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|
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
c Using macro definitions from Einstein
#include "CactusEinstein/Einstein/src/Einstein.h"
/*@@
@file teukwaves.F
@date Jan 96
@author Joan Masso + Malcolm Tobias
@desc
Routines for the teukolsky waves initialization.
@enddesc
@@*/
/*@@
@routine teukwaves
@date Jan 96
@author Malcolm Tobias + Joan Masso
@desc
Generates the analytic solutions of the
metric components for linearized quadrupolar (teukolsky) waves.
More changes for cactus port: all 3d arrays are converted
to point calculations. What a pain!!!
Three and a half years later....
Converted to Cactus4.0
@enddesc
@@*/
subroutine teukwaves(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
CCTK_REAL amp,m,ra,pi
CCTK_REAL wave,wave2,wave3,wave4,wave5,wave6,wave7,wave8
INTEGER ipacket,iparity
INTEGER ingoing,outgoing
CCTK_REAL kappa
c point values of x.y z,r
CCTK_REAL xp,yp,zp,rp
c spherical metric
CCTK_REAL teuk_grr,teuk_grt,teuk_grp,teuk_gtt,teuk_gtp,teuk_gpp
CCTK_REAL teuk_hrr,teuk_hrt,teuk_hrp,teuk_htt,teuk_htp,teuk_hpp
c special coefficeints needed for teukolsky waves
c All these were 3d arrays in old versions of Newage,G,etc..
c uffff....
CCTK_REAL teuk_tp,teuk_tn
CCTK_REAL tp2,tn2,fp,fn,fpa,fna,fpb,fnb,fpc,fnc,fpd,fnd,fpe,fne
CCTK_REAL ca,cb,cc,ck,cl,frr,frt,frp,ftt1,ftt2,ftp,fpp1,fpp2
CCTK_REAL cadot,cbdot,ccdot,ckdot,cldot
CCTK_REAL drt,drp,dtt,dtp,dpp,sint,cost,sinp,cosp,tmp
c from old spheretocart
CCTK_REAL drx,dry,drz,dtx,dty,dtz,dpx,dpy,dpz
CHARACTER*200 infoline
INTEGER i,j,k
INTEGER CCTK_Equals
DECLARE_CCTK_PARAMETERS
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
pi = 3.14159265358979
kappa = sqrt(143.0d0/pi)/12288.0d0
if (wavecenter.ne.0.) then
call CCTK_WARN(0,"Teukwaves: wavecenter must be zero for time symmetry")
endif
c CACTUS 4.0: all REAL/INTEGER parameter are available as variables and
c need not be derived from the database. Nevertheless I will assign
c the parameter variables to the variables of CAC3.0, to allow for
c easy portation (wavepulse stays wavepulse btw). (GERD)
amp = amplitude
m = mvalue
wave = wavelength
ra = wavecenter
c to be consistent with Evans & Abrahams, rescale the amplitude
c by kappa, because they use that in the packet and
c 4/3 because they use I not Teuk. F
if (CCTK_Equals(packet,'eppley') == 1) then
ipacket = 1
call CCTK_INFO('Teukolsky Packet = eppley')
elseif (CCTK_Equals(packet,'evans') == 1) then
ipacket = 2
call CCTK_INFO('Teukolsky Packet = evans')
c to be consistent with Evans & Abrahams, rescale the amplitude
c by kappa, because they use that in the packet and
c 4/3 because they use I not Teuk. F
amp = amp*(4.0d0/3.0d0)*kappa
elseif (CCTK_Equals(packet,'square') == 1) then
ipacket = 3
call CCTK_INFO('Teukolsky Packet = square')
end if
write(infoline,'(A13,G12.7)')
& ' amplitude = ',amp
call CCTK_INFO(infoline)
