Boundary conditions

The following tables list all possible boundary condition labels.

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Boundary conditions bcx

Module boundcond.f90

Variable	Meaning
0	zero value in ghost zones, free value on boundary
p	periodic
s	symmetry, \(f_{N+i}=f_{N-i}\) ; implies \(f'(x_N)=f'''(x_0)=0\)
sf	symmetry with respect to interface
ss	symmetry, plus function value given
sds	symmetric-derivative-set
s0d	symmetry, function value such that df/dx=0
a	antisymmetry, \(f_{N+i}=-f_{N-i}\) ; implies \(f(x_N)=f''(x_0)=0\)
af	antisymmetry with respect to interface
a2	antisymmetry relative to boundary value, \(f_{N+i}=2 f_{N}-f_{N-i}\) ; implies \(f''(x_0)=0\)
a2v	set boundary value and antisymmetry relative to it \(f_{N+i}=2 f_{N}-f_{N-i}\) ; implies \(f''(x_0)=0\)
a2r	sets \(d^2f/dr^2 +2df/dr- 2f/r^2 = 0\) This is the replacement of zero second derivative in spherical coordinates, in radial direction.
cpc	cylindrical perfect conductor implies \(f''+f'/R=0\)
cpp	cylindrical perfect conductor for Aphi implies \(RA''+A'=0\)
cpz	cylindrical perfect conductor for Az implies \(R(RA)''-(RA)'=0\)
spr	spherical perfect conductor implies \(f''+2f'/R=0\) and \(f(x_N)=0\)
v	vanishing third derivative
cop	copy value of last physical point to all ghost cells
1s	onesided
d1s	onesided for 1st/2nd derivative in two first inner points, Dirichlet in boundary point
n1s	onesided for 1st/2nd derivative in two first inner points, Neumann in boundary point
1so	onesided
cT	constant temperature (implemented as condition for entropy \(s\) or temperature \(T\) )
c1	constant conductive flux
Fgs	black body: - chi_trhoTgrad(s) - Kgrad(T) = sigmaSBtT*4
Fct	Fbot = - Kgrad(T) - chi_trhoTgrad(s)
Fcm	\(Fbot = - Kgrad(\overline{T})\) :math:` - chi_toverline{rho}overline{T}grad(overline{s})`
sT	symmetric temperature, \(T_{N-i}=T_{N+i}\) ; implies \(T'(x_N)=T'''(x_0)=0\)
asT	select entropy for uniform ghost temperature matching fluctuating boundary value, \(T_{N-i}=T_{N}=\) ; implies \(T'(x_N)=T'(x_0)=0\)
db	low-order one-sided derivatives (``no boundary condition’’) for density
f	``freeze’’ value, i.e. maintain initial value; antisymm wrt boundary
fg	``freeze’’ value, i.e. maintain initial value at boundary, also mantaining the ghost zones at the initial coded value, i.e., keep the gradient frozen as well
1	\(f=1\) (for debugging)
set	set boundary value to var{fbcx}
st	set boundary value to value generated by function bc_st. Special time-dependent boundary condition to model temporal changes.
st2	set boundary value to value generated by function bc_st. Special time-dependent boundary condition to model temporal changes.
der	set derivative on boundary to var{fbcx}
slo	set slope at the boundary = var{fbcx}
slp	set slope at the boundary and in ghost cells = var{fbcx}
shx	set shearing boundary proportional to x with slope=var{fbcx} and abscissa=var{fbcx2}
shy	set shearing boundary proportional to y with slope=var{fbcx} and abscissa=var{fbcx2}
shz	set shearing boundary proportional to z with slope=var{fbcx} and abscissa=var{fbcx2}
dr0	set boundary value [really??]
ovr	overshoot boundary condition ie \((d/dx-1/\mathrm{dist}) f = 0.\)
out	allow outflow, but no inflow forces ghost cells and boundary to not point inwards
e1o	allow outflow, but no inflow uses the e1 extrapolation scheme
ant	stops and prompts for adding documentation
e1	extrapolation [describe]
e2	extrapolation [describe]
e2h	extrapolation [describe]
e3	extrapolation in log [maintain a power law]
el	linear extrapolation from last two active cells
pl	extrapolate using power law with the power index specified by fbcx
hat	top hat jet profile in spherical coordinate.
jet	top hat jet profile in cartezian coordinate.
spd	sets \(d(rA_{\alpha})/dr = \mathtt{fbcx(j)}\)
sfr	stress-free boundary condition for spherical coordinate system.
sr1	Stress-free bc for spherical coordinate system. Implementation with one-sided derivative.
nfr	Normal-field bc for spherical coordinate system. Some people call this the ``(angry) hedgehog bc’’.
nr1	Normal-field bc for spherical coordinate system. Some people call this the ``(angry) hedgehog bc’’. Implementation with one-sided derivative.
sa2	\((d/dr)(r B_{\phi}) = 0\) imposes boundary condition on 2nd derivative of \(r A_{\phi}\) . Same applies to \(\theta\) component.
pfc	perfect-conductor in spherical coordinate: \(d/dr( A_r) + 2/r = 0\) .
fix	set boundary value [really??]
fil	set boundary value from a file
cfb	radial centrifugal balance
g	set to given value(s) or function
ioc	inlet/outlet on western/eastern hemisphere in cylindrical coordinates
tay
exp	exponentiate x ghost zone of other variable
slc	set x ghost zones from slice.
density_wind	‘wind’ bc for lnrho
nil, ‘’, no	do nothing; assume that everything is set

