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/*@@
@file GRHydro_Bondi.F90
@date Wed Jan 13 13:00:49 EST 2010
@author Scott C. Noble
@desc
Hydro initial data for the relativistic Bondi solution about
a single Schwarzschild black hole.
@enddesc
@@*/
/*
Calculates the Bondi solution, or the spherically symmetric hydrostationary
solution to a fluid on a static fixed background spacetime. We assume that one can
calculate a radius "r" from the grid and that with respect to this radial coordinate,
the solution satisfies
d (\rho u^r) / dr = 0
Assumes that the equation of state is P = K \rho^\Gamma and K is set by
the location of the sonic point.
-- Implicitly assumes that there is no spin in the geometry as there is no Bondi
solution for spinning black holes. If a spin is specified, a spherically symmetric
is still assumed but the 4-velocity is set consistently with the spinning spacetime.
*/
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "cctk_Functions.h"
#include "GRHydro_Macros.h"
# define M_PI 3.14159265358979323846d0 /* pi */
!!$Newton-Raphson parameters:
#define velx(i,j,k) vel(i,j,k,1)
#define vely(i,j,k) vel(i,j,k,2)
#define velz(i,j,k) vel(i,j,k,3)
#define sx(i,j,k) scon(i,j,k,1)
#define sy(i,j,k) scon(i,j,k,2)
#define sz(i,j,k) scon(i,j,k,3)
#define Bvecx(i,j,k) Bvec(i,j,k,1)
#define Bvecy(i,j,k) Bvec(i,j,k,2)
#define Bvecz(i,j,k) Bvec(i,j,k,3)
#define Bconsx(i,j,k) Bcons(i,j,k,1)
#define Bconsy(i,j,k) Bcons(i,j,k,2)
#define Bconsz(i,j,k) Bcons(i,j,k,3)
subroutine GRHydro_BondiM_Iso(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
CCTK_INT :: i, j, k, nx, ny, nz, imin, jb,N_points
CCTK_REAL :: ONEmTINY, tiny
PARAMETER (N_points=100000,ONEmTINY=0.999999d0,tiny=1.0d-12)
CCTK_REAL :: M, Msq, Mdot, rs, gam, rmin_bondi, rmax_bondi, cs_sq,cs,vs_sq,vs,rhos,gtemp,hs, Kval, Qdot
CCTK_REAL :: logrmin,dlogr,rhotmp,utmp,vtmp,rspher
CCTK_REAL :: r_bondi(N_points), logr_bondi(N_points), rho_bondi(N_points), u_bondi(N_points), v_bondi(N_points)
CCTK_REAL :: drhodr, det, rhocheck, rhocheck2, riso, rnew, rsch, ucheck
CCTK_REAL :: uiso, uisocheck, vcheck, ucheck2, vcheck2, xhat,yhat, zhat, xp, yp, zp
CCTK_REAL :: f,df,ddf,a,b,c,rsm,roverm,dudr,uisocheck2,auiso,buiso
CCTK_REAL :: bondi_bsmooth
character(400) :: debug_message
!!$set_bondi_parameters
M = bondi_central_mass(1)
Msq = M*M
Mdot = mdot_sonicpt_bondi
rs = r_sonicpt_bondi
gam = gl_gamma
write(debug_message,'(a,4f22.14)') "Bondi_pars: ",M,mdot_sonicpt_bondi, &
r_sonicpt_bondi,gl_gamma
call CCTK_INFO(debug_message)
rmin_bondi = M * bondi_rmin(1)
rmax_bondi = M * bondi_rmax(1)
cs_sq = M / ( 2.*rs - 3.*M )
if( cs_sq > (gam - 1.)) then
cs_sq = gam - 1.
rs = 0.5 * M * ( 3. + 1./cs_sq )
endif
cs = sqrt(cs_sq)
vs_sq = M / ( 2. * rs )
vs = sqrt(vs_sq)
rhos = Mdot / ( 4. * M_PI * vs * rs * rs )
gtemp = gam - 1.
