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/*@@
@file brilldata.F
@date
@author Carsten Gundlach, Miguel Alcubierre.
@desc
Construct Brill wave q function.
@enddesc
@version $Header$
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
function brillq(rho,z,phi)
C Calculates the function q that appear in the conformal
C metric for Brill waves:
C
C ds^2 = psi^4 ( e^(2q) (drho^2 + dz^2) + rho^2 dphi^2 )
C
C There are three different choices for the form of q depending
C on the value of the parameter "brill_q":
C
C brill_q = 0:
C 2
C 2+b - (rho-rho0) 2 2
C q = a rho e (z/sz) / r
C
C
C brill_q = 1: (includes Eppleys form as special case)
C
C
C b 2 2 2 c/2
C q = a (rho/srho) / { 1 + [ ( r - r0 ) / sr ] }
C
C
C brill_q = 2: (includes Holz et al form as special case)
C
C 2 2 2 c/2
C b - [ ( r - r0 ) / sr ]
C q = a (rho/srho) e
C
C
C If we want 3D initial data, the function q is multiplied by an
C additional factor:
C
C m 2 m
C q -> q [ 1 + d rho cos (n (phi)+phi0 ) / ( 1 + e rho ) ]
implicit none
DECLARE_CCTK_PARAMETERS
logical firstcall
integer qtype
real*8 brillq,rho,z,phi
real*8 a,b,c,r0,sr,rho0,srho,brill_sz
real*8 d,e,m,n,phi0
data firstcall /.true./
save firstcall,qtype,a,b,c,r0,sr,rho0,srho,brill_sz
save d,e,m,n,phi0
C Get parameters at first call.
if (firstcall) then
qtype = brill_q
a = brill_a
b = brill_b
c = brill_c
r0 = brill_r0
sr = brill_sr
rho0 = brill_rho0
srho = brill_srho
brill_sz = brill_sz
if (axisym.eq.0) then
d = brill_d
e = brill_e
m = brill_m
n = brill_n
phi0 = brill_phi0
end if
firstcall = .false.
end if
if (rho.lt.0) call CCTK_WARN(1,"Warning: negative rho in brillq:")
C Calculate q(rho,z) from a choice of forms. Type 0, 1 and 2 are those
C of Bruegmann.
C brill_q = 0.
if (qtype .eq. 0) then
brillq = a * rho**(2.d0+b)
$ / dexp((rho - rho0)**2) / (rho**2 + z**2)
if (brill_sz .ne. 0.d0) then
brillq = brillq / exp((z/brill_sz)**2)
end if
else if (qtype .eq. 1) then
C brill_q = 1. This includes Eppleys choice of q.
C But note that q(Eppley) = 2q(Cactus).
brillq = a * (rho/srho)**b
$ / ( 1.d0 + ((rho**2 + z**2 - r0**2) / sr**2)**(c/2) )
else if (qtype .eq. 2) then
C brill_q = 2. This includes my (Carstens) notion of what a
C smooth "pure quadrupole" q should be.
brillq = a * (rho/srho)**b
$ / dexp( ((rho**2 + z**2 - r0**2) / sr**2)**(c/2) )
else
C Unknown type for q function.
call CCTK_WARN(0,"Unknown type of Brill function q.")
end if
C If desired, multiply with phi dependent factor.
if (axisym.eq.0) then
brillq = brillq*(1.0D0 + d*rho**m*cos(n*(phi-phi0))**2
. /(1.0D0 + e*rho**m))
end if
return
end
|
