xx smallbPoynET

smallbPoynET

Zachariah B.xEtienne <zachetie *at* gmail *dot* com >

Documentation by Leonardo R.xWerneck <wernecklr *at* gmail *dot* com >

Feb 2, 2022

Abstract

smallbPoynET is an Einstein Toolkit thorn for computing the time-component of the fluid four-velocity, , the magnetic field measured by a comoving observer , and the Poynting vector .

1 Overview We want to compute the time-component of the fluid four-velocity, , the magnetic field measured by a comoving observer , and the Poynting vector . We are given the ADMBase and HydroBase gridfunctions. First, note that the magnetic field measured by a comoving observer, , is given by (see e.g.,x[1]) where are the spatial components of the magnetic field, is the fluid four-velocity, and is the lapse function. Furthermore, the spatial components of the fluid four-velocity are given by where is the shift vector and is the Valencia three-velocity. This means that all that we are missing in order to compute and is the time-component of the fluid four-velocity, .

Consider, thus, the definition of the Lorentz factor , where is the physical spatial metric. Furthermore, consider the constraint , from which we find

where we have used the ADM decomposition of the spacetime metric Therefore we find that Therefore after computing using the ADMBase and HydroBase variables, we are able to compute and therefore and .

The Poynting vector, , is computed using Eq. (11) inx[2] but adopting the sign convention ofx[3], i.e.,

where .

2 Basic usage

In other to use the smallbPoynET thorn, the user must activate it in the parfile and specify the frequency in which the quantities above are computed. Note that by default the frequency is set to zero, which effectively disables the thorn. If you are using thorns that evolves gridfunctions other than those defined by ADMBase or HydroBase, then you must make sure to convert your gridfunctions to the ones used by this thorn when before calling it.

Adding the following lines to your parfile will activate this thorn and trigger the computation of , , and once every 16 time steps.

ActiveThornsx=x"smallbPoynET"
#xConfigurexthornxtoxcomputexu^{0},xb^{mu},xandxS^{i}xeveryx16xtimexsteps
smallbPoynET::smallbPoynET_compute_everyx=x16

References

[1]xxxM.D. Duez, Y.T. Liu, S.L. Shapiro, & B.C. Stephens, Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests, Physical Review D, 72, 2, 024028 (2005).

[2]xxxB.xJ.xKelly, J.xG.xBaker, Z.xB.xEtienne, B.xGiacomazzo, & J.xSchnittman, Prompt electromagnetic transients from binary black hole mergers, Physical Review D, 96(12), 123003 (2017).

[3]xxxB.xD.xFarris, R.xGold, V.xPaschalidis, Z.xB.xEtienne, & S.xL.xShapiro, Binary black-hole mergers in magnetized disks: simulations in full general relativity, Physical Review Letters, 109(22), 221102 (2012).

3 Parameters

11enablexwarning  10Scope: privatex01  INT

11Description: Warn if regridxevery divided by smallbPoynETxcomputexevery is not an integer >= 1. You may see AMR artifacts otherwise!

11  Range  10  x01  Default: 1
110:1  10zero (disable) or one (enable)

11

11smallbpoynetxcomputexevery 10Scope: privatex01  INT

11Description: How often to compute smallbPoyn?

11 Range 10 x01 Default: (none)
110:100000  10zero (disable computation) or some other number (1 = every iteration)

11

11timelevels  10Scope: shared from HYDROBASEx01INT

11

4 Interfaces

General Implements: smallbpoynet

Inherits: grid hydrobase admbase

Grid Variables

4.0.1 PRIVATE GROUPS

11x Group Names x10x Variable Names xx01 Details x11x
11 smallbpoynetgfs 10  x01  compact110
11                 10  smallbt  x01 dimensions113
11                 10  smallbx  x01 distribution11DEFAULT
11                 10  smallby  x01 group type11GF
11                 10  smallbz  x01  tags11InterpNumTimelevels=1 prolongation=”none” Checkpoint=”no”
11                 10  smallb2  x01 timelevels111
11                 10  Poynx  x01variable type11REAL

11

5 Schedule This section lists all the variables which are assigned storage by thorn WVUThornsxDiagnostics/smallbPoynET. 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.

Storage x

11Always:  11x
11smallbPoynETGFs  11x
11ADMBase::metric[metricxtimelevels] ADMBase::curv[metricxtimelevels] ADMBase::lapse[lapsextimelevels] ADMBase::shift[shiftxtimelevels]11x
11HydroBase::rho[timelevels] HydroBase::press[timelevels] HydroBase::eps[timelevels] HydroBase::vel[timelevels] HydroBase::Bvec[timelevels] 11x

11x  11x

11

Scheduled Functions

CCTKxANALYSIS x computexbixb2xpoynxfluxet x set bm̂ u, bˆ2 , and poynting flux gridfunctions. x

11x11Before: 11volumeintegralgroup
11 x 11Language:11c
11 x 11Options: 11global-early
11 x 11x  11loop-local
11 x 11Type: 11function