hs = 1. / ( 1. - cs_sq / (gam - 1.) )
Kval = hs * cs_sq * rhos**(-gtemp) / gam
Qdot = hs * hs * ( 1. - 3. * vs_sq )
logrmin = log10(rmin_bondi)
dlogr = (log10(rmax_bondi) - logrmin)/(1.*(N_points-1))
write(debug_message,'(a,8f22.14)') "More pars: ",cs,vs,rhos,hs,Kval,Qdot,&
logrmin,dlogr
call CCTK_INFO(debug_message)
rhotmp=1.0d30
imin=1
do i=1,N_points
logr_bondi(i) = logrmin + dlogr*(i-1)
r_bondi(i) = 10.**(logr_bondi(i))
utmp = abs(r_bondi(i) - r_sonicpt_bondi)
if (utmp < rhotmp) then
rhotmp = utmp
imin = i
endif
enddo
!!$ rhotmp = -1. !!$ start with guess
rhotmp=rhos !!$ start with value at sonic point!
do i=imin,N_points
rspher = r_bondi(i)
call find_bondi_solution( rspher, rhotmp, utmp, vtmp, rs, rhos, M, Mdot, Kval, gam, Qdot )
if(rhotmp < initial_rho_abs_min) then
rhotmp = initial_rho_abs_min
utmp = Kval * rhotmp**gl_gamma / (gl_gamma - 1.)
endif
rho_bondi(i) = rhotmp
u_bondi(i) = utmp
v_bondi(i) = vtmp
end do
!!$ rhotmp = -1.
rhotmp=rhos !!$ start with value at sonic point!
do i=imin-1,1,-1
rspher = r_bondi(i)
call find_bondi_solution( rspher, rhotmp, utmp, vtmp, rs, rhos, M, Mdot, Kval, gam, Qdot )
if(rhotmp < initial_rho_abs_min) then
rhotmp = initial_rho_abs_min
utmp = K * rhotmp**gl_gamma / (gl_gamma - 1.)
endif
rho_bondi(i) = rhotmp
u_bondi(i) = utmp
v_bondi(i) = vtmp
enddo
open (47,file="bondi.asc",form="formatted")
do i=1,N_points
write(47,'(i5,4f22.14)')i,r_bondi(i),rho_bondi(i),&
u_bondi(i),v_bondi(i)
end do
close(47)
!!$ write(debug_message,'(a,4f22.14)') "i=1:",r_bondi(1),rho_bondi(1),&
!!$ u_bondi(1),v_bondi(1)
!!$ call CCTK_INFO(debug_message)
!!$ write(debug_message,'(a,4f22.14)') "i=100:",r_bondi(100),rho_bondi(100),&
!!$ u_bondi(100),v_bondi(100)
!!$ call CCTK_INFO(debug_message)
!!$ write(debug_message,'(a,4f22.14)') "i=1000:",r_bondi(1000),rho_bondi(1000),&
!!$ u_bondi(1000),v_bondi(1000)
!!$ call CCTK_INFO(debug_message)
!!$ write(debug_message,'(a,4f22.14)') "i=1500:",r_bondi(1500),rho_bondi(1500),&
!!$ u_bondi(1500),v_bondi(1500)
!!$ call CCTK_INFO(debug_message)
!!$ // find the derivative near r=M in isotropic coords = r=9/4M in schwarzschild;
rnew = 2.25 * M
j = floor ((log10(rnew) - logrmin) / dlogr + 1.0)
!!$ j = NINT((log10(rnew) - logrmin) / dlogr + 1.0)
rhocheck = rho_bondi(j)
call find_bondi_solution(rnew,rhocheck, ucheck, vcheck, rs, rhos, M, Mdot, Kval, gam, Qdot )
uisocheck = 4.0*vcheck/3.0
!!$ the previous point was r=M in isotropic coords = r=9/4M in schwarzschild; this one is r=1.01M in isotropic
rnew = 0.25 * 3.02**2 * M/1.01
j = floor((log10(rnew) - logrmin) / dlogr + 1.0)
!!$ j = NINT((log10(rnew) - logrmin) / dlogr + 1.0)
rhocheck2 = rho_bondi(j)
call find_bondi_solution( rnew, rhocheck2, ucheck2, vcheck2, rs, rhos, M, Mdot, Kval, gam, Qdot )
