Boundary Conditions - Multiphysics#

This subsection’s purpose is defining the boundary conditions associated to multiphysic problems.

Heat Transfer#

For heat transfer boundary conditions, the possible types are noflux (default), temperature and convection-radiation-flux. The default parameters for temperature and convection-radiation-flux are shown:

subsection boundary conditions heat transfer
  set number         = 2
  set time dependent = false
  subsection bc 0
    set id   = 0
    set type = temperature
    subsection value
      set Function expression = 0
    end
  end
  subsection bc 1
    set id   = 1
    set type = convection-radiation-flux
    subsection h
      set Function expression = 0
    end
    subsection Tinf
      set Function expression = 0
    end
    subsection emissivity
      set Function expression = 0
    end
    subsection heat_flux
      set Function expression = 0
    end
  end
  set Stefan-Boltzmann constant = 0.000000056703
end

number: This is the number of boundary conditions of the problem.
time dependent specifies if a boundary condition is time-dependent (true) or steady (false). By default, this parameter is set to false. This is here to improve the computational efficiency for transient cases in which the boundary conditions do not change.

Warning

The number of boundary conditions must be specified explicitly. This is often a source of error.

Note

The index in subsection bc .. must be coherent with the number of boundary conditions set: if number = 2, bc 0 and bc 1 are created but bc 2 does not exist.

Likewise, if number = 2 and there is no subsection bc 0 explicitly stated, the boundary is still created, with noflux by default.

id is the number associated with the boundary condition. By default, Lethe assumes that the id is equivalent to the number of the bc.
type: type of boundary condition being imposed. At the moment, choices are:
- noflux (default) so that there is no heat transfer boundary condition,
- temperature (Dirichlet BC), to impose a given temperature value at the boundary,
- convection-radiation-flux (Robin BC) for cooling/heating, depending on the environment temperature at the boundary Tinf, with a given heat transfer coefficient h and emissivity of the boundary \(\mathbf{\epsilon}\) following Newton’s law of cooling (and heating) and Stefan-Boltzmann law of radiation. It is also possible to impose a given heat flux (\(q_0\)) by using the parameter heat_flux. This BC can be represented by:
\[\frac{ \partial T}{\partial \mathbf{n}} = h (T - T_{inf}) + \epsilon \sigma (T^4 - T_{inf}^4) + q_0\]

where \(\mathbf{\sigma}\) is the Stefan-Boltzmann constant.

Important

The flux represented by the convection-radiation-flux BC follow the direction of the normal vector to the boundary, i.e., pointing outwards the boundary. As consequence, a positive value for heat_flux, for example, will result on heat being extracted from the boundary.

Tracer#

For tracer boundary conditions, the defaults parameters are:

subsection boundary conditions tracer
  set number         = 1
  set time dependent = false
  subsection bc 0
    set id   = 0
    set type = dirichlet
    subsection dirichlet
      set Function expression = 0
    end
  end
end

number: This is the number of boundary conditions of the problem.
time dependent specifies if a boundary condition is time-dependent (true) or steady (false). By default, this parameter is set to false. This improves the computational efficiency for transient cases in which the boundary conditions do not change.
id is the number associated with the boundary condition. By default, Lethe assumes that the id is equivalent to the number of the bc.
type: This is the type of boundary condition being imposed. At the moment, only dirichlet boundary conditions can be imposed for tracer.

VOF#

For VOF boundary conditions (multiphase flow), the possible types are none (default) and dirichlet, as shown below.

subsection boundary conditions VOF
  set number         = 2
  set time dependent = false
  subsection bc 0
    set id   = 0
    set type = none
  end
  subsection bc 1
    set id   = 1
    set type = dirichlet
    subsection dirichlet
      set Function expression = 0
    end
  end
end

Warning

The number of boundary conditions must be specified explicitly. This is often a source of error.

Note

The index in subsection bc .. must be coherent with the number of boundary conditions set: if number = 2, bc 0 and bc 1 are created but bc 2 does not exist.

Likewise, if number = 2 and there is no subsection bc 0 explicitly stated, the boundary is still created, with none by default.

number: This is the number of boundary conditions of the problem.
time dependent specifies if a boundary condition is time-dependent (true) or steady (false). By default, this parameter is set to false. This improves the computational efficiency for transient cases in which the boundary conditions do not change.
id is the number associated with the boundary condition. By default, Lethe assumes that the id is equivalent to the number of the bc.
type: This is the type of boundary condition being imposed. At the moment, choices are:
- none for which nothing happens.
- dirichlet for inlet and outlet boundary conditions, to specify which fluid should be at the selected boundary.

Note

For periodic boundary conditions, there is no need to specify anything in the boundary conditions VOF subsection. The periodic boundary condition must be specified in the boundary conditions subsection (see Boundary Conditions - CFD).

Cahn-Hilliard#

For Cahn-Hilliard boundary conditions, the available types are noflux (default), dirichlet, angle_of_contact, and free_angle. The parameters for each type of Cahn-Hilliard boundary conditions are:

subsection boundary conditions cahn hilliard
  set number         = 3
  set time dependent = false
  subsection bc 0
      set id            = 0
      set type          = dirichlet
      subsection phi
          set Function expression = 0
      end
   end
  subsection bc 1
    set id              = 1
    set type            = angle_of_contact
    set angle value     = 90 # The angle is given in degrees (°)
  end
  subsection bc 2
    set id              = 2
    set type            = free_angle
  end
end

number: This is the number of boundary conditions of the problem.
time dependent specifies if a boundary condition is time-dependent (true) or not (false). By default, this parameter is set to false. It is used to improve the computational efficiency of transient cases in which the boundary conditions do not change.
id is the number associated with the boundary condition. By default, Lethe assumes that the id is equivalent to the number of the bc.
type: Type of boundary condition being imposed. At the moment, the choices are:
- noflux (default): no phase leaves the simulation domain.
- dirichlet: Imposes a given phase order parameter function on the boundary. This function can depend on position (\(x,y,z\)) and on time (\(t\)).
- angle_of_contact: Imposes a given angle of contact angle value between the two phases at the boundary. It refers to the inner angle of contact, in degrees (°).
- free_angle: Leaves the angle as a free variable to be solved.