write(infoline,'(A11,G12.7)')
& ' m value = ',m
call CCTK_INFO(infoline)
write(infoline,'(A14,G12.7)')
& ' wavecenter = ',ra
call CCTK_INFO(infoline)
write(infoline,'(A14,G12.7)')
& ' wavelength = ',wave
call CCTK_INFO(infoline)
if (CCTK_Equals(parity,'even') == 1) then
iparity = 0
elseif (CCTK_Equals(parity,'odd') == 1) then
iparity = 1
endif
if(CCTK_Equals(wavesgoing,'in') == 1) then
ingoing = 1
endif
if(CCTK_Equals(wavesgoing,'out') == 1) then
outgoing = 1
endif
if(CCTK_Equals(wavesgoing,'both') == 1) then
ingoing = 1
outgoing = 1
endif
if (ipacket.eq.1) then
if (ingoing.eq.0.or.outgoing.eq.0) then
call CCTK_WARN(4,'Epply packet is only non-singular at the origin for ingoing-outgoing combination of waves')
endif
endif
wave2 = wave*wave
wave3 = wave2*wave
wave4 = wave3*wave
wave5 = wave4*wave
wave6 = wave5*wave
wave7 = wave6*wave
wave8 = wave7*wave
c ****************************************
c initial data for teukolsky waves
c ****************************************
do k=1,cctk_lsh(3)
do j=1,cctk_lsh(2)
do i=1,cctk_lsh(1)
xp = x(i,j,k)
yp = y(i,j,k)
zp = z(i,j,k)
rp = r(i,j,k)
teuk_tp = (cctk_time+rp-ra)
teuk_tn = (cctk_time-rp+ra)
tp2 = teuk_tp**2
tn2 = teuk_tn**2
c initialize everything to zero
fp = 0.0d0
fpa = 0.0d0
fpb = 0.0d0
fpc = 0.0d0
fpd = 0.0d0
fpe = 0.0d0
fn = 0.0d0
fna = 0.0d0
fnb = 0.0d0
fnc = 0.0d0
fnd = 0.0d0
fne = 0.0d0
c eppley package --> x exp(-x^2)
if (ipacket.eq.1) then
c to keep the analytic solution valid for the eppley packet:
if (ra.ne.0.and.ingoing.eq.1.and.outgoing.eq.1) then
teuk_tn = (cctk_time-rp-ra)
tn2 = teuk_tn**2
endif
if (ingoing.eq.1) then
tmp = exp(-tp2)
fp = amp * teuk_tp*tmp
fpa = amp * (1 - 2*tp2)*tmp
fpb = amp * teuk_tp*(4*tp2 - 6)*tmp
fpc = amp * (24*tp2 - 8*tp2*tp2 - 6)*tmp
fpd = amp * teuk_tp*(60 - 80*tp2 + 16*tp2*tp2)*tmp
fpe = amp * (
& (60 - 360*tp2 + 240*tp2*tp2 - 32*tp2*tp2*tp2)*tmp )
if (outgoing.eq.0.and.(teuk_tp+wavepulse).le.0)
& then
fp = 0.0d0
fpa = 0.0d0
fpb = 0.0d0
fpc = 0.0d0
fpd = 0.0d0
fpe = 0.0d0
endif
endif
if (outgoing.eq.1) then
tmp = exp(-tn2)
fn = amp * teuk_tn*tmp
fna = amp * (1 - 2*tn2)*tmp
fnb = amp * teuk_tn*(4*tn2 - 6)*tmp
fnc = amp * (24*tn2 - 8*tn2*tn2 -6)*tmp
fnd = amp * teuk_tn*(60 - 80*tn2 + 16*tn2*tn2)*tmp
fne = amp * (
& (60 - 360*tn2 + 240*tn2*tn2 - 32*tn2*tn2*tn2)*tmp )
endif
endif
c evans package --> w^4(1-x^2/w^2)^6
if(ipacket.eq.2) then
if (ingoing.eq.1) then
tmp = 1.0d0 - tp2/wave2
if (abs(teuk_tp).lt.wave) then
fp = amp*wave5*tmp**6
fpa = -12.0d0*amp*wave3*teuk_tp*tmp**5
fpb = -12.0d0*amp*wave3*(
& tmp**5 - 10.0d0*tp2/wave2*tmp**4 )
fpc = 120.0d0*amp*wave3*(
& 3.0d0*teuk_tp/wave2*tmp**4
& -8.0d0*teuk_tp*tp2/wave4*tmp**3 )
fpd = 360.0d0*amp*wave3*(
& 1.0d0/wave2*tmp**4
& -16.0d0*tp2/wave4*tmp**3
& +16.0d0*tp2*tp2/wave6*tmp**2 )
fpe = 2880.0d0*amp*wave3*(
& -5.0d0*teuk_tp/wave4*tmp**3
& +20.0d0*teuk_tp*tp2/wave6*tmp**2
& -8.0d0*teuk_tp*tp2*tp2/wave8*tmp )
else
fp=0.