uisocheck2 = vcheck2 / (1.0 - 1.0/2.02) / (1.0+ 1.0/2.02)
drhodr = 100.0*(rhocheck2-rhocheck)/M
!!$ Don't divide by M here, to simplify the math
dudr = 100.0*(uisocheck2-uisocheck)
write(debug_message,'(a,3f22.14)') 'Rhocheck:',rhocheck,rhocheck2,drhodr
call CCTK_INFO(debug_message)
write(debug_message,'(a,3f22.14)') 'Ucheck:',uisocheck,uisocheck2,dudr
call CCTK_INFO(debug_message)
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
do i=1,nx
do j=1,ny
do k=1,nz
xp=x(i,j,k)
yp=y(i,j,k)
zp=z(i,j,k)
riso = sqrt(xp*xp + yp*yp + zp*zp +1.0e-16)
xhat = xp/riso
yhat = yp/riso
zhat = zp/riso
roverm = riso/M
bondi_bsmooth = 1.0d0
if(roverm > ONEmTINY) then
rsch = 0.25 * ( 2.*riso + M)**2 / riso
!!$ jb = floor( 0.5 + (log10(rsch) - logrmin) / dlogr )
jb = floor( (log10(rsch) - logrmin) / dlogr + 1.0)
!!$ jb = NINT((log10(rsch) - logrmin) / dlogr + 1.0)
if(jb >= N_points) jb = N_points-1
rhotmp = rho_bondi(jb)+(rho_bondi(jb+1)-rho_bondi(jb))*&
(rsch-r_bondi(jb))/(r_bondi(jb+1)-r_bondi(jb))
!!$ call find_bondi_solution_bracket( rsch,rhotmp, utmp, vtmp, rs, rhos, M, Mdot, Kval, gam, Qdot, &
!!$ rho_bondi(jb),rho_bondi(jb+1))
call find_bondi_solution( rsch,rhotmp, utmp, vtmp, rs, rhos, M, Mdot, Kval, gam, Qdot)
rho(i,j,k) = rhotmp
uiso = vtmp / (1.0 - M/2.0/riso) / (1.0+ M/2.0/riso)
else
if(roverm > 0.5d0*ONEmTINY) then
rho(i,j,k) = rhocheck+drhodr*riso*(riso-M)/M
else
rho(i,j,k) = (rhocheck-drhodr*M/4.0)*(1.-cos(2.*M_PI*riso/M))/2.0
bondi_bsmooth = 8.0d0*riso**3
endif
utmp = Kval * rho(i,j,k)**( gam ) / (gam - 1.)
!!$ match to uiso and dudr at roverm=1
!!$ a R + b R^3 ---> a+b = uisocheck; a+3b = dudr
!!$ b = (dudr-uisocheck)/2; a=3*uisocheck-dudr)/2
auiso = 1.5*uisocheck-0.5*dudr
buiso = 0.5*dudr-0.5*uisocheck
uiso = roverm*(auiso+buiso*roverm**2)
endif
eps(i,j,k) = utmp/rhotmp
w_lorentz(i,j,k) = sqrt(1.0+gxx(i,j,k) * uiso**2)
velx(i,j,k) = -1.0*uiso * xhat / w_lorentz(i,j,k)
vely(i,j,k) = -1.0*uiso * yhat / w_lorentz(i,j,k)
velz(i,j,k) = -1.0*uiso * zhat / w_lorentz(i,j,k)
det=SPATIAL_DETERMINANT(gxx(i,j,k),gxy(i,j,k),gxz(i,j,k),gyy(i,j,k),gyz(i,j,k),gzz(i,j,k))
Bvecx(i,j,k) = bondi_bsmooth*bondi_bmag*M**2*xhat/sqrt(det)/riso**2
Bvecy(i,j,k) = bondi_bsmooth*bondi_bmag*M**2*yhat/sqrt(det)/riso**2
Bvecz(i,j,k) = bondi_bsmooth*bondi_bmag*M**2*zhat/sqrt(det)/riso**2
call Prim2ConGenM(GRHydro_eos_handle,gxx(i,j,k),gxy(i,j,k), &
gxz(i,j,k),gyy(i,j,k),gyz(i,j,k),gzz(i,j,k), &
det, dens(i,j,k),sx(i,j,k),sy(i,j,k),sz(i,j,k), &
tau(i,j,k),Bconsx(i,j,k),Bconsy(i,j,k),Bconsz(i,j,k), &
rho(i,j,k),velx(i,j,k),vely(i,j,k),velz(i,j,k), &
eps(i,j,k),press(i,j,k), &
Bvecx(i,j,k),Bvecy(i,j,k),Bvecz(i,j,k),w_lorentz(i,j,k))
end do
end do
end do
densrhs = 0.d0
srhs = 0.d0
taurhs = 0.d0
Bconsrhs = 0.d0
return
end subroutine GRHydro_BondiM_Iso
|
