===================
Boundary conditions
===================
The following tables list all possible boundary condition labels.

.. raw:: html

   <div>Filter: <input type='text' id='custombcsearch' /></div><br/>


Boundary conditions *bcx*
-------------------------
Module *boundcond.f90*
~~~~~~~~~~~~~~~~~~~~~~
.. list-table::
   :header-rows: 1
   :widths: 25 75

   * - Variable
     - Meaning
   * - *0*
     - zero value in ghost zones, free value on boundary
   * - *p*
     - periodic
   * - *s*
     - symmetry, :math:`f_{N+i}=f_{N-i}` ; implies :math:`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, :math:`f_{N+i}=-f_{N-i}` ; implies :math:`f(x_N)=f''(x_0)=0`
   * - *af*
     - antisymmetry with respect to interface
   * - *a2*
     - antisymmetry relative to boundary value, :math:`f_{N+i}=2 f_{N}-f_{N-i}` ; implies :math:`f''(x_0)=0`
   * - *a2v*
     - set boundary value and antisymmetry relative to it :math:`f_{N+i}=2 f_{N}-f_{N-i}` ; implies :math:`f''(x_0)=0`
   * - *a2r*
     - sets :math:`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 :math:`f''+f'/R=0`
   * - *cpp*
     - cylindrical perfect conductor for Aphi implies :math:`RA''+A'=0`
   * - *cpz*
     - cylindrical perfect conductor for Az implies :math:`R(RA)''-(RA)'=0`
   * - *spr*
     - spherical perfect conductor implies :math:`f''+2f'/R=0`  and :math:`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 :math:`s`  or temperature :math:`T` )
   * - *c1*
     - constant conductive flux
   * - *Fgs*
     - black body: - chi_t*rho*T*grad(s) - K*grad(T) = sigmaSBt*T**4
   * - *Fct*
     - Fbot = - K*grad(T) - chi_t*rho*T*grad(s)
   * - *Fcm*
     - :math:`Fbot = - K*grad(\overline{T})`  :math:`      - chi_t*\overline{rho}*\overline{T}*grad(\overline{s})`
   * - *sT*
     - symmetric temperature, :math:`T_{N-i}=T_{N+i}` ; implies :math:`T'(x_N)=T'''(x_0)=0`
   * - *asT*
     - select entropy for uniform ghost temperature matching fluctuating boundary value, :math:`T_{N-i}=T_{N}=` ; implies :math:`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*
     - :math:`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 :math:`(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 :math:`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*
     - :math:`(d/dr)(r B_{\phi}) = 0`  imposes boundary condition on 2nd derivative of :math:`r A_{\phi}` . Same applies to :math:`\theta`  component.
   * - *pfc*
     - perfect-conductor in spherical coordinate: :math:`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*
~~~~~~~~~~~~~~~~~~~~~~~~~~
.. list-table::
   :header-rows: 1
   :widths: 25 75