fpa=0.
fpb=0.
fpc=0.
fpd=0.
fpe=0.
endif
endif
if (outgoing.eq.1) then
tmp = 1.0d0 - tn2/wave2
if (abs(teuk_tn).lt.wave) then
fn = amp*wave5*tmp**6
fna = -12.0d0*amp*wave3*teuk_tn*tmp**5
fnb = -12.0d0*amp*wave3*(
& tmp**5 - 10.0d0*tn2/wave2*tmp**4 )
fnc = 120.0d0*amp*wave3*(
& 3.0d0*teuk_tn/wave2*tmp**4
& -8.0d0*teuk_tn*tn2/wave4*tmp**3 )
fnd = 360.0d0*amp*wave3*(
& 1.0d0/wave2*tmp**4
& -16.0d0*tn2/wave4*tmp**3
& +16.0d0*tn2*tn2/wave6*tmp**2 )
fne = 2880.0d0*amp*wave3*(
& -5.0d0*teuk_tn/wave4*tmp**3
& +20.0d0*teuk_tn*tn2/wave6*tmp**2
& -8.0d0*teuk_tn*tn2*tn2/wave8*tmp )
else
fn=0.
fna=0.
fnb=0.
fnc=0.
fnd=0.
fne=0.
endif
endif
endif
c square package --> (1-x^2/w^2)^2
if(ipacket.eq.3) then
call CCTK_WARN(4,'Need to calculate fpe,fne')
call CCTK_WARN(4,'Need conditionals for in out waves')
if (abs(teuk_tp).lt.wave) then
fp = amp * (1-(tp2/wave2))**2
fpa = amp * (-4*teuk_tp)*(1-tp2/wave2)/wave2
fpb = amp * (8*tp2/wave4-4*(1-tp2/wave2)/wave2)
fpc = amp * 24*teuk_tp/wave4
fpd = amp * 24/wave4
else
fp=0.
fpa=0.
fpb=0.
fpc=0.
fpd=0.
endif
if (abs(teuk_tn).lt.wave) then
fn = amp * (1-(tn2/wave2))**2
fna = amp * (-4*teuk_tn)*(1-tn2/wave2)/wave2
fnb = amp * (8*tn2/wave4-4*(1-tn2/wave2)/wave2)
fnc = amp * 24*teuk_tn/wave4
fnd = amp * 24/wave4
else
fn=0.
fna=0.
fnb=0.
fnc=0.
fnd=0.
