# Listing of Parameters
# ---------------------
# In computations, the time step $k$ is chosen according to $k = c \min_K
# \frac{h_K}{\|u\|_{\infty,K} p_T}$ where $h_K$ is the diameter of cell $K$,
# and the denominator is the maximal magnitude of the velocity on cell $K$
# times the polynomial degree $p_T$ of the temperature discretization. The
# dimensionless constant $c$ is called the CFL number in this program. For
# time discretizations that have explicit components, $c$ must be less than a
# constant that depends on the details of the time discretization and that is
# no larger than one. On the other hand, for implicit discretizations such as
# the one chosen here, one can choose the time step as large as one wants (in
# particular, one can choose $c>1$) though a CFL number significantly larger
# than one will yield rather diffusive solutions. Units: None.
set CFL number                             = 1.0

# The end time of the simulation. Units: years if the 'Use years in output
# instead of seconds' parameter is set; seconds otherwise.
set End time                               = 1e12

# The name of the directory into which all output files should be placed. This
# may be an absolute or a relative path.
set Output directory                       = output

# A flag indicating whether the computation should be resumed from a
# previously saved state (if true) or start from scratch (if false).
set Resume computation                     = false

# The start time of the simulation. Units: years if the 'Use years in output
# instead of seconds' parameter is set; seconds otherwise.
set Start time                             = 0

# When computing results for mantle convection simulations, it is often
# difficult to judge the order of magnitude of results when they are stated in
# MKS units involving seconds. Rather, some kinds of results such as
# velocities are often stated in terms of meters per year (or, sometimes,
# centimeters per year). On the other hand, for non-dimensional computations,
# one wants results in their natural unit system as used inside the code. If
# this flag is set to 'true' conversion to years happens; if it is 'false', no
# such conversion happens.
set Use years in output instead of seconds = true


subsection Boundary temperature model
  # Select one of the following models:
  # 
  # `spherical constant': A model in
  # which the temperature is chosen constant on the inner and outer boundaries
  # of a spherical shell. Parameters are read from subsection 'Sherical
  # constant'.
  # 
  # `box': A model in which the temperature is chosen constant on
  # the left and right sides of a box.
  set Model name = spherical constant


  subsection Spherical constant
    # Temperature at the inner boundary (core mantle boundary). Units: K.
    set Inner temperature = 4273

    # Temperature at the outer boundary (lithosphere water/air). Units: K.
    set Outer temperature = 973
  end

end


subsection Discretization
  # The polynomial degree to use for the velocity variables in the Stokes
  # system. Units: None.
  set Stokes velocity polynomial degree       = 2

  # The polynomial degree to use for the temperature variable. Units: None.
  set Temperature polynomial degree           = 2

  # Whether to use a Stokes discretization that is locally conservative at the
  # expense of a larger number of degrees of freedom (true), or to go with a
  # cheaper discretization that does not locally conserve mass, although it is
  # globally conservative (false).
  set Use locally conservative discretization = false


  subsection Stabilization parameters
    # The exponent $\alpha$ in the entropy viscosity stabilization. Units:
    # None.
    set alpha = 2

    # The $\beta$ factor in the artificial viscosity stabilization. An
    # appropriate value for 2d is 0.052 and 0.078 for 3d. Units: None.
    set beta  = 0.078

    # The $c_R$ factor in the entropy viscosity stabilization. Units: None.
    set cR    = 0.11
  end

end


subsection Geometry model
  # Select one of the following models:
  # 
  # `spherical shell': A geometry
  # representing a spherical shell or a pice of it. Inner and outer radii are
  # read from the parameter file in subsection 'Spherical shell'.
  # 
  # `box': A
  # box geometry parallel to the coordinate directions. The extent of the box
  # in each coordinate direction is set in the parameter file.
  set Model name = spherical shell



  subsection Spherical shell
    # Inner radius of the spherical shell. Units: m.
    set Inner radius  = 3481000

