Velocity Source#

This subsection allows you to define velocity-dependent source terms. Two families of velocity source terms are supported. They enable the simulation of problems in a Lagrangian reference frame for which the Coriolis and centrifugal forces must be added or of problems including porous media.

Rotating Frame#

Rotating frame simulations use the following parameters:

subsection velocity source
  set rotating frame type    = none
  set omega_x                = 0
  set omega_y                = 0
  set omega_z                = 0
end

  • The rotating frame type parameter specifies the type of reference frame that is selected. The options are none for an Eulerian reference frame or srf for a single rotating frame. By selecting srf the additional contributions of the centrifugal force and Coriolis force induced by the rotating movement are taken into account in the Navier-Stokes equations.

  • The omega_x parameter is a double representing the \(x\) component of the angular velocity of the reference frame.

  • The omega_y parameter is a double representing the \(y\) component of the angular velocity of the reference frame.

  • The omega_z parameter is a double representing the \(z\) component of the angular velocity of the reference frame.

Darcy Penalization#

A Darcy-like source term can be added to the simulation using the following parameters:

subsection velocity source
  set Darcy type                       = none
  set enable Darcy multiply by density = false
end

  • The Darcy type parameter specifies the type of Darcy penalization term to be applied to the Navier-Stokes equations. The options are none or phase_change. The phase_change model uses the values of the Darcy penalty liquid and Darcy penalty solid set-up within the phase change subsection of the Physical Properties.

    Caution

    The phase change Darcy model does not currently have a Cahn-Hilliard implementation.

  • The enable Darcy multiply by density parameter enables the multiplication by the density within the Darcy force term (\(\boldsymbol{F}_\mathrm{Darcy}\)). This is for dimensional consistency when solving the pressure (\(p\)) rather than the kinematic pressure (\(p^* = p / \rho\), with \(\rho\) the density of the fluid) in the momentum equation. This parameter should be used when coupling of the CLS equation with the incompressible Navier-Stokes equations.

    \[\boldsymbol{F}_\mathrm{Darcy} = \left(\rho K\right)_\mathrm{eff} \boldsymbol{u}\]

    where

    • \(\left(\rho K\right)_\mathrm{eff} = (1-\phi)\rho_0 K_\mathrm{0} + \phi \rho_1 K_\mathrm{1}\) is the effective Darcy penalization coefficient. It corresponds to the weighted product of the Darcy penalty \(\left(K_i [=] T^{-1}\right)\) and the density \(\left(\rho_i[=] M L^{-3}\right)\) by the phase indicator (\(\phi\)). If the phase_change model is enabled in a fluid, the Darcy penalty in this fluid is computed with the penalty values in the liquid (\(K_{i\mathrm{,l}}\)) and solid (\(K_{i\mathrm{,s}}\)), and the liquid fraction (\(\alpha_\mathrm{l}\)): \(K_i = \alpha_\mathrm{l}K_{i\mathrm{,l}} + (1-\alpha_\mathrm{l})K_{i\mathrm{,s}}\), and;

    • \(\boldsymbol{u}\) is the velocity vector.