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|
c This routine calculates Bona-Masso initial data, making use of the
c subroutine Exact__metric() to calculate the spacetime metric and its
c inverse. Note that this use of the Bona-Masso variables is independent
c of how (or even if) we are evolving the Einstein equations -- here
c the Bona-Masso variables are "just" used as intermediate variables.
c $Header$
#include "cctk.h"
subroutine Exact__Bona_Masso_data(
$ decoded_exact_model,
$ x, y, z, t,
$ gxx, gyy, gzz, gxy, gyz, gxz,
$ hxx, hyy, hzz, hxy, hyz, hxz,
$ psi, psix, psiy, psiz,
$ psixx, psiyy, psizz, psixy, psiyz, psixz,
$ dxgxx, dxgyy, dxgzz, dxgxy, dxgyz, dxgxz,
$ dygxx, dygyy, dygzz, dygxy, dygyz, dygxz,
$ dzgxx, dzgyy, dzgzz, dzgxy, dzgyz, dzgxz,
$ alp, ax, ay, az, betax, betay, betaz,
$ bxx, bxy, bxz, byx, byy, byz, bzx, bzy, bzz)
implicit none
CCTK_INT decoded_exact_model
CCTK_INT psi_on
CCTK_REAL x, y, z, t,
$ gxx, gyy, gzz, gxy, gyz, gxz,
$ hxx, hyy, hzz, hxy, hyz, hxz,
$ psi, psix, psiy, psiz,
$ psixx, psiyy, psizz, psixy, psiyz, psixz,
$ dxgxx, dxgyy, dxgzz, dxgxy, dxgyz, dxgxz,
$ dygxx, dygyy, dygzz, dygxy, dygyz, dygxz,
$ dzgxx, dzgyy, dzgzz, dzgxy, dzgyz, dzgxz,
$ alp, ax, ay, az, betax, betay, betaz,
$ bxx, bxy, bxz, byx, byy, byz, bzx, bzy, bzz
C gxx is g_xx etc.
C hxx is K_xx etc.
C dxgyy is (/2) dg_yy / dx (sic!)
C alp is N, betax is N^x etc.
C bxy is (/2) dN^y / dx (sic and sic!)
C ax is dN / dx / N (sic!)
CCTK_REAL eps, four_eps2,
$ gdtt, gdtx, gdty, gdtz,
$ gutt, gutx, guty, gutz,
$ guxx, guyy, guzz, guxy, guyz, guxz,
$ gdtt_p, gdtx_p, gdty_p, gdtz_p,
$ gdxx_p, gdyy_p, gdzz_p, gdxy_p, gdyz_p, gdxz_p,
$ gutt_p, gutx_p, guty_p, gutz_p,
$ guxx_p, guyy_p, guzz_p, guxy_p, guyz_p, guxz_p,
$ psix_p, psiy_p, psiz_p,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_m, psiy_m, psiz_m,
$ psix_px_p, psix_py_p, psix_pz_p,
$ psiy_py_p, psiy_pz_p,
$ psiz_pz_p,
$
$ psix_mx_m, psix_my_m, psix_mz_m,
$ psiy_my_m, psiy_mz_m,
$ psiz_mz_m,
$
$ psix_py_m, psix_pz_m,
$ psiy_pz_m,
$
$ psix_my_p, psix_mz_p,
$ psiy_mz_p
parameter (eps=1.d-6)
C Save, if we have to provide the conformal factor
if (psi .gt. 0.0d0) then
psi_on=1
else
psi_on=0
end if
C Get the spacetime metric and its inverse at the base point.
call Exact__metric(
$ decoded_exact_model,
$ x, y, z, t,
$ gdtt, gdtx, gdty, gdtz,
$ gxx, gyy, gzz, gxy, gyz, gxz,
$ gutt, gutx, guty, gutz,
$ guxx, guyy, guzz, guxy, guyz, guxz,
$ psi)
C Calculate lapse and shift from the upper metric.
alp = 1.d0 / sqrt(-gutt)
betax = - gutx / gutt
betay = - guty / gutt
betaz = - gutz / gutt
C In order to calculate the derivatives of the lapse and shift from
C the contravariant metric, use g^tt = -1/N^2 and g^i0 = N^i / N^2
C Note that ax is dN/dx / N and that bxy is 1/2 dN^y / dx.