    # Opening angle in degrees of the section of the shell that we want to
    # build. Units: degrees.
    set Opening angle = 90

    # Outer radius of the spherical shell. Units: m.
    set Outer radius  = 6336000
  end

end


subsection Gravity model
  # Select one of the following models:
  # 
  # `vertical': A gravity model in which
  # the gravity direction is vertically downward and at constant
  # magnitude.
  # 
  # `radial constant': A gravity model in which the gravity
  # direction is radially inward and at constant magnitude. The magnitude is
  # read from the parameter file in subsection 'Radial constant'.
  # 
  # `radial earth-like': A gravity model in which the gravity direction is radially
  # inward and with a magnitude that matches that of the earth at the
  # core-mantle boundary as well as at the surface and in between is
  # physically correct under the assumption of a constant density.
  set Model name = radial earth-like


  subsection Radial constant
    # Magnitude of the gravity vector in $m/s^2$. The direction is always
    # radially outward from the center of the earth.
    set Magnitude = 9.81
  end

end


subsection Initial conditions
  # Select one of the following models:
  # 
  # `spherical hexagonal perturbation':
  # An initial temperature field in which the temperature is perturbed
  # following a six-fold pattern in angular direction from an otherwise
  # spherically symmetric state.
  # 
  # `spherical gaussian perturbation': An
  # initial temperature field in which the temperature is perturbed by a
  # single Gaussian added to an otherwise spherically symmetric state.
  # Additional parameters are read from the parameter file in subsection
  # 'Spherical gaussian perturbation'.
  # 
  # `perturbed box': An initial
  # temperature field in which the temperature is perturbed slightly from an
  # otherwise constant value equal to one. The perturbation is chosen in such
  # a way that the initial temperature is constant to one along the entire
  # boundary.
  set Model name = spherical hexagonal perturbation


  subsection Spherical gaussian perturbation
    # The amplitude of the perturbation.
    set Amplitude             = 0.01

    # The angle where the center of the perturbation is placed.
    set Angle                 = 0e0

    # The non-dimensional radial distance where the center of the perturbation
    # is placed.
    set Non-dimensional depth = 0.7

    # The standard deviation of the Gaussian perturbation.
    set Sigma                 = 0.2

    # The sign of the perturbation.
    set Sign                  = 1
  end

end


subsection Material model
  # Select one of the following models:
  # 
  # `table': A material model that reads
  # tables of pressure and temperature dependent material coefficients from
  # files.
  # 
  # `Steinberger': lookup from the paper of
  # Steinberger/Calderwood
  # 
  # `simple': A simple material model that has
  # constant values for all coefficients but the density. This model uses the
  # formulation that assumes an incompressible medium despite the fact that
  # the density follows the law $\rho(T)=\rho_0(1-\beta(T-T_{\text{ref}})$.
  # The value for the components of this formula and additional parameters are
  # read from the parameter file in subsection 'Simple model'.
  set Model name = simple


  subsection Simple model
    # Reference density $\rho_0$. Units: $kg/m^3$.
    set Reference density             = 3300

    # The reference temperature $T_0$. Units: $K$.
    set Reference temperature         = 293

    # The value of the thermal conductivity $k$. Units: $W/m/K$.
    set Thermal conductivity          = 4.7#1e-6

    # The value of the thermal expansion coefficient $\beta$. Units: $1/K$.
    set Thermal expansion coefficient = 4e-5

    # The value of the constant viscosity. Units: $kg/m/s$.
    set Viscosity                     = 1e22
  end


end


subsection Mesh refinement
  # A list of times so that if the end time of a time step is beyond this
  # time, an additional round of mesh refinement is triggered. This is mostly
  # useful to make sure we can get through the initial transient phase of a
  # simulation on a relatively coarse mesh, and then refine again when we are
  # in a time range that we are interested in and where we would like to use a
  # finer mesh. Units: each element of the list has units years if the 'Use
  # years in output instead of seconds' parameter is set; seconds otherwise.
  set Additional refinement times        = 