Module boundcond_alt.f90

Variable	Meaning
0	do nothing; assume that everything is set zero value in ghost zones, free value on boundary
p	periodic
s	symmetry, \(f_{N+i}=f_{N-i}\) ; implies \(f'(x_N)=f'''(x_0)=0\)
ss	symmetry, plus function value given
s0d	symmetry, function value such that df/dx=0
a	antisymmetry, \(f_{N+i}=-f_{N-i}\) ; implies \(f(x_N)=f''(x_0)=0\)
a2	antisymmetry relative to boundary value, \(f_{N+i}=2 f_{N}-f_{N-i}\) ; implies \(f''(x_0)=0\)
a2r	sets \(d^2f/dr^2 +2df/dr- 2f/r^2 = 0\) This is the replacement of zero second derivative in spherical coordinates, in radial direction.
cpc	cylindrical perfect conductor implies \(f''+f'/R=0\)
cpp	cylindrical perfect conductor implies \(f''+f'/R=0\)
cpz	cylindrical perfect conductor implies \(f''+f'/R=0\)
spr	spherical perfect conductor implies \(f''+2f'/R=0\) and \(f(x_N)=0\)
v	vanishing third derivative
cop	copy value of last physical point to all ghost cells
1s	onesided
1so	onesided
cT	constant temperature (implemented as condition for entropy \(s\) or temperature \(T\) )
c1	constant temperature (or maybe rather constant conductive flux??)
Fgs	Fconv = - chi_trhoT*grad(s)
Fct	Fbot = - Kgrad(T) - chi_trhoTgrad(s)
Fcm	\(Fbot = - Kgrad(\overline{T})\) :math:` - chi_toverline{rho}overline{T}grad(overline{s})`
sT	symmetric temperature, \(T_{N-i}=T_{N+i}\) ; implies \(T'(x_N)=T'''(x_0)=0\)
asT	select entropy for uniform ghost temperature matching fluctuating boundary value, \(T_{N-i}=T_{N}=\) ; implies \(T'(x_N)=T'(x_0)=0\)
db
f	``freeze’’ value, i.e. maintain initial
fg	``freeze’’ value, i.e. maintain initial
1	\(f=1\) (for debugging)
set	set boundary value to var{fbcx12}
der	set derivative on boundary to var{fbcx12}
slo	set slope at the boundary = var{fbcx12}
dr0	set boundary value [really??]
ovr	overshoot boundary condition ie \((d/dx-1/\mathrm{dist}) f = 0.\)
out	allow outflow, but no inflow forces ghost cells and boundary to not point inwards
e1o	allow outflow, but no inflow uses the e1 extrapolation scheme
ant	stops and prompts for adding documentation
e1	extrapolation [describe]
e2	extrapolation [describe]
e3	extrapolation in log [maintain a power law]
hat	top hat jet profile in spherical coordinate.
jet	top hat jet profile in cartezian coordinate.
spd	sets \(d(rA_{\alpha})/dr = \mathtt{fbcx12(j)}\)
sfr	stress-free boundary condition for spherical coordinate system.
nfr	Normal-field bc for spherical coordinate system. Some people call this the ``(angry) hedgehog bc’’.
sa2	\((d/dr)(r B_{\phi}) = 0\) imposes boundary condition on 2nd derivative of \(r A_{\phi}\) . Same applies to \(\theta\) component.
pfc	perfect-conductor in spherical coordinate: \(d/dr( A_r) + 2/r = 0\) .
fix	set boundary value [really??]
fil	set boundary value from a file
g	set to given value(s) or function
ioc	do nothing; assume that everything is set inlet/outlet on western/eastern hemisphere in cylindrical coordinates
tay

