Hello everyone,

Could someone please clarify the shift evolution equation implemented in ML_BSSN?

Just looking at the parameter file it seems like it is:

     d/dt beta^i = shiftGammaCoeff  Xt^i - betaDriver alpha^shiftAlphaPower beta^i

looking at McLachlan_BSSN.m (for GammaDriver and without advection and dissipation), I think it is:

     d/dt beta^a =  shiftGammaCoeff alpha^shiftAlphaPower B^a
with
     d/dt B^a = d/dt Xt^a - betaDriver B^a

Whereas looking at Alcubierre's book Eq 4.3.33 and 4.3.34 I would expect it to be 

     d/dt beta^i =  B^i
with
     d/dt B^i = shiftGammaCoeff alpha^shiftAlphaPower d/dt Xt^a - betaDriver B^a

the link to describe the Gamma driver shift condition http://grwiki.physics.ncsu.edu/wiki/Shift_Conditions doesn't work but looking at the 2019 version on the wayback machine the evolution described is

     d/dt beta^a = (3/4) B^a
with
     d/dt B^a = d/dt Xt^a - betaDriver B^a

where here (and in Alcubierre) d/dt = partial_t - beta^c partial_c. Does the McLachlan code have that second term beta^c partial_c ?

This is confusing me, so what is actually implemented? Where are the parameters shiftGammaCoeff, betaDriver and shiftAlphaPower in the evolution equation? And these are all constant positive reals right? In Alcubierre's book xi (that I think is shiftGammaCoeff) can be function of space and the lapse.

Thank you,
Robyn