- 7.1.4.1 character side_bound
- 7.1.4.2 character top_bound
- 7.1.4.3 character bottom_bound
- 7.1.4.4 character heat_mode
- 7.1.4.5 character hdcoreheatprofile
- 7.1.4.6 real luminositypervolume
- 7.1.4.7 real s_inflow
- 7.1.4.8 real s_inflradgrad
- 7.1.4.9 real s_infllatgrad
- 7.1.4.10 real c_schange
- 7.1.4.11 real c_pchange
- 7.1.4.12 real c_v3changelinbottom
- 7.1.4.13 real c_v3changesqrbottom
- 7.1.4.14 real c_visbound
- 7.1.4.15 real c_rhochangetop
- 7.1.4.16 real c_tchange
- 7.1.4.17 real c_tsurf
- 7.1.4.18 real c_hptopfactor
- 7.1.4.19 real c_radhtautop
- 7.1.4.20 real r1_rad
- 7.1.4.21 real rho_min
- 7.1.4.22 real c_coredrag
- 7.1.4.23 character hdcoredragprofile

7.1.4 Boundary conditions (general)

The boundary conditions at the six sides of the computational box cannot be specified independently. For the naming convention of the boundaries a gravitational acceleration in -x3 direction is assumed. Accordingly, there is a bottom and a top boundary, and four side boundaries.

All boundary conditions of the hydrodynamic case are available in the MHD module.

c0='closed, transmitting, periodic'

transmitting

`reflective`

: closed wall, no gravity, no radiation. The velocity vector is mirrored at the boundary.`constant`

: open boundary with constant extrapolation of all values, no gravity, no radiation.`closed`

,`closedtop`

: closed wall, can handle gravity, open for outward radiation.`periodic`

: periodic boundaries for hydrodynamics, radiation.`transmitting`

: transmitting boundary for hydro and outward radiation.

`MSrad`

radiation transport module
the side boundaries `periodic`

.
In simulations of a red supergiant all boundaries (including the sides) will typically
be `transmitting`

. As an alternative, `closed`

boundaries can be chosen in this case.

transmitting

`reflective`

: closed wall, no gravity, no radiation. The velocity vector is mirrored at the boundary.`constant`

: open boundary with constant extrapolation of all values, no gravity, no radiation`closed`

,`closedtop`

: closed wall, can handle gravity, open for outward radiation.`periodic`

: periodic boundaries for hydrodynamics.`transmitting`

: transmitting boundary for hydro and outward radiation: exponential decrease of density (standard open boundary condition).`transmitting2`

: transmitting boundary for hydro and outward radiation: exponential decrease of density and extra velocity treatment.`transmitting3`

: transmitting boundary for hydro and outward radiation: constant density extrapolation.

`transmitting`

top
boundary will be selected, the `closed`

one is an alternative.
The `periodic`

condition is only recognized by the hydrodynamics routines
and not by any radiation transport routine.

7.1.4.3 character bottom_bound

c0=closedbottom

transmitting

`reflective`

: closed wall, no gravity, no radiation. The velocity vector is mirrored at the boundary.`constant`

: open boundary with constant extrapolation of all values, no gravity, no radiation.`closed`

,`closedtop`

: closed wall, can handle gravity, open for outward radiation.`closedbottom`

: closed wall, handles gravity, radiation in diffusion approximation.`closedbottom2`

: closed wall, handles gravity, radiation in diffusion approximation. In this version, the extrapolation of quantities should be smoother than for`closedbottom`

.`periodic`

: periodic boundaries for hydrodynamics.`transmitting`

: transmitting boundary for hydro and outward radiation. The parameters`real c_tchange`

,`real c_tsurf`

, and`real c_hptopfactor`

have to be specified.`inoutflow`

: "classical" open lower boundary for deep convection, gravity and radiation possible. The parameters`real s_inflow`

,`real c_schange`

, and`real c_pchange`

have to be specified.`inoutflow2`

: variant of the open lower boundary condition. The parameters`real s_inflow`

,`real c_schange`

,`real c_pchange`

have to be specified. In this version, the extrapolation of quantities should be smoother than for`inoutflow`

.

`MSrad`

radiation transport module
the bottom boundary is typically of type ```inoutflow`

''.
A supergiant simulation will have a `transmitting`

lower boundary.

