# Listing of Parameters
# ---------------------
# In order to make the problem in the first time step easier to solve, we need
# a reasonable guess for the temperature and pressure. To obtain it, we use an
# adiabatic pressure and temperature field. This parameter describes what the
# `adiabatic' temperature would be at the surface of the domain (i.e. at depth
# zero). Note that this value need not coincide with the boundary condition
# posed at this point. Rather, the boundary condition may differ significantly
# from the adiabatic value, and then typically induce a thermal boundary
# layer.
# For more information, see the section in the manual that discusses the
# general mathematical model.
set Adiabatic surface temperature          = 0

# 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 number of space dimensions you want to run this program in.
set Dimension                              = 2

# 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                               = 0.5     # default: 1e8

# A relative tolerance up to which linear systems in each time or nonlinear
# step should be solved. The absolute tolerance will then be the norm of the
# right hand side of the equation times this tolerance. A given tolerance
# value of 1 would mean that a zero solution vector is an acceptable solution
# since in that case the norm of the residual of the linear system equals the
# norm of the right hand side. A given tolerance of 0 would mean that the
# linear system has to be solved exactly, since this is the only way to obtain
# a zero residual.
# 
# In practice, you should choose the value of this parameter to be so that if
# you make it smaller the results of your simulation do not change any more
# (qualitatively) whereas if you make it larger, they do. For most cases, the
# default value should be sufficient. However, for cases where the static
# pressure is much larger than the dynamic one, it may be necessary to choose
# a smaller value.
set Linear solver tolerance                = 1e-15   # default: 1e-7

# A flag indicating whether the Stokes+Advection equation should be solved
# once per time step (false) or resolved using a fixed-point iteration
# (true).
set Nonlinear iteration                    = false

# The kind of scheme used to resolve the nonlinearity in the system. 'IMPES'
# is the classical IMplicit Pressure Explicit Saturation scheme in which ones
# solves the temperatures and Stokes equations exactly once per time step, one
# after the other. The 'iterated IMPES' scheme iterates this decoupled
# approach by alternating the solution of the temperature and Stokes systems.
# The 'iterated Stokes' scheme solves the temperature equation once at the
# beginning of each time step and then iterates out the solution of the Stokes
# equation.
set Nonlinear solver scheme                = IMPES

# 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

# If and how to normalize the pressure after the solution step. This is
# necessary because depending on boundary conditions, in many cases the
# pressure is only determined by the model up to a constant. On the other
# hand, we often would like to have a well-determined pressure, for example
# for table lookups of material properties in models or for comparing
# solutions. If the given value is `surface', then normalization at the end of
# each time steps adds a constant value to the pressure in such a way that the
# average pressure at the surface of the domain is zero; the surface of the
# domain is determined by asking the geometry model whether a particular face
# of the geometry has a zero or small `depth'. If the value of this parameter
# is `volume' then the pressure is normalized so that the domain average is
# zero. If `no' is given, the no pressure normalization is performed.
set Pressure normalization                 = surface

# 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

# The mathematical equations that describe thermal convection only determine
# the pressure up to an arbitrary constant. On the other hand, for comparison
# and for looking up material parameters it is important that the pressure be
# normalized somehow. We do this by enforcing a particular average pressure
# value at the surface of the domain, where the geometry model determines
# where the surface is. This parameter describes what this average surface
# pressure value is supposed to be. By default, it is set to zero, but one may
# want to choose a different value for example for simulating only the volume
# of the mantle below the lithosphere, in which case the surface pressure
# should be the lithostatic pressure at the bottom of the lithosphere.
# For more information, see the section in the manual that discusses the
# general mathematical model.
set Surface pressure                       = 0

# The relative tolerance up to which the linear system for the temperature
# system gets solved. See 'linear solver tolerance' for more details.
set Temperature solver tolerance           = 1e-15   # default: 1e-12

# How frequently in timesteps to output timing information. This is generally
# adjusted only for debugging and timing purposes.
set Timing output frequency                = 100

# 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 = false   # default: true


subsection Boundary temperature model
  # Select one of the following models:
  # 
  # `Tan Gurnis': A model for the Tan/Gurnis benchmark.
  # 
  # `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 all the
  # sides of a box.
  set Model name = box # default: 


  subsection Box
    # Temperature at the Bottom boundary. Units: K.
    set Bottom temperature = 1 # default: 0

