7.1.5 Boundary conditions (MHD only)

The following parameters are specific to MHD simulations. For MHD calculations they must be set additional to the hydrodynamic boundary parameters.

7.1.5.1 character side_bound_mag_x1 and side_bound_mag_x2

The boundary condition at the sides perpendicular to the x1 direction and perpendicular to the x2 direction, respectively. They are given by e.g.

character side_bound_mag_x1   f=A80 b=80 n='side boundary conditions magnetic x1'
fixed
character side_bound_mag_x2   f=A80 b=80 n='side boundary conditions magnetic x2'
periodic

Possible values are:

• constant: constant extrapolation of all magnetic field components into the ghost cells.
• periodic: periodic continuation of all magnetic field components into the ghost cells.
• fixed: the component normal to the boundary is kept fixed at its inital value. Constant extrapolation applies for the transversal components.
• vertical: constant extrapolation for the vertical component. The transversal cell-centered field is mirrored, with the opposite sign. That should result in transversal components of the boundary-centered field being zero at the boundary.
• vertical2: constant extrapolation for the vertical component. The transversal cell-centered field is set to zero.
• reflective: The magnetic field is mirrored at the boundary. This boundary condition is unphysical, because the magnetic field is an axial vector and because it violates the divergence free property of the magnetic field. Therefore, this boundary condition should be used with caution.

The fixed conditions are realized by setting the electric field at those cell edges that coincide with the physical boundary zero. This is done in the constrained transport module.

7.1.5.2 character top_bound_mag

The boundary condition at the top of the model is given by for instance

character top_bound_mag f=A80 b=80 n='bottom boundary conditions magnetic'
vertical

Possible values are:

• constant: constant extrapolation of all magnetic field components into the ghost cells.
• periodic: periodic continuation of all magnetic field components into the ghost cells.
• fixed: the component normal to the boundary is kept fixed at its inital value. Constant extrapolation applies for the transversal components.
• vertical: constant extrapolation for the vertical component. The transversal cell-centered field is mirrored, with the opposite sign. That should result in transversal components of the boundary-centered field being zero at the boundary.
• vertical2: constant extrapolation for the vertical component. The transversal cell-centered field is set to zero.
• oblique: magnetic fields with a given inclination at the boundary. The inclination is specified through parameters C_magthetaB and C_magphiB.

7.1.5.3 character bottom_bound_mag

The boundary condition at the bottom of the model is given by for instance

character bottom_bound_mag f=A80 b=80 n='bottom boundary conditions magnetic'
inoutflow

Possible values are:

• constant: constant extrapolation of all magnetic field components into the ghost cells.
• periodic: periodic continuation of all magnetic field components into the ghost cells.
• fixed: the component normal to the boundary is kept fixed at its inital value. Constant extrapolation applies for the transversal components.
• vertical: constant extrapolation for the vertical component. The transversal cell-centered field is mirrored, with the opposite sign. That should result in transversal components of the boundary-centered field being zero at the boundary.
• vertical2: constant extrapolation for the vertical component. The transversal cell-centered field is set to zero.
• oblique: magnetic fields with a given inclination at the boundary. The inclination is specified through parameters C_magthetaB and C_magphiB.
• inoutflow: magnetic field can be advected into the computational domain by ascending material flow. Its strength can be specified with the parameter b1_inflow. The boundary condition for the hydrodynamic variables must be set to inoutflow too, otherwise this boundary condition is the same like constant.

In the case of inoutflow the magnetic field, which is advected into the computational domain has a unique component which is in the x1 direction and it is only present where a velocity in the positive x3 direction exists. In all other places, the magnetic field components are constantly extrapolated into the ghost cells.

7.1.5.4 real b1_inflow

This parameter controls the strength of the inflowing horizontal magnetic field at the lower boundary in connection with bottom_bound_mag=inoutflow. The default value is 0.0. Example:

real b1_inflow f=E15.8 b=4 &
    n='Strength of inflowing horizontal magnetic field'           u=G
10.0

The unit of this parameter is gauss (no factor $\sqrt{4\pi}$!).

7.1.5.5 real c_magthetab

This parameter specifies the angle between the magnetic field vector and the x3-axis (in radians) in the case of oblique boundary conditions. The default value is 0.0. Example:

real c_magthetab f=E15.8 b=4 &
  n='angle magnetic field w.r. to the vertical direction' &
  u=rad c0='used in combination with oblique conditions'
0.523598775598299

7.1.5.6 real c_magphib

This parameter specifies the angle between the horizontal component of the magnetic field vector and the x1-axis (in radians) in the case of oblique boundary conditions. The default value is 0.0. Example:

real c_magphib f=E15.8 b=4 n='angle magnetic field w.r. to the x-axis' &
  u=rad c0='used in combination with oblique conditions'
0.0