7.1.4.4 character heat_mode

`s_inflow`

(see Sect.7.1.4.7) and
`luminositypervolume`

(see Sect.7.1.4.6).
Example:
c0='-/bottom_entropy1/bottom_energy1' &

c1='core_entropy1/core_energyentropy1/core_energy1/core_energy2'

bottom_entropy1

`closedbottom`

) or by convection + radiation (for an open bottom boundary`inoutflow`

).`bottom_entropy1`

: The entropy in the bottom layers (defined as being less than`r0_grav`

above the bottom of the model) is adjusted towards`s_inflow`

on a rate given by`c_schange`

.`bottom_energy1`

: Energy in the bottom layers (defined as being less than`r0_grav`

above the bottom of the model) is added according to`teff`

.`core_entropy1`

: The entropy in the core is adjusted towards`s_inflow`

on a rate given by`c_schange`

.`core_energyentropy1`

: The entropy in the core is adjusted towards the mean core entropy (i.e., smoothed) on a rate given by`c_schange`

. However, the total energy input is added according to`luminositypervolume`

. This avoids a local pile up of energy in case of a strong core drag force (Sect.7.1.4.22) or just slow flows.`core_energy1`

: Energy in the core is added according to`luminositypervolume`

.`core_energy2`

: Energy in the core is added according to`luminositypervolume`

with a Gaussian distribution of the energy source.

7.1.4.5 character hdcoreheatprofile

Constant

`Constant`

,`Constantdei`

: Apply the same change of in all core volume elements, (old) default. This gives a larger change of than`Constantdrhoei`

in the central part of the core where the density is higher.`Constantdrhoei`

: Apply the same change of in all core volume elements.

7.1.4.6 real luminositypervolume

`heat_mode`

can be set with this parameter.
To avoid numbers that do not fit into a 4 Byte real the luminosity per volume
has to be specified as e.g. in
u='erg/cm^3/s'

4.5E-02

`0.0`

or below the entropy of the
material within the core (defined by as all cells within radius `r0_grav`

)
is adjusted instead.

7.1.4.7 real s_inflow

`inoutflow`

''
into the model can be specified e.g. with
u=erg/K/g

3.25E+09

`central`

potential, the entropy in a sphere with radius
`r0_grav`

is adjusted towards this entropy value.
In both geometries (supergiant as well as solar) this value is very important as
it finally (but indirectly) determines the luminosity and
effective temperature of the star.
A value of `0.0`

(default) or below disables this energy input.

7.1.4.8 real s_inflradgrad

`central`

potential, one can decrease the entropy
in the very center of the core to generate some extra braking buoyancy, e.g. with
u=erg/K/g

1.0E+06

`s_inflow`

is typically of the order of
`1.0E+09`

, this parameter is typically of the order of `1.0E+06`

.
A value of `0.0`

(default) causes a zero gradient.

7.1.4.9 real s_infllatgrad

`central`

potential, one can enforce a meridional flow
(the axis is the axis) by enforcing a lateral entropy gradient in the
core, e.g. with
u=erg/K/g

1.0E+06

`s_inflow`

is typically of the order of
`1.0E+09`

, this parameter is typically of the order of `1.0E+06`

.
A value of `0.0`

(default) causes a zero gradient.

`s_inflow`

of the material in the bottom layer
(solar case, `inoutflow`

boundary condition)
or the central region of the (global) model is not just
set to the specified but adjusted towards it. The adjustment rate can be
controlled with e.g.
n='Rate of entropy change for open lower boundary' u=1

0.3

`1.0`

: fast adjustment`0.3`

: typical value`0.1`

: slow adjustment`<=0.0`

: not allowed

`inoutflow`

boundary condition not only controls entropy and velocity
but also the pressure in the bottom layers:
It is locally adjusted towards the global average to damp out possible
instabilities.
The adjustment rate can be specified e.g., with
n='Rate of pressure change for open lower boundary' u=1

1.0

7.1.4.12 real c_v3changelinbottom

`inoutflow`

and `inoutflow2`

),
a damping of the vertical velocity at the open boundary can be specified,
e.g., with
n='Linear velocity reduction rate at bottom' u=1

0.0025

`0.0`

: off: no linear damping`0.002`

: small reasonable value`0.005`

: large, possible useful value

`inoutflow`

and `inoutflow2`

),
an additional damping of the vertical velocity at the open boundary can be specified,
e.g., with
n='Quadratic velocity reduction rate at bottom' u=1

0.002

`transmitting`

boundary condition is chosen. The value can be
set e.g. with
n='Boundary drag viscosity parameter' u=1

0.001

`c_visbound`

=`0.0`

).