  # The number of adaptive refinement steps performed after initial global
  # refinement but while still within the first time step.
  set Initial adaptive refinement        = 3

  # The number of global refinement steps performed on the initial coarse
  # mesh, before the problem is first solved there.
  set Initial global refinement          = 4

  # The fraction of cells with the largest error that should be flagged for
  # refinement.
  set Refinement fraction                = 0.3

  # The fraction of cells with the smallest error that should be flagged for
  # coarsening.
  set Coarsening fraction                = 0.05

  # The method used to determine which cells to refine and which to coarsen.
  set Strategy                           = Temperature

  # The number of time steps after which the mesh is to be adapted again based
  # on computed error indicators.
  set Time steps between mesh refinement = 5
end


subsection Model settings
  # A comma separated list of integers denoting those boundaries on which the
  # temperature is fixed and described by the boundary temperature object
  # selected in its own section of this input file. All boundary indicators
  # used by the geometry but not explicitly listed here will end up with
  # no-flux (insulating) boundary conditions.
  set Fixed temperature boundary indicators   = 0,1

  # Whether to include shear heating into the model or not. From a physical
  # viewpoint, shear heating should always be used but may be undesirable when
  # comparing results with known benchmarks that do not include this term in
  # the temperature equation.
  set Include shear heating                   = true

  # A comma separated list of integers denoting those boundaries on which the
  # velocity is tangential but prescribed, i.e., where external forces act to
  # prescribe a particular velocity. This is often used to prescribe a
  # velocity that equals that of overlying plates.
  set Prescribed velocity boundary indicators = 

  # H0
  set Radiogenic heating rate                 = 0e0

  # A comma separated list of integers denoting those boundaries on which the
  # velocity is tangential and unrestrained, i.e., where no external forces
  # act to prescribe a particular tangential velocity (although there is a
  # force that requires the flow to be tangential).
  set Tangential velocity boundary indicators = 1,2,3

  # A comma separated list of integers denoting those boundaries on which the
  # velocity is zero.
  set Zero velocity boundary indicators       = 0
end


subsection Postprocess
  # A comma separated list of postprocessor objects that should be run at the
  # end of each time step. Some of these postprocessors will declare their own
  # parameters which may, for example, include that they will actually do
  # something only every so many time steps or years. Alternatively, the text
  # 'all' indicates that all available postprocessors should be run after each
  # time step.
  # 
  # The following postprocessors are available:
  # 
  # `visualization':
  # A postprocessor that takes the solution and writes it into files that can
  # be read by a graphical visualization program. Additional run time
  # parameters are read from the parameter subsection
  # 'Visualization'.
  # 
  # `velocity statistics': A postprocessor that computes
  # some statistics about the velocity field.
  # 
  # `temperature statistics': A
  # postprocessor that computes some statistics about the temperature
  # field.
  # 
  # `velocity statistics for the table model': A postprocessor that
  # computes some statistics about the velocity field.
  # 
  # `heat flux statistics
  # for the table model': A postprocessor that computes some statistics about
  # the heat flux across boundaries.
  # 
  # `heat flux statistics': A postprocessor
  # that computes some statistics about the heat flux across boundaries.
  set List of postprocessors = visualization,velocity statistics,temperature statistics,heat flux statistics, depth average


  subsection Visualization

    set Number of grouped files       = 0

    # The file format to be used for graphical output.
    set Output format                 = vtu

    # The time interval between each generation of graphical output files. A
    # value of zero indicates that output should be generated in each time
    # step. Units: years if the 'Use years in output instead of seconds'
    # parameter is set; seconds otherwise.
    set Time between graphical output = 1e6
  end

  subsection Depth average
    set Time between graphical output = 1e6
  end

end