherical feature:analytical-solution

Advection in Annulus

# The advection benchmark creates a simple, 2d annulus
# with prescribed Stokes flow creating 4 convection cells.
# Various parameters can be changed to test their effect
# on the overall cooling of the model.
#
# See run_all_models.sh for running multiple iterations
# of various parameters in a row.
#
# Also see creates_formatted_tables for grabbing specific
# data points from the log file.

############### Global parameters
# We use a 2d setup. We are only interested in
# advection, so we prescribe a Stokes flow and
# solve only for advection.

set Additional shared libraries            = ./libadvection_in_annulus.so
set Dimension                              = 2
set Start time                             = 0
set End time                               = 1
set Use years instead of seconds           = false
set Nonlinear solver scheme                = single Advection, no Stokes
set Output directory                       = output_advection_in_annulus
set Pressure normalization                 = surface
set Timing output frequency                = 100

subsection Prescribed Stokes solution
  set Model name = advection in annulus
end

############### Parameters describing the model
# We are interested in the flow of heat out of the top
# boundary and how the advection is stabilized. Interesting
# values to look at are in subsection Discretization, which
# control the stabilization directly, as well as thermal
# conductivity which effectively controls the Rayleigh number.
# The thermal conductivity and Rayleigh number are inversely
# proportional.

subsection Geometry model
  set Model name = spherical shell

  # NOTE: the analytical solutions are hard-coded
  # to these geometry values: do not change them.
  subsection Spherical shell
    set Inner radius = 1
    set Outer radius = 2
    set Opening angle = 360
  end
end

subsection Discretization
  set Temperature polynomial degree = 2

  subsection Stabilization parameters
    set beta = 0.052
    set cR = 0.11
  end
end

subsection Material model
  set Model name = simpler

  subsection Simpler model
    set Reference density = 1.0
    set Reference temperature = 1.0
    set Viscosity = 1.0
    set Thermal conductivity = 1e-3
    set Reference specific heat = 1.0
    set Thermal expansion coefficient = 0
  end
end

subsection Gravity model
  set Model name = radial constant

  subsection Radial constant
    set Magnitude =  1
  end
end

############### Parameters describing the temperature field
# Since we are interested in the flow of heat through
# the top of the model, we set the temperature to 1
# everywhere within the model except for the top
# boundary, which is set to 0.

subsection Boundary temperature model
  set List of model names = function
  set Fixed temperature boundary indicators = top

  subsection Function
    set Function expression = 0
  end
end

subsection Initial temperature model
  set Model name = function

  subsection Function
    set Function expression = 1
  end
end

subsection Mesh refinement
  set Initial adaptive refinement        = 0
  set Initial global refinement          = 2
  set Time steps between mesh refinement = 0
  set Refinement fraction                = 0.2
  set Strategy                           = velocity
end

subsection Postprocess
  set List of postprocessors = visualization, velocity statistics, temperature statistics, heat flux statistics, entropy viscosity statistics, depth average

  subsection Visualization
    set List of output variables = heat flux map, artificial viscosity
    set Time between graphical output = 0.1
  end
end