    # Temperature at the Left boundary. Units: K.
    set Left temperature   = 0 # default: 1

    # Temperature at the Right boundary. Units: K.
    set Right temperature  = 0

    # Temperature at the Top boundary. Units: K.
    set Top temperature    = 0
  end

  subsection Spherical constant
    # Temperature at the inner boundary (core mantle boundary). Units: K.
    set Inner temperature = 6000

    # Temperature at the outer boundary (lithosphere water/air). Units: K.
    set Outer temperature = 0
  end

end


subsection Boundary velocity model
  subsection Function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the fparser
    # library.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = 0; 0

    # The name of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated is `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,y,t
  end

end


subsection Checkpointing
  # The number of timesteps between performing checkpoints. If 0 and time
  # between checkpoint is not specified, checkpointing will not be performed.
  # Units: None.
  set Steps between checkpoint = 0

  # The wall time between performing checkpoints. If 0, will use the
  # checkpoint step frequency instead. Units: Seconds.
  set Time between checkpoint  = 0
end


subsection Discretization
  # The polynomial degree to use for the velocity variables in the Stokes
  # system. The polynomial degree for the pressure variable will then be one
  # less in order to make the velocity/pressure pair conform with the usual
  # LBB (Babuska-Brezzi) condition. In other words, we are using a Taylor-Hood
  # element for the Stoeks equations and this parameter indicates the
  # polynomial degree of it. 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).
  # 
  # When using a locally conservative discretization, the finite element space
  # for the pressure is discontinuous between cells and is the polynomial
  # space $P_{-q}$ of polynomials of degree $q$ in each variable separately.
  # Here, $q$ is one less than the value given in the parameter ``Stokes
  # velocity polynomial degree''. As a consequence of choosing this element,
  # it can be shown if the medium is considered incompressible that the
  # computed discrete velocity field $\mathbf u_h$ satisfies the property
  # $\int_{\partial K} \mathbf u_h \cdot \mathbf n = 0$ for every cell $K$,
  # i.e., for each cell inflow and outflow exactly balance each other as one
  # would expect for an incompressible medium. In other words, the velocity
  # field is locally conservative.
  # 
  # On the other hand, if this parameter is set to ``false'', then the finite
  # element space is chosen as $Q_q$. This choice does not yield the local
  # conservation property but has the advantage of requiring fewer degrees of
  # freedom. Furthermore, the error is generally smaller with this choice.
  # 
  # For an in-depth discussion of these issues and a quantitative evaluation
  # of the different choices, see \cite{KHB12}.
  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. The box
  # geometry labels its 2*dim sides as follows: in 2d, boundary indicators 0
  # through 3 denote the left, right, bottom and top boundaries; in 3d,
  # boundary indicators 0 through 5 indicate left, right, front, back, bottom
  # and top boundaries. See also the documentation of the deal.II class
  # ``GeometryInfo''.
  set Model name = box # default: 


  subsection Box
    # Extent of the box in x-direction. Units: m.
    set X extent = 1.2 # default: 1

    # Extent of the box in y-direction. Units: m.
    set Y extent = 1.0 # default: 1

    # Extent of the box in z-direction. This value is ignored if the
    # simulation is in 2d Units: m.
    set Z extent = 1
  end

  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 = 360

    # 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 a constant magnitude by default equal to one.
  # 
  # `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 = vertical # default: 


  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 = 30
  end

  subsection Vertical
    # Value of the gravity vector in $m/s^2$ directed along negative y (2D) or
    # z (3D) axis.
    set Magnitude = 1e14 # default: 1
  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'.
  # 
  # `function': Temperature is given in terms of an explicit formula
  # 
  # `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 = perturbed box


  subsection Function
    # Sometimes it is convenient to use symbolic constants in the expression
    # that describes the function, rather than having to use its numeric value
    # everywhere the constant appears. These values can be defined using this
    # parameter, in the form `var1=value1, var2=value2, ...'.
    # 
    # A typical example would be to set this runtime parameter to
    # `pi=3.1415926536' and then use `pi' in the expression of the actual
    # formula. (That said, for convenience this class actually defines both
    # `pi' and `Pi' by default, but you get the idea.)
    set Function constants  = p=0.01, L=1, pi=3.1415926536, k=1   # default: 