7.1.4.15 real c_rhochangetop

`transmitting`

upper boundary condition
can smooth density fluctuations with this parameter.
It is locally adjusted towards the global average to damp out possible
instabilities. It appears to be useful for the HLLMHD solver.
For simulations without magnetic fields, there is no need to set this parameter, so far.
The adjustment rate can be specified e.g. with
n='Rate of density change for open upper boundary' u=1

1.0

`1.0`

.

`transmitting`

upper or outer boundary
the temperature of the material streaming into the model
is adjusted with a rate given e.g. by
n='Rate of temperature change for open upper boundary' u=1

0.3

`transmitting`

upper or outer boundary
the temperature of the material streaming into the model
is adjusted towards a temperature `teff`

*`c_tsurf`

.
This temperature can be specified as fraction of the effective temperature
e.g. with
0.62

`transmitting`

upper or outer boundary
the density stratification outside the model has to be extrapolated properly.
Assumptions about this density affects the amount of mass flowing
into the model.
For the extrapolation it is assumed that the density scale scales
with the pressure scale height as
=/`c_hptopfactor`

.
n='Correction factor for surface pressure scale height' u=1

0.8

- C
`0.0`

: No effect (actually, a value of`1.0`

is chosen). `0.0`

C`1.0`

: The density scale height is enlarged to account for possible effects of turbulent pressure on the scale height: The density decays less rapidly with height than in an (isothermal) hydrostatic stratification.- C
`1.0`

: Density scale height is pressure scale height. - C
`1.0`

: Density scale height is smaller than pressure scale height. Not really useful.

7.1.4.19 real c_radhtautop

60.0E+05

- C
`0.0`

: Older version: (both`MSrad`

and`SHORTRAD`

). - C
`0.0`

: New version: . In this case, a value of`C_radHtautop=-1.0`

might be a good choice (`MSrad`

only).

`r1_rad`

can specify a radius beyond which only positive contributions
of the radiative energy transport to the energy budget are taken into account. This
ruins the conservativity of the code in these layers and should be applied only in very
remote corners which are then considered only as sort of extended boundary region but
not as part of the ``real'' model.
The parameter can be specified e.g. with
c0='0.0: Not used'

8.00000e+13

`0.0`

(default) or below deactivates this feature.

1.0E-25

`0.0`

(default) or below deactivates this feature.

7.1.4.22 real c_coredrag

`r0_grav`

)
can be applied.
It is controlled e.g. with
1.0

`0.0`

(default) or below deactivates this feature.

7.1.4.23 character hdcoredragprofile

Linear

`Constant`

: Use a local drag force that depends on core radius`r0_grav`

, local sound speed, and`real c_coredrag`

(default). The overlaid radial profile is a constant.`Linear`

: Use a local drag force that employs as overlay a linear decay from center to`r0_grav`

.`Cosine`

: Use a local drag force that employs as overlay a cosine function from center to`r0_grav`

.`CosSqr`

: Use a local drag force that employs as overlay a (cosine) function from center to`r0_grav`

.`Constant-Radial`

: Use the same radial profile as`Constant`

but apply the drag force to the radial velocity component only.`Linear-Radial`

: Use the same radial profile as`Linear`

but apply the drag force to the radial velocity component only.`Cosine-Radial`

: Use the same radial profile as`Cosine`

but apply the drag force to the radial velocity component only.`CosSqr-Radial`

: Use the same radial profile as`CosSqr`

but apply the drag force to the radial velocity component only.`Constant-Meridional`

: Use the same radial profile as`Constant`

but apply the drag force to the meridional velocity components only ( is the axis).`Linear-Meridional`

: Use the same radial profile as`Linear`

but apply the drag force to the meridional velocity components only.`Cosine-Meridional`

: Use the same radial profile as`Cosine`

but apply the drag force to the meridional velocity components only.`CosSqr-Meridional`

: Use the same radial profile as`CosSqr`

but apply the drag force to the meridional velocity components only.