endif
endif
c
c coefficients
c
ca = 3*( (fpb-fnb)/rp**3 -3*(fna+fpa)/rp**4 +3*(fp-fn)/rp**5 )
cb = -( -(fnc+fpc)/rp**2 +3*(fpb-fnb)/rp**3 -6*(fna+fpa)/rp**4
& +6*(fp-fn)/rp**5 )
cc = ( (fpd-fnd)/rp -2*(fnc+fpc)/rp**2 +9*(fpb-fnb)/rp**3
& -21*(fna+fpa)/rp**4 +21*(fp-fn)/rp**5 )/4
ck = (fpb-fnb)/rp**2-3*(fpa+fna)/rp**3+3*(fp-fn)/rp**4
cl = -(fpc+fnc)/rp+2*(fpb-fnb)/rp**2-3*(fpa+fna)/rp**3+
& 3*(fp-fn)/rp**4
c If we only have an outgoing wave, we should flip the sign
c of the above coefficients. That is because the above coefficients
c assume an ingoing and outgoing wave packet of the form:
c wave = ingoing - outgoing. For a single wave, we want ingoing
c and outgoing to have the same sign.
if(ingoing.eq.0.and.outgoing.eq.1) then
ca=-ca
cb=-cb
cc=-cc
ck=-ck
cl=-cl
endif
sint = (xp**2+yp**2)**0.5/rp
cost = zp/rp
sinp = yp/(xp**2+yp**2)**0.5
cosp = xp/(xp**2+yp**2)**0.5
c mvalue
if (m.eq.0) then
frr = 2-3*sint**2
frt = -3*sint*cost
frp = 0.
ftt1 = 3*sint**2
ftt2 = -1.
ftp = 0.
fpp1 = -ftt1
fpp2 = 3*sint**2-1
drt = 0.
drp = -4*cost*sint
dtt = 0.
dtp = -sint**2
dpp = 0.
elseif (m.eq.-1) then
frr = 2*sint*cost*sinp
frt = (cost**2-sint**2)*sinp
frp = cost*cosp
ftt1 = -frr
ftt2 = 0.
ftp = sint*cosp
fpp1 = -ftt1
fpp2 = ftt1
drt = -2*cost*sinp
drp = -2*(cost**2-sint**2)*cosp
dtt = -sint*sinp
dtp = -cost*sint*cosp
dpp = sint*sinp
elseif (m.eq.-2) then
frr = sint**2*2*sinp*cosp
frt = sint*cost*2*sinp*cosp
frp = sint*(1-2*sinp**2)
ftt1 = (1+cost**2)*2*sinp*cosp
ftt2 = -2*sinp*cosp
fpp1 = -ftt1
fpp2 = cost**2*2*sinp*cosp
drt = 8*sint*sinp*cosp
drp = 4*sint*cost*(1-2*sinp**2)
dtt = -4*cost*sinp*cosp
dtp = (2-sint**2)*(2*sinp**2-1)
dpp = 2*cost*2*sinp*cosp
elseif (m.eq.1) then
frr = 2*sint*cost*cosp
frt = (cost**2-sint**2)*cosp
frp = -cost*sinp
ftt1 = -2*sint*cost*cosp
ftt2 = 0.
ftp = -sint*sinp
fpp1 = -ftt1
fpp2 = ftt1
drt = -2*cost*cosp
drp = 2*(cost**2-sint**2)*sinp
dtt = -sint*cosp
dtp = cost*sint*sinp
dpp = sint*cosp
elseif (m.eq.2) then
frr = sint**2*(1-2*sinp**2)
frt = sint*cost*(1-2*sinp**2)
frp = -sint*2*sinp*cosp
ftt1 = (1+cost**2)*(1-2*sinp**2)
ftt2 = (2*sinp**2-1)
ftp = cost*2*sinp*cosp
fpp1 = -ftt1
fpp2 = cost**2*(1-2*sinp**2)
drt = 4*sint*(1-2*sinp**2)
drp = -4*sint*cost*2*sinp*cosp
dtt = -2*cost*(1-2*sinp**2)
dtp = (2-sint**2)*2*sinp*cosp
dpp = 2*cost*(1-2*sinp**2)
else
call CCTK_WARN(0,'m should be one of -2,-1,0,1,2')
endif
c parity
if (iparity.eq.0) then
teuk_grr = 1 + ca*frr
teuk_grt = cb*frt*rp
teuk_grp = cb*frp*(xp**2+yp**2)**0.5
teuk_gtt = rp**2*(1 + cc*ftt1 + ca*ftt2)
teuk_gtp = (ca - 2*cc)*ftp*rp*(xp**2+yp**2)**0.5
teuk_gpp = (xp**2+yp**2)*(1 + cc*fpp1 + ca*fpp2)
else
teuk_grr = 1.