    # The formula that denotes the function you want to evaluate for
    # particular values of the independent variables. This expression may
    # contain any of the usual operations such as addition or multiplication,
    # as well as all of the common functions such as `sin' or `cos'. In
    # addition, it may contain expressions like `if(x>0, 1, -1)' where the
    # expression evaluates to the second argument if the first argument is
    # true, and to the third argument otherwise. For a full overview of
    # possible expressions accepted see the documentation of the fparser
    # library.
    # 
    # If the function you are describing represents a vector-valued function
    # with multiple components, then separate the expressions for individual
    # components by a semicolon.
    set Function expression = (1.0-z) - p*cos(k*pi*x/L)*sin(pi*z) # default: 0

    # The name of the variables as they will be used in the function,
    # separated by commas. By default, the names of variables at which the
    # function will be evaluated is `x' (in 1d), `x,y' (in 2d) or `x,y,z' (in
    # 3d) for spatial coordinates and `t' for time. You can then use these
    # variable names in your function expression and they will be replaced by
    # the values of these variables at which the function is currently
    # evaluated. However, you can also choose a different set of names for the
    # independent variables at which to evaluate your function expression. For
    # example, if you work in spherical coordinates, you may wish to set this
    # input parameter to `r,phi,theta,t' and then use these variable names in
    # your function expression.
    set Variable names      = x,z                                 # default: x,y,t
  end

  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 file from which the initial geotherm table is to be read. The format
    # of the file is defined by what is read in
    # source/initial_conditions/spherical_shell.cc.
    set Filename for initial geotherm table = initial_geotherm_table

    # 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:
  # 
  # `Tan Gurnis': A simple compressible material model based on a benchmark
  # from the paper of Tan/Gurnis (2007). This does not use the temperature
  # equation, but has a hardcoded temperature.
  # 
  # `table': A material model that reads tables of pressure and temperature
  # dependent material coefficients from files. The default values for this
  # model's runtime parameters use a material description taken from the paper
  # \textit{Complex phase distribution and seismic velocity structure of the
  # transition zone: Convection model predictions for a magnesium-endmember
  # olivine–pyroxene mantle} by Michael H.G. Jacobs and Arie P. van den
  # Berg, Physics of the Earth and Planetary Interiors, Volume 186, Issues
  # 1–2, May 2011, Pages 36–48. See
  # \url{http://www.sciencedirect.com/science/article/pii/S0031920111000422}.
  # 
  # `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'.
  # 
  # `SolCx': A material model that corresponds to the 'SolCx' benchmark
  # defined in Duretz et al., G-Cubed, 2011.
  # 
  # `SolKz': A material model that corresponds to the 'SolKz' benchmark
  # defined in Duretz et al., G-Cubed, 2011.
  # 
  # `Inclusion': A material model that corresponds to the 'Inclusion'
  # benchmark defined in Duretz et al., G-Cubed, 2011.
  set Model name = simple # default: 


  subsection Inclusion
    # Viscosity in the Inclusion.
    set Viscosity jump = 1e3
  end

  subsection Simple model
    # Reference density $\rho_0$. Units: $kg/m^3$.
    set Reference density             = 1     # default: 3300

    # The value of the specific heat $cp$. Units: $J/kg/K$.
    set Reference specific heat       = 1     # default: 1250

    # The reference temperature $T_0$. Units: $K$.
    set Reference temperature         = 0     # default: 293

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

    # The value of the thermal expansion coefficient $\beta$. Units: $1/K$.
    set Thermal expansion coefficient = 1e-10 # default: 2e-5

    # The value of the constant viscosity. Units: $kg/m/s$.
    set Viscosity                     = 1     # default: 5e24
  end

  subsection SolCx
    # Density value upon which the variation of this testcase is overlaid.
    # Since this background density is constant it does not affect the flow
    # pattern but it adds to the total pressure since it produces a nonzero
    # adiabatic pressure if set to a nonzero value.
    set Background density = 0

    # Viscosity in the right half of the domain.
    set Viscosity jump     = 1e6
  end

  subsection Table model
    # The Composition of the model.
    set Composition                   = olixene

