gravity_tidal_potential.prm

# This parameter file tests the gravity model plugin for a case where the
# tidal potential by flattening and non-synchronnous rotation changes gravity with position and time.
# 
# The equation implemented in this heating model is from Tobie et al. (2025) (https://doi.org/10.1007/s11214-025-01136-y),
# which is defined as:
# g = - magnitude - gradient ( - tidal potential ).
# potential = 3 G M_p R_s^2 / 2 a_s^3 r^2 (Tstar + T0)
# Tstar = 1/6 *(1-3*cos(theta)^2) and T0=1/2sin(theta)^2*cos(2*lambda + 2*b*t),
# where G: gravitational constant, M_p: mass of planet, R_s: radius of satellite, a_s: semimajor axis of satellite's orbit, b = angular rate of nonsynchronous rotation.
# r, theta and lambda are radial distance, polar angle and azimuthal angle, respectively.
#
# Model shows the Europa's icy shell without conduction in simpler model.
# Visualization 'gravity' shows gravity distribution.

set Dimension                              = 3
set Use years instead of seconds           = true
set End time                               = 1e4

set Output directory                       = gravity_tidal_potential

set Maximum first time step                    = 1e3
set CFL number                                 = 0.8
set Maximum time step                          = 1e3


set Pressure normalization                 = surface
set Surface pressure                       = 0


subsection Geometry model
  set Model name = spherical shell
  subsection Spherical shell
    set Outer radius = 1560800
    set Inner radius = 1460800
    set Opening angle = 360
  end
end


subsection Initial temperature model
  set Model name = function
  subsection Function
    set Coordinate system = spherical
    set Variable names = r, phi,theta
    set Function expression = 100
  end
end


subsection Boundary velocity model
  set Zero velocity boundary indicators = top, bottom
end


subsection Gravity model
  set Model name = radial linear with tidal potential
  subsection Radial linear
    set Magnitude at surface = 1.3
    set Magnitude at bottom = 1.3
  end
  subsection Radial linear with tidal potnetial
  end
end


subsection Material model
  set Model name = simpler
  subsection Simpler model
    set Reference density = 917
    set Reference specific heat = 2110
    set Reference temperature = 100
    set Thermal conductivity = 0 #1.93
    set Thermal expansion coefficient = 0 #1.6e-4
    set Viscosity = 1e20
  end
end


subsection Formulation
  set Formulation = Boussinesq approximation
end


subsection Mesh refinement
  set Initial global refinement                = 0
  set Initial adaptive refinement              = 0
  set Time steps between mesh refinement       = 0
end


subsection Postprocess
  set List of postprocessors = velocity statistics, temperature statistics, visualization, basic statistics, \
			       pressure statistics, material statistics

  subsection Visualization
    set Time between graphical output = 1e3
    set Output format                 = vtu
    set List of output variables      = material properties, strain rate, shear stress, stress, nonadiabatic pressure, gravity
  end
end