teuk_grt = ck*drt*rp
teuk_grp = ck*drp*rp*sint
teuk_gtt = (1+cl*dtt)*rp**2
teuk_gtp = cl*dtp*rp**2*sint
teuk_gpp = (1+cl*dpp)*rp**2*sint**2
endif
c Finally, convert the spherical components to cartesian
c define derivatives drx = (dr/dx)
drx = xp/rp
dry = yp/rp
drz = zp/rp
dtx = xp*zp/(rp**2*sqrt(xp**2+yp**2))
dty = yp*zp/(rp**2*sqrt(xp**2+yp**2))
dtz = (zp**2/rp**2-1)/sqrt(xp**2+yp**2)
dpx = -yp/(xp**2+yp**2)
dpy = xp/(xp**2+yp**2)
dpz = 0.
c cartesian g
gxx(i,j,k) = drx**2*teuk_grr+2.*drx*dtx*teuk_grt
& +2.*drx*dpx*teuk_grp+dtx**2*teuk_gtt
& +2.*dtx*dpx*teuk_gtp+dpx**2*teuk_gpp
gyy(i,j,k) = dry**2*teuk_grr+2.*dry*dty*teuk_grt
& +2.*dry*dpy*teuk_grp+dty**2*teuk_gtt
& +2.*dty*dpy*teuk_gtp+dpy**2*teuk_gpp
gzz(i,j,k) = drz**2*teuk_grr+2.*drz*dtz*teuk_grt
& +2.*drz*dpz*teuk_grp+dtz**2*teuk_gtt
& +2.*dtz*dpz*teuk_gtp+dpz**2*teuk_gpp
gxy(i,j,k) = drx*dry*teuk_grr+(drx*dty+dtx*dry)*teuk_grt
& +(drx*dpy+dpx*dry)*teuk_grp
& +dtx*dty*teuk_gtt+(dtx*dpy+dpx*dty)*teuk_gtp+
& dpx*dpy*teuk_gpp
gxz(i,j,k) = drx*drz*teuk_grr+(drx*dtz+dtx*drz)*teuk_grt
& +(drx*dpz+dpx*drz)*teuk_grp
& +dtx*dtz*teuk_gtt+(dtx*dpz+dpx*dtz)*teuk_gtp+
& dpx*dpz*teuk_gpp
gyz(i,j,k) = dry*drz*teuk_grr+(dry*dtz+dty*drz)*teuk_grt
& +(dry*dpz+dpy*drz)*teuk_grp
& +dty*dtz*teuk_gtt+(dty*dpz+dpy*dtz)*teuk_gtp+
& dpy*dpz*teuk_gpp
c for the ext. curv. well need...
cadot = 3*( (fpc-fnc)/rp**3 -3*(fnb+fpb)/rp**4
& +3*(fpa-fna)/rp**5 )
cbdot = -( -(fnd+fpd)/rp**2 +3*(fpc-fnc)/rp**3
& -6*(fnb+fpb)/rp**4
& +6*(fpa-fna)/rp**5 )
ccdot = ( (fpe-fne)/rp -2*(fnd+fpd)/rp**2 +9*(fpc-fnc)/rp**3
& -21*(fnb+fpb)/rp**4 +21*(fpa-fna)/rp**5 )/4
ckdot = (fpc-fnc)/rp**2-3*(fpb+fnb)/rp**3+3*(fpa-fna)/rp**4
cldot = -(fpd+fnd)/rp+2*(fpc-fnc)/rp**2-3*(fpb+fnb)/rp**3+
& 3*(fpa-fna)/rp**4
c parity
if (iparity.eq.0) then
teuk_hrr = -0.5*(cadot*frr)
teuk_hrt = -0.5*(cbdot*frt*rp)
teuk_hrp = -0.5*(cbdot*frp*(xp**2+yp**2)**0.5)
teuk_htt = -0.5*(rp**2*(ccdot*ftt1 + cadot*ftt2))
teuk_htp =
& -0.5*((cadot - 2*ccdot)*ftp*rp*(xp**2+yp**2)**0.5)
teuk_hpp = -0.5*((xp**2+yp**2)*(ccdot*fpp1 + cadot*fpp2))
else
teuk_hrr = 0.