    # whether the model is compressible.
    set Compressible                  = true

    # whether to compute phases.
    set ComputePhases                 = false

    # The value of the gravity constant.Units: $m/s^2$.
    set Gravity                       = 30

    # The path to the model data.
    set Path to model data            = datadir

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

    # The value of the specific heat $cp$. Units: $J/kg/K$.
    set Reference specific heat       = 1250

    # 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

    # The value of the thermal expansion coefficient $\beta$. Units: $1/K$.
    set Thermal expansion coefficient = 2e-5


  end

  subsection Tan Gurnis model
    set Di                            = 0.5
    # Reference density $\rho_0$. Units: $kg/m^3$.
    set Reference density             = 3300

    # The value of the specific heat $cp$. Units: $J/kg/K$.
    set Reference specific heat       = 1250

    # 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

    # The value of the thermal expansion coefficient $\beta$. Units: $1/K$.
    set Thermal expansion coefficient = 2e-5

    # The value of the constant viscosity. Units: $kg/m/s$.
    set Viscosity                     = 5e24
    set a                             = 0
    set gamma                         = 1
    set wavenumber                    = 1
  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 fraction of cells with the smallest error that should be flagged for
  # coarsening.
  set Coarsening fraction                      = 0.05

  # The number of adaptive refinement steps performed after initial global
  # refinement but while still within the first time step.
  set Initial adaptive refinement              = 0                       # default: 2

  # The number of global refinement steps performed on the initial coarse
  # mesh, before the problem is first solved there.
  set Initial global refinement                = 4                       # default: 2

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

  # Whether or not the postproccessors should be run at the end of each of ths
  # initial adaptive refinement cycles at the of the simulation start.
  set Run postprocessors on initial refinement = false

  # The method used to determine which cells to refine and which to coarsen.
  set Strategy                                 = Density c_p temperature

  # The number of time steps after which the mesh is to be adapted again based
  # on computed error indicators. If 0 then the mesh will never be changed.
  set Time steps between mesh refinement       = 0                       # default: 10
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.
  # 
  # This parameter only describes which boundaries have a fixed temperature,
  # but not what temperature should hold on these boundaries. The latter piece
  # of information needs to be implemented in a plugin in the
  # BoundaryTemperature group, unless an existing implementation in this group
  # already provides what you want.
  set Fixed temperature boundary indicators   = 2,3     # default: 

  # Whether to include adiabatic heating into the model or not. From a
  # physical viewpoint, adiabatic 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 adiabatic heating               = false

  # 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                   = false   # default: true

  # A comma separated list 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.
  # 
  # The format of valid entries for this parameter is that of a map given as
  # ``key1: value1, key2: value2, key3: value3, ...'' where each key must be a
  # valid boundary indicator and each value must be one of the currently
  # implemented boundary velocity models.
  # 
  # Note that the no-slip boundary condition is a special case of the current
  # one where the prescribed velocity happens to be zero. It can thus be
  # implemented by indicating that a particular boundary is part of the ones
  # selected using the current parameter and using ``zero velocity'' as the
  # boundary values. Alternatively, you can simply list the part of the
  # boundary on which the velocity is to be zero with the parameter ``Zero
  # velocity boundary indicator'' in the current parameter section.
  set Prescribed velocity boundary indicators = 

  # H0
  set Radiogenic heating rate                 = 0       # default: 0e0

  # A comma separated list of integers denoting those boundaries on which the
  # velocity is tangential and unrestrained, i.e., free-slip 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 = 0,1,2,3 # default: 

