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program doit
implicit real*8 (a-h,o-z)
include 'param.h'
common/bfss4/rad,starm,pindex,jout(kmax2),jin(kmax2),ktop(jmax2)
common/bfss5/rho(jmax2,kmax2),drhor(jmax2,kmax2),
1 drhoz(jmax2,kmax2),angmo(jmax2)
common/bfss7/avquad(jmax2),davquad(jmax2)
common/poten2/delphi(2,jmax2,kmax2)
common/ivp1/time,dt,cc(15,jmax2,kmax2),ee(neq,jmax2,kmax2)
c potential solver common blocks
common/blok6/dtheta,cosign(lmax),sign(lmax),pi,grav
common/inside/tmass,enew,elost,edif,phichk,klocat
common/pois/phi3d(jmax2,kmax2,lmax)
common/grid/r(jmax2),z(kmax2),rhf(jmax1),zhf(kmax1),
1 g(jmax2),h(kmax2)
common/tstep/tstepPower,max_steps
character*80 filen,pulsefile
common/normal/delr,omegamax,wsum,totJ,toverw
pulsefile='pulse'
open(24,file='pulsefile',form='formatted',status='unknown')
write(6,12)
12 format(' version 10/9/2010 gfortran compiler only')
write(6,10)
10 format(' data file')
read(5,11) filen
write(6,17) filen
11 format(a80)
17 format(1x,a80)
read(5,15) mode
write(6,14) mode
14 format(' mode =',1i2)
15 format(2i5)
read(5,15) nevolve
write(6,16) nevolve
16 format(' model =',1i2)
read(5,*) pindex,koji,rin
write(6,19) pindex
19 format(' polytropic index:',1p1e10.3)
write(6,20) koji,rin
20 format(' koji =',i4,' rin =',f10.6)
read(5,*) angpow
read(5,*) tstepPower
read(5,*) max_steps
write(6,21) angpow, tstepPower, max_steps
21 format(' q =',1p1e9.3,' tstepPower =',1p1e8.1,
1 ' max steps =',1i8)
write(6,*) ' Parameters: ',jmax3,kmax3,lmax,max
open ( unit = 1 , file = filen , form = 'formatted',
1 status = 'old')
if (koji.ge.1) then
call kojima(koji,rin)
else
call reads_toman(nevolve,jrhomax)
end if
call equil(mode,scale,jrhomax,koji)
call perturbation(mode,jrhomax,koji)
call evolve(mode,scale,jrhomax,koji,angpow)
end
subroutine reads_toman(nevolve,jrhomax)
implicit real*8 (a-h,o-z)
include 'param.h'
common/bfss4/rad,starm,pindex,jout(kmax2),jin(kmax2),ktop(jmax2)
common/bfss5/rho(jmax2,kmax2),drhor(jmax2,kmax2),
1 drhoz(jmax2,kmax2),angmo(jmax2)
common/bfss7/avquad(jmax2),davquad(jmax2)
common/poten2/delphi(2,jmax2,kmax2)
common/ivp1/time,dt,cc(15,jmax2,kmax2),ee(neq,jmax2,kmax2)
c potential solver common blocks
common/blok6/dtheta,cosign(lmax),sign(lmax),pi,grav
common/inside/tmass,enew,elost,edif,phichk,klocat
common/pois/phi3d(jmax2,kmax2,lmax)
common/grid/r(jmax2),z(kmax2),rhf(jmax1),zhf(kmax1),
1 g(jmax2),h(kmax2)
common/angular/angold(jmax2)
common/contour/kcontour(jmax2,10)
dimension rho_read(jmax2,jmax2)
common/normal/delr,omegamax,wsum,totJ,toverw
c.....read models
nrun = 0
10 nrun = nrun + 1
c.....zero density array
do j=1,jmax2
do k=1,kmax2
rho(j,k)=0.0
end do
end do
read(1,*,end=9000) jscf,kscf
read(1,*) rad,starm
write(6,39) starm
39 format(' star mass =',1p1e9.1)
read(1,*) ((rho_read(j,k),j=2,jmax1),k=2,jmax1)
read(1,*) (angold(j),j=2,jmax1)
40 format(1p6e13.5)
c....."correct" model number?