   * - Variable
     - Meaning
   * - *0*
     - do nothing; assume that everything is set zero value in ghost zones, free value on boundary
   * - *p*
     - periodic
   * - *s*
     - symmetry, :math:`f_{N+i}=f_{N-i}` ; implies :math:`f'(x_N)=f'''(x_0)=0`
   * - *ss*
     - symmetry, plus function value given
   * - *s0d*
     - symmetry, function value such that df/dx=0
   * - *a*
     - antisymmetry, :math:`f_{N+i}=-f_{N-i}` ; implies :math:`f(x_N)=f''(x_0)=0`
   * - *a2*
     - antisymmetry relative to boundary value, :math:`f_{N+i}=2 f_{N}-f_{N-i}` ; implies :math:`f''(x_0)=0`
   * - *a2r*
     - sets :math:`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 :math:`f''+f'/R=0`
   * - *cpp*
     - cylindrical perfect conductor implies :math:`f''+f'/R=0`
   * - *cpz*
     - cylindrical perfect conductor implies :math:`f''+f'/R=0`
   * - *spr*
     - spherical perfect conductor implies :math:`f''+2f'/R=0`  and :math:`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 :math:`s`  or temperature :math:`T` )
   * - *c1*
     - constant temperature (or maybe rather constant conductive flux??)
   * - *Fgs*
     - Fconv = - chi_t*rho*T*grad(s)
   * - *Fct*
     - Fbot = - K*grad(T) - chi_t*rho*T*grad(s)
   * - *Fcm*
     - :math:`Fbot = - K*grad(\overline{T})`  :math:`      - chi_t*\overline{rho}*\overline{T}*grad(\overline{s})`
   * - *sT*
     - symmetric temperature, :math:`T_{N-i}=T_{N+i}` ; implies :math:`T'(x_N)=T'''(x_0)=0`
   * - *asT*
     - select entropy for uniform ghost temperature matching fluctuating boundary value, :math:`T_{N-i}=T_{N}=` ; implies :math:`T'(x_N)=T'(x_0)=0`
   * - *db*
     -
   * - *f*
     - ``freeze'' value, i.e. maintain initial
   * - *fg*
     - ``freeze'' value, i.e. maintain initial
   * - *1*
     - :math:`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 :math:`(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 :math:`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*
     - :math:`(d/dr)(r B_{\phi}) = 0`  imposes boundary condition on 2nd derivative of :math:`r A_{\phi}` . Same applies to :math:`\theta`  component.
   * - *pfc*
     - perfect-conductor in spherical coordinate: :math:`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*
~~~~~~~~~~~~~~~~~~~~~~
.. list-table::
   :header-rows: 1
   :widths: 25 75

   * - 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 :math:`\ln\rho`  and :math:`s` : constant heat flux through the boundary
   * - *c1s*
     - complex
   * - *Fgs*
     - black body: - chi_t*rho*T*grad(s) - K*grad(T) = sigmaSBt*T**4
   * - *Fct*
     - Fbot = - K*grad(T) - chi_t*rho*T*grad(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, :math:`T_{N-i}=T_{N}=` ; implies :math:`T'(x_N)=T'(x_0)=0`
   * - *c2*
     - special boundary condition for s: constant temperature at the boundary --- requires boundary condition 'a2' for :math:`\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 :math:`\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 :math:`\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*
~~~~~~~~~~~~~~~~~~~~~~~~~~
.. list-table::
   :header-rows: 1
   :widths: 25 75

   * - 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_t*rho*T*grad(s)
   * - *Fct*
     - Fbot = - K*grad(T) - chi_t*rho*T*grad(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, :math:`T_{N-i}=T_{N}=` ; implies :math:`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 :math:`\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 :math:`\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*
~~~~~~~~~~~~~~~~~~~~~~
.. list-table::
   :header-rows: 1
   :widths: 25 75

   * - 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, :math:`f_{N+i}=f_{N-i}` ; implies :math:`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, :math:`T_{N-i}=T_{N}=` ; implies :math:`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 :math:`\theta`  boundary :math:`f''+\cot\theta f'=0`  and :math:`f(x_N)=0`
   * - *pfc*
     - perfect conducting boundary condition along :math:`\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*
~~~~~~~~~~~~~~~~~~~~~~~~~~
.. list-table::
   :header-rows: 1
   :widths: 25 75

   * - Variable
     - Meaning
   * - *sds*
     - symmetric-derivative-set
   * - *p*
     - periodic
   * - *pp*
     - periodic across the pole
   * - *ap*
     - anti-periodic across the pole
   * - *s*
     - symmetry symmetry, :math:`f_{N+i}=f_{N-i}` ; implies :math:`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, :math:`T_{N-i}=T_{N}=` ; implies :math:`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 :math:`\theta`  boundary :math:`f''+\cot\theta f'=0`  and :math:`f(x_N)=0`
   * - *pfc*
     - perfect conducting boundary condition along :math:`\theta`  boundary
   * - *str*
     -
   * - *nil, ''*
     - do nothing; assume that everything is set