  # A comma separated list of integers denoting those boundaries on which the
  # velocity is zero.
  set Zero velocity boundary indicators       = 
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.
  # 
  # `tracers': Postprocessor that propagates tracer particles based on the
  # velocity field.
  # 
  # `temperature statistics': A postprocessor that computes some statistics
  # about the temperature field.
  # 
  # `Tan Gurnis error': A postprocessor that compares the solution of the
  # benchmarks from the Tan/Gurnis (2007) paper with the one computed by
  # ASPECT by outputing data that is compared using a matlab script.
  # 
  # `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.
  # 
  # `DuretzEtAl error': A postprocessor that compares the solution of the
  # benchmarks from the Duretz et al., G-Cubed, 2011, paper with the one
  # computed by ASPECT and reports the error. Specifically, it can compute the
  # errors for the SolCx, SolKz and inclusion benchmarks. The postprocessor
  # inquires which material model is currently being used and adjusts which
  # exact solution to use accordingly.
  # 
  # `depth average': A postprocessor that computes depth averaged quantities
  # and writes them out.
  set List of postprocessors = visualization, velocity statistics, temperature statistics, heat flux statistics # default: all


  subsection Depth average
    # 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 = 1e8
  end

  subsection Tracers
    # File format to output raw particle data in.
    set Data output format       = none

    # Total number of tracers to create (not per processor or per element).
    set Number of tracers        = 1e3

    # The time interval between each generation of output files. A value of
    # zero indicates that output should be generated every time step. Units:
    # years if the 'Use years in output instead of seconds' parameter is set;
    # seconds otherwise.
    set Time between data output = 1e8
  end

  subsection Visualization
    # A comma separated list of visualization objects that should be run
    # whenever writing graphical output. By default, the graphical output
    # files will always contain the primary variables velocity, pressure, and
    # temperature. However, one frequently wants to also visualize derived
    # quantities, such as the thermodynamic phase that corresponds to a given
    # temperature-pressure value, or the corresponding seismic wave speeds.
    # The visualization objects do exactly this: they compute such derived
    # quantities and place them into the output file. The current parameter is
    # the place where you decide which of these additional output variables
    # you want to have in your output file.
    # 
    # The following postprocessors are available:
    # 
    # `viscosity ratio': A visualization output object that generates output
    # for the ratio between dislocation viscosity and diffusion viscosity.
    # 
    # `viscosity': A visualization output object that generates output for the
    # viscosity.
    # 
    # `thermodynamic phase': A visualization output object that generates
    # output for the integer number of the phase that is thermodynamically
    # stable at the temperature and pressure of the current point.
    # 
    # `strain rate': A visualization output object that generates output for
    # the norm of the strain rate, i.e., for the quantity
    # $\sqrt{\varepsilon(\mathbf u):\varepsilon(\mathbf u)}$ in the
    # incompressible case and $\sqrt{[\varepsilon(\mathbf u)-\tfrac
    # 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I]:[\varepsilon(\mathbf
    # u)-\tfrac 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I]}$ in the
    # compressible case.
    # 
    # `specific heat': A visualization output object that generates output for
    # the specific heat $C_p$.
    # 
    # `seismic vs': A visualization output object that generates output for
    # the seismic S-wave speed.
    # 
    # `seismic vp': A visualization output object that generates output for
    # the seismic P-wave speed.
    # 
    # `partition': A visualization output object that generates output for the
    # parallel partition that every cell of the mesh is associated with.
    # 
    # `nonadiabatic temperature': A visualization output object that generates
    # output for the non-adiabatic component of the pressure.
    # 
    # `nonadiabatic pressure': A visualization output object that generates
    # output for the non-adiabatic component of the pressure.
    # 
    # `friction heating': A visualization output object that generates output
    # for the amount of friction heating often referred to as $\tau:\epsilon$.
    # More concisely, in the incompressible case, the quantity that is output
    # is defined as $\eta \varepsilon(\mathbf u):\varepsilon(\mathbf u)$ where
    # $\eta$ is itself a function of temperature, pressure and strain rate. In
    # the compressible case, the quantity that's computed is $\eta
    # [\varepsilon(\mathbf u)-\tfrac 13(\textrm{tr}\;\varepsilon(\mathbf
    # u))\mathbf I]:[\varepsilon(\mathbf u)-\tfrac
    # 13(\textrm{tr}\;\varepsilon(\mathbf u))\mathbf I]$.
    # 
    # `density': A visualization output object that generates output for the
    # density.
    set List of output variables      = 

    # VTU file output supports grouping files from several CPUs into one file
    # using MPI I/O when writing on a parallel filesystem. Select 0 for no
    # grouping. This will disable parallel file output and instead write one
    # file per processor in a background thread. A value of 1 will generate
    # one big file containing the whole solution.
    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 = 0.01 # default: 1e8
  end

end