Boundary conditions bcz

Module boundcond.f90

Variable	Meaning
in	allow inflow, but no outflow forces ghost cells and boundary to not point outwards
0	zero value in ghost zones, free value on boundary
p	periodic
yy	Yin-Yang grid
s	symmetry
sf	symmetry with respect to interface
s0d	symmetry, function value such that df/dz=0
0ds	symmetry, function value such that df/dz=0
a	antisymmetry
a2	antisymmetry relative to boundary value
a2v	set boundary value and antisymmetry relative to it
af	antisymmetry with respect to interface
a0d	antisymmetry with zero derivative
v	vanishing third derivative
v3	vanishing third derivative
1s	one-sided
d1s	onesided for 1st and 2nd derivative in two first inner points, Dirichlet in boundary point
n1s	onesided for 1st and 2nd derivative in two first inner points, Neumann in boundary point
a1s	special for perfect conductor with const alpha and etaT when A considered as B; one-sided for 1st and 2nd derivative in two first inner points
fg	``freeze’’ value, i.e. maintain initial value at boundary, also mantaining the ghost zones at the initial coded value, i.e., keep the gradient frozen as well
c1	special boundary condition for \(\ln\rho\) and \(s\) : constant heat flux through the boundary
c1s	complex
Fgs	black body: - chi_trhoTgrad(s) - Kgrad(T) = sigmaSBtT*4
Fct	Fbot = - Kgrad(T) - chi_trhoTgrad(s)
c3	constant flux at the bottom with a variable hcond
pfe	potential field extrapolation
p1D	potential field extrapolation in 1D
pot	potential magnetic field
pwd	a variant of ‘pot’ for nprocx=1
d2z
hds	hydrostatic equilibrium with a high-frequency filter
cT	constant temperature. If used for lnrho, sets both lnrho and ss (in which case the BC for ss should be set to ‘nil’) If used for ss, sets only ss.
cT1	constant temperature using one-sided derivatives
cT2	constant temp. (keep lnrho)
cT3	constant temp. (keep lnrho)
hs	hydrostatic equilibrium
hse	hydrostatic extrapolation rho or lnrho is extrapolated linearily and the temperature is calculated in hydrostatic equilibrium.
cp	constant pressure
sT	symmetric temp.
ctz	for interstellar runs copy T
cdz	for interstellar runs limit rho
ism	exponential decay/growth in rho/T by scale height
asT	select entropy for uniform ghost temperature matching fluctuating boundary value, \(T_{N-i}=T_{N}=\) ; implies \(T'(x_N)=T'(x_0)=0\)
c2	special boundary condition for s: constant temperature at the boundary — requires boundary condition ‘a2’ for \(\ln\rho\)
db	low-order one-sided derivatives (``no boundary condition’’) for density
ce	complex
e1	extrapolation
e2	extrapolation
ex	simple linear extrapolation in first order
exf	simple linear extrapolation in first order
exd	simple linear extrapolation in first order
exm	simple linear extrapolation in first order
b1	extrapolation with zero value (improved ‘a’)
b2	extrapolation with zero value (improved ‘a’)
b3	extrapolation with zero value (improved ‘a’)
f, fa	freeze value + antisymmetry
fs	freeze value + symmetry
fBs	frozen-in B-field (s)
fB	frozen-in B-field (a2)
g	set to given value(s) or function
gs
1	f=1 (for debugging)
StS	solar surface boundary conditions
set	set boundary value
sep	set boundary value
der	set derivative on the boundary
div	set the divergence of \(\uv\) to a given value use bc = ‘div’ for iuz
ovr	set boundary value
inf	allow inflow, but no outflow
ouf	allow outflow, but no inflow
out	allow outflow, but no inflow forces ghost cells and boundary to not point inwards
crk	no-inflow: copy value of last physical point to all ghost cells, but suppressing any inflow
in0	allow inflow, but no outflow forces ghost cells and boundary to not point outwards relaxes to vanishing 1st derivative at boundary
ou0	allow outflow, but no inflow forces ghost cells and boundary to not point inwards relaxes to vanishing 1st derivative at boundary
ind	allow inflow, but no outflow forces ghost cells and boundary to not point outwards creates inwards pointing or zero 1st derivative at boundary
oud	allow outflow, but no inflow forces ghost cells and boundary to not point inwards creates outwards pointing or zero 1st derivative at boundary
ubs	copy boundary outflow, reduce inflow speed outside the boundary
win	forces massflux given as \(\Sigma \rho_i ( u_i + u_0)=\textrm{fbcz1/2}(\rho)\)
cop	copy value of last physical point to all ghost cells
str
tay
exp	exponentiate z ghost zone of other variable
slc	set z ghost zones from slice.
nil, ‘’, no	do nothing; assume that everything is set