C Calculate x-derivatives.
call Exact__metric(
$ decoded_exact_model,
$ x+eps, y, z, t,
$ gdtt_p, gdtx_p, gdty_p, gdtz_p,
$ gdxx_p, gdyy_p, gdzz_p, gdxy_p, gdyz_p, gdxz_p,
$ gutt_p, gutx_p, guty_p, gutz_p,
$ guxx_p, guyy_p, guzz_p, guxy_p, guyz_p, guxz_p,
$ psix_p)
call Exact__metric(
$ decoded_exact_model,
$ x-eps, y, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_m)
dxgxx = (gdxx_p - gdxx_m) / 4.d0 / eps
dxgyy = (gdyy_p - gdyy_m) / 4.d0 / eps
dxgzz = (gdzz_p - gdzz_m) / 4.d0 / eps
dxgxy = (gdxy_p - gdxy_m) / 4.d0 / eps
dxgyz = (gdyz_p - gdyz_m) / 4.d0 / eps
dxgxz = (gdxz_p - gdxz_m) / 4.d0 / eps
ax = - 0.5d0 * (gutt_p - gutt_m) / 2.d0 / eps / gutt
bxx = ((- gutx_p / gutt_p) - (- gutx_m / gutt_m)) / 4.d0 / eps
bxy = ((- guty_p / gutt_p) - (- guty_m / gutt_m)) / 4.d0 / eps
bxz = ((- gutz_p / gutt_p) - (- gutz_m / gutt_m)) / 4.d0 / eps
psix = (psix_p - psix_m) / 2.0d0 / eps
C Calculate y-derivatives.
call Exact__metric(
$ decoded_exact_model,
$ x, y+eps, z, t,
$ gdtt_p, gdtx_p, gdty_p, gdtz_p,
$ gdxx_p, gdyy_p, gdzz_p, gdxy_p, gdyz_p, gdxz_p,
$ gutt_p, gutx_p, guty_p, gutz_p,
$ guxx_p, guyy_p, guzz_p, guxy_p, guyz_p, guxz_p,
$ psiy_p)
call Exact__metric(
$ decoded_exact_model,
$ x, y-eps, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiy_m)
dygxx = (gdxx_p - gdxx_m) / 4.d0 / eps
dygyy = (gdyy_p - gdyy_m) / 4.d0 / eps
dygzz = (gdzz_p - gdzz_m) / 4.d0 / eps
dygxy = (gdxy_p - gdxy_m) / 4.d0 / eps
dygyz = (gdyz_p - gdyz_m) / 4.d0 / eps
dygxz = (gdxz_p - gdxz_m) / 4.d0 / eps
ay = - 0.5d0 * (gutt_p - gutt_m) / 2.d0 / eps / gutt
byx = ((- gutx_p / gutt_p) - (- gutx_m / gutt_m)) / 4.d0 / eps
byy = ((- guty_p / gutt_p) - (- guty_m / gutt_m)) / 4.d0 / eps
byz = ((- gutz_p / gutt_p) - (- gutz_m / gutt_m)) / 4.d0 / eps
psiy = (psiy_p - psiy_m) / 2.0d0 / eps
C Calculate z-derivatives.
call Exact__metric(
$ decoded_exact_model,
$ x, y, z+eps, t,
$ gdtt_p, gdtx_p, gdty_p, gdtz_p,
$ gdxx_p, gdyy_p, gdzz_p, gdxy_p, gdyz_p, gdxz_p,
$ gutt_p, gutx_p, guty_p, gutz_p,
$ guxx_p, guyy_p, guzz_p, guxy_p, guyz_p, guxz_p,
$ psiz_p)
call Exact__metric(
$ decoded_exact_model,
$ x, y, z-eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiz_m)
dzgxx = (gdxx_p - gdxx_m) / 4.d0 / eps
dzgyy = (gdyy_p - gdyy_m) / 4.d0 / eps
dzgzz = (gdzz_p - gdzz_m) / 4.d0 / eps
dzgxy = (gdxy_p - gdxy_m) / 4.d0 / eps
dzgyz = (gdyz_p - gdyz_m) / 4.d0 / eps
dzgxz = (gdxz_p - gdxz_m) / 4.d0 / eps
az = - 0.5d0 * (gutt_p - gutt_m) / 2.d0 / eps / gutt
bzx = ((- gutx_p / gutt_p) - (- gutx_m / gutt_m)) / 4.d0 / eps
bzy = ((- guty_p / gutt_p) - (- guty_m / gutt_m)) / 4.d0 / eps
bzz = ((- gutz_p / gutt_p) - (- gutz_m / gutt_m)) / 4.d0 / eps
psiz = (psiz_p - psiz_m) / 2.0d0 / eps
C Calculate t-derivatives, and extrinsic curvature.
