Base thorn to provide the variables for the static conformal factor
This thorn provides the variables defining a static conformal factor which is used to transform the physical metric. If this thorn is active and the ADMBase::metric_type parameter is set to static conformal, then the ADMBase::g... variables are the conformal values as opposed to the physical values.
The transformation is
The extrinsic curvature is not transformed.
Memory is provided for the conformal factor psi, its first derivatives psix, psiy, psiz, and its second derivatives psixx, psixy, psixz, psiyy, psiyz, and psizz depending on the setting of the conformal_storage parameter.
Note that the first and second “derivative” grid functions have an additional factor of \(1 / \psi \) normalisation since this is the most common use of the derivative. I.e., the grid functions are
Thorns need to check the value of the grid scalar conformal_state to determine how many levels of these variables have actually been calculated before using the conformal factor:
conformal_state=0
No conformal factor has been calculated — thorns may assume the conformal factor is 1 at all points. (I.e., the metric is physical.)
conformal_state=1
The conformal factor has been calulated, but no derivatives.
conformal_state=2
The conformal factor and its first derivatives have been calculated.
conformal_state=3
The conformal factor and its first and second derivatives have been calculated.
Note that this means that if you only want to know whether psi contains the values for the conformal factor you can check for conformal_state > 0.
StaticConformal provides aliased functions to convert between physical and conformal 3-metric values. It is very important to understand that these functions apply the conversion in place. That is, if gxx contains the conformal metric value, when the routine is exited it will now contain the physical metric value. These functions do not change the value of conformal_state and should be used with due care. (These functions are for example used by some analysis thorns who work only with the physical metric, they apply the transformation on entry to the analysis routine and switch it back on exit).
Convert from conformal to physical:
subroutine ConfToPhysInPlace (nx, ny, nz,
psi,
gxx, gxy, gxz, gyy, gyz, gzz)
implicit none
CCTK_INT, intent(in) :: nx, ny, nz
CCTK_REAL, dimension(nx, ny, nz), intent(in) :: psi
CCTK_REAL, dimension(nx, ny, nz), intent(inout) :: gxx, gxy, gxz, gyy, gyz, gzz
end subroutine ConfToPhysInPlace
Convert from physical to conformal:
subroutine PhysToConfInPlace (nx, ny, nz,
psi,
gxx, gxy, gxz, gyy, gyz, gzz)
implicit none
CCTK_INT, intent(in) :: nx, ny, nz
CCTK_REAL, dimension(nx, ny, nz), intent(in) :: psi
CCTK_REAL, dimension(nx, ny, nz), intent(inout) :: gxx, gxy, gxz, gyy, gyz, gzz
end subroutine ConfToPhysInPlace
The StaticConformal thorn itself does not calculate any conformal factor, but does initialise the conformal_state variable to 0.
| conformal_storage | Scope: restricted | KEYWORD |
| Description: How much conformal storage do we have ?
| ||
| Range | Default: factor+derivs+2nd derivs | |
| factor | Just the conformal factor
| |
| factor+derivs | Conformal factor plus first derivatives
| |
| see [1] below | Conformal factor plus first and second derivatives
| |
[1]
factor+derivs+2nd derivs
| metric_type | Scope: shared from ADMBASE | KEYWORD |
| Extends ranges:
| ||
| static conformal | Metric is conformal with static conformal factor, extrinsic curvature is physical
| |
Implements:
staticconformal
Inherits:
grid
| Group Names | Variable Names | Details | |
| conformal_state | conformal_state | compact | 0 |
| dimensions | 0 | ||
| distribution | CONSTANT | ||
| group type | SCALAR | ||
| timelevels | 1 | ||
| variable type | INT | ||
| confac | compact | 0 | |
| psi | description | Conformal factor | |
| dimensions | 3 | ||
| distribution | DEFAULT | ||
| group type | GF | ||
| tags | tensortypealias=”Scalar” Prolongation=”None” InterpNumTimelevels=1 | ||
| timelevels | 1 | ||
| variable type | REAL | ||
| confac_1derivs | compact | 0 | |
| psix | description | First spatial derivatives of conformal factor divided by psi | |
| psiy | dimensions | 3 | |
| psiz | distribution | DEFAULT | |
| group type | GF | ||
| tags | tensortypealias=”U” Prolongation=”None” InterpNumTimelevels=1 | ||
| timelevels | 1 | ||
| variable type | REAL | ||
| confac_2derivs | compact | 0 | |
| psixx | description | Second spatial derivatives of conformal factor divided by psi | |
| psixy | dimensions | 3 | |
| psixz | distribution | DEFAULT | |
| psiyy | group type | GF | |
| psiyz | tags | tensortypealias=”dd_sym” Prolongation=”None” InterpNumTimelevels=1 | |
| psizz | timelevels | 1 | |
| variable type | REAL | ||
Provides:
ConfToPhysInPlace to
PhysToConfInPlace to
This section lists all the variables which are assigned storage by thorn EinsteinBase/StaticConformal. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.
| Always: | Conditional: |
| conformal_state | confac[1] |
| confac[1] confac_1derivs[1] | |
| confac[1] confac_1derivs[1] confac_2derivs[1] | |
CCTK_INITIAL
staticconformal_initialisestate
set the conformal_state variable to 0
| Before: | admbase_initialdata | |
| Language: | c | |
| Type: | function | |
| Writes: | staticconformal::conformal_state(everywhere) | |