Module boundcond_alt.f90

Variable	Meaning
cfb	radial centrifugal balance
fBs	frozen-in B-field (s)
fB	frozen-in B-field (a2)
0	zero value in ghost zones, free value on boundary
p	periodic
s	symmetry
sf	symmetry with respect to interface
s0d	symmetry, function value such that df/dz=0
0ds	symmetry, function value such that df/dz=0
a	antisymmetry
a2	antisymmetry relative to boundary value
af	antisymmetry with respect to interface
a0d	antisymmetry with zero derivative
v	vanishing third derivative
v3	vanishing third derivative
1s	one-sided
fg	``freeze’’ value, i.e. maintain initial
c1	complex
Fgs	Fconv = - chi_trhoT*grad(s)
Fct	Fbot = - Kgrad(T) - chi_trhoTgrad(s)
c3	constant flux at the bottom with a variable hcond
pfe	potential field extrapolation
p1D	potential field extrapolation in 1D
pot	potential magnetic field
pwd	a variant of ‘pot’ for nprocx=1
d2z
hds	hydrostatic equilibrium with a high-frequency filter
cT	constant temp.
cT2	constant temp. (keep lnrho)
cT3	constant temp. (keep lnrho)
hs	hydrostatic equilibrium
hse	hydrostatic extrapolation rho or lnrho is extrapolated linearily and the temperature is calculated in hydrostatic equilibrium.
cp	constant pressure
sT	symmetric temp.
ctz	for interstellar runs copy T
cdz	for interstellar runs limit rho
asT	select entropy for uniform ghost temperature matching fluctuating boundary value, \(T_{N-i}=T_{N}=\) ; implies \(T'(x_N)=T'(x_0)=0\)
c2	complex
db	complex
ce	complex
e1	extrapolation
e2	extrapolation
ex	simple linear extrapolation in first order
exf	simple linear extrapolation in first order
exd	simple linear extrapolation in first order
exm	simple linear extrapolation in first order
b1	extrapolation with zero value (improved ‘a’)
b2	extrapolation with zero value (improved ‘a’)
b3	extrapolation with zero value (improved ‘a’)
f, fa	freeze value + antisymmetry
fs	freeze value + symmetry
g	set to given value(s) or function
gs
1	f=1 (for debugging)
StS	solar surface boundary conditions
set	set boundary value
der	set derivative on the boundary
div	set the divergence of \(\uv\) to a given value use bc = ‘div’ for iuz
ovr	set boundary value
inf	allow inflow, but no outflow
ouf	allow outflow, but no inflow
in	allow inflow, but no outflow forces ghost cells and boundary to not point outwards
out	allow outflow, but no inflow forces ghost cells and boundary to not point inwards
in0	allow inflow, but no outflow forces ghost cells and boundary to not point outwards relaxes to vanishing 1st derivative at boundary
ou0	allow outflow, but no inflow forces ghost cells and boundary to not point inwards relaxes to vanishing 1st derivative at boundary
ind	allow inflow, but no outflow forces ghost cells and boundary to not point outwards creates inwards pointing or zero 1st derivative at boundary
oud	allow outflow, but no inflow forces ghost cells and boundary to not point inwards creates outwards pointing or zero 1st derivative at boundary
ubs	copy boundary outflow,
win	forces massflux given as \(\Sigma \rho_i ( u_i + u_0)=\textrm{fbcz1/2}(\rho)\)
cop	copy value of last physical point to all ghost cells
nil	do nothing; assume that everything is set

