set Additional shared libraries            = libanalytical_topography.so
set Dimension                              = 2
set Use years in output instead of seconds = false
set End time                               = 0.005
set Maximum time step                      = 0.0005
set Output directory                       = output-1_sine_zero_flux_ci_toppresvel_subtractmeshvel/
set Nonlinear solver scheme = single Advection, single Stokes
set Pressure normalization                 = surface
set Surface pressure                       = 0

# 1x1 box with an initial hill topography
subsection Geometry model
  set Model name = box

  subsection Box
    set X extent = 1
    set Y extent = 1
  end

  subsection Initial topography model
    set Model name = function

    subsection Function
      set Function constants = A=0.150, L=1.
      set Function expression = \
                                if(x<0.5,A * sin((x+0.5)*pi),0)
    end
  end
end

# Temperature effects are ignored
subsection Initial temperature model
  set Model name = function

  subsection Function
    set Function expression = 0
  end
end

subsection Boundary temperature model
  set Fixed temperature boundary indicators = bottom, top
  set List of model names = initial temperature
end

subsection Compositional fields
  set Number of fields = 3
  set Names of fields = layer_1, layer_2, layer_3
end

subsection Initial composition model
  set Model name = function

  subsection Function
    set Variable names = x,z
    set Coordinate system = cartesian #depth
    #set Function expression = if(x<.05, 1, 0); if(x>=0.05 && x<0.1, 1, 0); 0
    set Function expression = if(z>1.07, 1, 0); 0; 0
  end
end

subsection Boundary composition model
  set Fixed composition boundary indicators = top
  set Allow fixed composition on outflow boundaries = false
  set List of model names = function
  subsection Function
    set Variable names = x,z,t
    set Function expression = if(t==0,1,0); 0; if(t==0,0,1)
  end
end

# Free slip on all boundaries
subsection Boundary velocity model
  set Tangential velocity boundary indicators = left, right, bottom
  set Prescribed velocity boundary indicators = top: function
  subsection Function
    set Variable names = x,z,t
    set Function expression = 0;0
  end
end

# The mesh will be deformed according to the displacement
# of the surface nodes due to diffusion of the topography.
# The mesh is allowed to move vertical along the left and
# right boundary.
subsection Mesh deformation
  set Mesh deformation boundary indicators = top: diffusion
  set Additional tangential mesh velocity boundary indicators = left, right

  subsection Diffusion
    # The diffusivity
    set Hillslope transport coefficient = 0.25
  end
end

# Vertical gravity
subsection Gravity model
  set Model name = vertical

  subsection Vertical
    set Magnitude = 0
  end
end

# One material with unity properties
subsection Material model
  set Model name = simple

  subsection Simple model
    set Reference density             = 1
    set Reference specific heat       = 1
    set Reference temperature         = 0
    set Thermal conductivity          = 1
    set Thermal expansion coefficient = 1
    set Viscosity                     = 1
  end
end

# We also have to specify that we want to use the Boussinesq
# approximation (assuming the density in the temperature
# equation to be constant, and incompressibility).
subsection Formulation
  set Formulation = Boussinesq approximation
end

# We here use a globally refined mesh without
# adaptive mesh refinement.
subsection Mesh refinement
  set Initial global refinement                = 6
  set Initial adaptive refinement              = 0
  set Time steps between mesh refinement       = 0
  set Strategy = minimum refinement function
  subsection Minimum refinement function
    set Variable names = x,z
    set Coordinate system = cartesian
    set Function expression = if(z>0.87,7,3)
  end
end

# We output the computed topography and the analytical topography
# value to file.
subsection Postprocess
  set List of postprocessors = velocity statistics, temperature statistics, heat flux statistics, visualization #, analytical topography

  subsection Topography
    set Output to file = true
    set Analytical solution of example = 1
    set Diffusivity = 0.25
    set Initial sinusoidal topography amplitude = 0.075
  end

  subsection Visualization
    set Time between graphical output = 0.0001
    set Output mesh velocity = true
    set Interpolate output = false
  end
end

subsection Solver parameters
  subsection Stokes solver parameters
    set Linear solver tolerance                         = 1e-7
  end
end