call Exact__metric(
$ decoded_exact_model,
$ x, y, z, t+eps,
$ gdtt_p, gdtx_p, gdty_p, gdtz_p,
$ gdxx_p, gdyy_p, gdzz_p, gdxy_p, gdyz_p, gdxz_p,
$ gutt_p, gutx_p, guty_p, gutz_p,
$ guxx_p, guyy_p, guzz_p, guxy_p, guyz_p, guxz_p,
$ psi)
call Exact__metric(
$ decoded_exact_model,
$ x, y, z, t-eps,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psi)
hxx = - (gdxx_p - gdxx_m) / 4.d0 / eps / alp
$ + (dxgxx * betax + dygxx * betay + dzgxx * betaz
$ + 2.d0 * (bxx * gxx + bxy * gxy + bxz * gxz)) / alp
hyy = - (gdyy_p - gdyy_m) / 4.d0 / eps / alp
$ + (dxgyy * betax + dygyy * betay + dzgyy * betaz
$ + 2.d0 * (byx * gxy + byy * gyy + byz * gyz)) / alp
hzz = - (gdzz_p - gdzz_m) / 4.d0 / eps / alp
$ + (dxgzz * betax + dygzz * betay + dzgzz * betaz
$ + 2.d0 * (bzx * gxz + bzy * gyz + bzz * gzz)) / alp
hxy = - (gdxy_p - gdxy_m) / 4.d0 / eps / alp
$ + (dxgxy * betax + dygxy * betay + dzgxy * betaz
$ + bxx * gxy + bxy * gyy + bxz * gyz
$ + byx * gxx + byy * gxy + byz * gxz) / alp
hyz = - (gdyz_p - gdyz_m) / 4.d0 / eps / alp
$ + (dxgyz * betax + dygyz * betay + dzgyz * betaz
$ + byx * gxz + byy * gyz + byz * gzz
$ + bzx * gxy + bzy * gyy + bzz * gyz) / alp
hxz = - (gdxz_p - gdxz_m) / 4.d0 / eps / alp
$ + (dxgxz * betax + dygxz * betay + dzgxz * betaz
$ + bxx * gxz + bxy * gyz + bxz * gzz
$ + bzx * gxx + bzy * gxy + bzz * gxz) / alp
C Calculate second derivatives of the conformal factor
if (psi_on .eq. 1) then
call Exact__metric(
$ decoded_exact_model,
$ x+eps+eps, y, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_px_p)
call Exact__metric(
$ decoded_exact_model,
$ x, y+eps+eps, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiy_py_p)
call Exact__metric(
$ decoded_exact_model,
$ x, y, z+eps+eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiz_pz_p)
call Exact__metric(
$ decoded_exact_model,
$ x-eps-eps, y, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_mx_m)
call Exact__metric(
$ decoded_exact_model,
$ x, y-eps-eps, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiy_my_m)
call Exact__metric(
$ decoded_exact_model,
$ x, y, z-eps-eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiz_mz_m)
call Exact__metric(
$ decoded_exact_model,
$ x+eps, y+eps, z, t,
$ gdtt_p, gdtx_p, gdty_p, gdtz_p,
$ gdxx_p, gdyy_p, gdzz_p, gdxy_p, gdyz_p, gdxz_p,
$ gutt_p, gutx_p, guty_p, gutz_p,
$ guxx_p, guyy_p, guzz_p, guxy_p, guyz_p, guxz_p,
$ psix_py_p)
call Exact__metric(
$ decoded_exact_model,
$ x+eps, y, z+eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_pz_p)
call Exact__metric(
$ decoded_exact_model,
$ x, y+eps, z+eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiy_pz_p)
call Exact__metric(
$ decoded_exact_model,
$ x-eps, y-eps, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_my_m)
call Exact__metric(
$ decoded_exact_model,
$ x-eps, y, z-eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_mz_m)
call Exact__metric(
$ decoded_exact_model,
$ x, y-eps, z-eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiy_mz_m)
call Exact__metric(
$ decoded_exact_model,
$ x+eps, y-eps, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_py_m)
call Exact__metric(
$ decoded_exact_model,
$ x+eps, y, z-eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_pz_m)
call Exact__metric(
$ decoded_exact_model,
$ x-eps, y+eps, z, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_my_p)
call Exact__metric(
$ decoded_exact_model,
$ x-eps, y, z+eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psix_mz_p)
call Exact__metric(
$ decoded_exact_model,
$ x, y+eps, z-eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiy_pz_m)
call Exact__metric(
$ decoded_exact_model,
$ x, y-eps, z+eps, t,
$ gdtt_m, gdtx_m, gdty_m, gdtz_m,
$ gdxx_m, gdyy_m, gdzz_m, gdxy_m, gdyz_m, gdxz_m,
$ gutt_m, gutx_m, guty_m, gutz_m,
$ guxx_m, guyy_m, guzz_m, guxy_m, guyz_m, guxz_m,
$ psiy_mz_p)
four_eps2 = 4.0d0 * eps**2
psixx = (psix_mx_m- 2*psi+ psix_px_p) / four_eps2
psiyy = (psiy_my_m- 2*psi+ psiy_py_p) / four_eps2
psizz = (psiz_mz_m- 2*psi+ psiz_pz_p) / four_eps2
psixy = (psix_my_m- psix_my_p- psix_py_m+ psix_py_p) / four_eps2
psixz = (psix_mz_m- psix_mz_p- psix_pz_m+ psix_pz_p) / four_eps2
psiyz = (psiy_mz_m- psiy_mz_p- psiy_pz_m+ psiy_pz_p) / four_eps2
end if
return
end
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