Boundary conditions bcy

Module boundcond.f90

Variable	Meaning
0	zero value in ghost zones, free value on boundary
p	periodic
pp	periodic across the pole
yy	Yin-Yang grid
ap	anti-periodic across the pole
s	symmetry, \(f_{N+i}=f_{N-i}\) ; implies \(f'(y_N)=f'''(y_0)=0\)
sf	symmetry with respect to interface
ss	symmetry, plus function value given
sds	symmetric-derivative-set
cds	complex symmetric-derivative-set
s0d	symmetry, function value such that df/dy=0
a	antisymmetry
af	antisymmetry with respect to interface
a2	antisymmetry relative to boundary value
v	vanishing third derivative
v3	vanishing third derivative
out	allow outflow, but no inflow forces ghost cells and boundary to not point inwards
1s	onesided
d1s	onesided for 1st and 2nd derivative in two first inner points, Dirichlet in boundary point
n1s	onesided for 1st and 2nd derivative in two first inner points, Neumann in boundary point
cT	constant temp.
sT	symmetric temp.
asT	select entropy for uniform ghost temperature matching fluctuating boundary value, \(T_{N-i}=T_{N}=\) ; implies \(T'(x_N)=T'(x_0)=0\)
f	freeze value
s+f	freeze value
fg	``freeze’’ value, i.e. maintain initial
fBs	frozen-in B-field (s)
fB	frozen-in B-field (a2)
1	f=1 (for debugging)
set	set boundary value
sse	symmetry, set boundary value
sep	set boundary value
e1	extrapolation
e2	extrapolation
e3	extrapolation in log [maintain a power law]
der	set derivative on the boundary
cop	outflow: copy value of last physical point to all ghost cells
c+k	no-inflow: copy value of last physical point to all ghost cells, but suppressing any inflow
sfr	stress-free boundary condition for spherical coordinate system.
nfr	Normal-field bc for spherical coordinate system. Some people call this the ``(angry) hedgehog bc’’.
spt	spherical perfect conducting boundary condition along \(\theta\) boundary \(f''+\cot\theta f'=0\) and \(f(x_N)=0\)
pfc	perfect conducting boundary condition along \(\theta\) boundary
str
tay
exp	exponentiate y ghost zone of other variable
slc	set x ghost zones from slice.
nil, ‘’, no	do nothing; assume that everything is set

Module boundcond_alt.f90

Variable	Meaning
sds	symmetric-derivative-set
p	periodic
pp	periodic across the pole
ap	anti-periodic across the pole
s	symmetry symmetry, \(f_{N+i}=f_{N-i}\) ; implies \(f'(y_N)=f'''(y_0)=0\)
ss	symmetry, plus function value given
cds	complex symmetric-derivative-set
s0d	symmetry, function value such that df/dy=0
a	antisymmetry
a2	antisymmetry relative to boundary value
v	vanishing third derivative
v3	vanishing third derivative
out	allow outflow, but no inflow forces ghost cells and boundary to not point inwards
1s	onesided
cT	constant temp.
sT	symmetric temp.
asT	select entropy for uniform ghost temperature matching fluctuating boundary value, \(T_{N-i}=T_{N}=\) ; implies \(T'(x_N)=T'(x_0)=0\)
f	freeze value
s+f	freeze value
fg	``freeze’’ value, i.e. maintain initial
1	f=1 (for debugging)
set	set boundary value
sse	symmetry, set boundary value
sep	set boundary value
e1	extrapolation
e2	extrapolation
e3	extrapolation in log [maintain a power law]
der	set derivative on the boundary
cop	outflow: copy value of last physical point to all ghost cells
c+k	no-inflow: copy value of last physical point to all ghost cells, but suppressing any inflow
sfr	stress-free boundary condition for spherical coordinate system.
nfr	Normal-field bc for spherical coordinate system. Some people call this the ``(angry) hedgehog bc’’.
spt	spherical perfect conducting boundary condition along \(\theta\) boundary \(f''+\cot\theta f'=0\) and \(f(x_N)=0\)
pfc	perfect conducting boundary condition along \(\theta\) boundary
str
nil, ‘’	do nothing; assume that everything is set