teuk_hrt = -0.5*(ckdot*drt*rp)
teuk_hrp = -0.5*(ckdot*drp*rp*sint)
teuk_htt = -0.5*((cldot*dtt)*rp**2)
teuk_htp = -0.5*(cldot*dtp*rp**2*sint)
teuk_hpp = -0.5*((cldot*dpp)*rp**2*sint**2)
endif
c time symmetry
kxx(i,j,k) = drx**2*teuk_hrr+2.*drx*dtx*teuk_hrt
& +2.*drx*dpx*teuk_hrp+dtx**2*teuk_htt
& +2.*dtx*dpx*teuk_htp+dpx**2*teuk_hpp
kyy(i,j,k) = dry**2*teuk_hrr+2.*dry*dty*teuk_hrt
& +2.*dry*dpy*teuk_hrp+dty**2*teuk_htt
& +2.*dty*dpy*teuk_htp+dpy**2*teuk_hpp
kzz(i,j,k) = drz**2*teuk_hrr+2.*drz*dtz*teuk_hrt
& +2.*drz*dpz*teuk_hrp+dtz**2*teuk_htt
& +2.*dtz*dpz*teuk_htp+dpz**2*teuk_hpp
kxy(i,j,k) = drx*dry*teuk_hrr+(drx*dty+dtx*dry)*teuk_hrt
& +(drx*dpy+dpx*dry)*teuk_hrp
& +dtx*dty*teuk_htt+(dtx*dpy+dpx*dty)*teuk_htp+
& dpx*dpy*teuk_hpp
kxz(i,j,k) = drx*drz*teuk_hrr+(drx*dtz+dtx*drz)*teuk_hrt
& +(drx*dpz+dpx*drz)*teuk_hrp
& +dtx*dtz*teuk_htt+(dtx*dpz+dpx*dtz)*teuk_htp+
& dpx*dpz*teuk_hpp
kyz(i,j,k) = dry*drz*teuk_hrr+(dry*dtz+dty*drz)*teuk_hrt
& +(dry*dpz+dpy*drz)*teuk_hrp
& +dty*dtz*teuk_htt+(dty*dpz+dpy*dtz)*teuk_htp+
& dpy*dpz*teuk_hpp
enddo
enddo
enddo
c initialize the conformal factor
c Check if we should create and store conformal factor stuff */
if (CCTK_EQUALS(metric_type, "static conformal")) then
conformal_state = 1
if(CCTK_EQUALS(conformal_storage,"factor+derivs")) then
conformal_state = 2;
else if(CCTK_EQUALS(conformal_storage,"factor+derivs+2nd derivs")) then
conformal_state = 3;
end if
do k=1,cctk_lsh(3)
do j=1,cctk_lsh(2)
do i=1,cctk_lsh(1)
psi(i,j,k) = 1d0
if(conformal_state .gt. 1) then
psix(i,j,k) = 0d0
psiy(i,j,k) = 0d0
psiz(i,j,k) = 0d0
endif
if(conformal_state .gt. 2) then
psixy(i,j,k) = 0d0
psixz(i,j,k) = 0d0
psiyz(i,j,k) = 0d0
psixx(i,j,k) = 0d0
psiyy(i,j,k) = 0d0
psizz(i,j,k) = 0d0
endif
end do
end do
end do
end if
return
end
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