if (nrun.lt.nevolve) go to 10
c--------------------------------------------------------------------
c find the stellar radius, the inner edge of the disk, and the
c outer edge of the disk
c
c star/disk model
go to 919
jbody=0
jdisk=0
do j=2,jmax1
if(rho_read(j,2).eq.0.0 .and. jbody.eq.0) then
js = j
jbody = 1
end if
if(rho_read(j,2).gt.0.0 .and. jbody.eq.1 .and. jdisk.eq.0) then
jd = j
jdisk = 1
end if
end do
rhostarmax=-100.0
rhodiskmax=-100.0
do j=2,jmax1
if(j.le.js) then
if(rho_read(j,2).gt.rhostarmax) rhostarmax=rho_read(j,2)
end if
if(j.ge.jd) then
if(rho_read(j,2).gt.rhodiskmax) rhodiskmax=rho_read(j,2)
end if
end do
c
write(6,*) 'rhomax ',js,jd,rhostarmax,rhodiskmax
c.....set rho cut-off
rhomax=-1.0e05
do j=2,jmax1
do k=2,kmax1
rho(j,k)=rho_read(j,k)
end do
if(rho(j,2).gt.rhomax) then
rhomax=rho(j,2)
jrhomax=j
end if
end do
rhomin=1.0e-07*rhostarmax
rhomind=1.0e-07*rhodiskmax
do j=2,jmax1
do k=2,kmax1
if(j.lt.js .and. rho(j,k).lt.rhomin) then
rho(j,k)=0.0e-00
end if
if(j.gt.jd .and. rho(j,k).lt.rhomind) then
rho(j,k)=0.0e-00
end if
end do
end do
c-------------------------------------------------------------------
c disk model
c
919 continue
rhomax=-100.0
ckz do j=10,jmax1
do j = 2,jmax1
if(rho_read(j,2).gt.rhomax) rhomax=rho_read(j,2)
end do
do j=2,jmax1
do k=2,kmax1
if(rho_read(j,k).le.1.0e-07*rhomax) then
rho(j,k)=0.0
else
rho(j,k)=rho_read(j,k)
end if
end do
end do
c.....re-center angular momentum
do j=3,jmax1
angmo(j)=0.5*(angold(j-1)+angold(j))
end do
angmo(1)=angmo(3)
angmo(2)=angmo(3)
c.....computational grid
delr=rad/float(jscf-2)
delz=delr
r(3)=delr
r(2)=0.0
r(1)=-r(3)
r(4)=2.0*delr
do j=5,jmax1
r(j)=r(j-1)+delr
end do
r(jmax2)=r(jmax1)+delr
z(3)=delz
z(2)=0.0
z(1)=-z(3)
z(4)=2.0*delz
do k=5,kmax1
z(k)=z(k-1)+delz
end do
z(kmax2)=z(kmax1)+delz
do j=1,jmax1
rhf(j)=0.5*(r(j+1)+r(j))
rho(j,kmax1)=0.0
end do
do k=1,kmax1
zhf(k)=0.5*(z(k+1)+z(k))
rho(jmax1,k)=0.0
end do
angmo(jmax1)=2.0*angmo(jmax)-angmo(jmax-1)
c.....zero coefficient array for linearized equations
c and locate surface in pomega and z
do j=2,jmax1
ktop(j)=2
do 500 k=2,kmax1
if(rho(j,k).gt.1.0e-07*rhomax) ktop(j)=k
if(rho(j,k).gt.0.9*rhomax) kcontour(j,1)=k
if(rho(j,k).gt.0.5*rhomax) kcontour(j,2)=k
if(rho(j,k).gt.0.1*rhomax) kcontour(j,3)=k
if(rho(j,k).gt.0.01*rhomax) kcontour(j,4)=k
if(rho(j,k).gt.0.001*rhomax) kcontour(j,5)=k
if(rho(j,k).gt.0.0001*rhomax) kcontour(j,6)=k
do 500 l=1,15
cc(l,j,k)=0.0
500 continue
end do
do 600 k=1,kmax2
jin(k)=2
jout(k)=2
600 continue
do 650 k=2,kmax1
do 650 j=2,jmax1
if(jin(k).eq.2 .and. rho(j,k).gt.1.0e-07*rhomax) jin(k)=j
if(jin(k).gt.2 .and. rho(j,k).gt.1.0e-07*rhomax) jout(k)=j
650 continue
return
9000 continue
stop
end
subroutine boundary(jrhomax)
c ********************************************
c * *
c * boundary conditions *
c * *
c ********************************************
implicit real*8 (a-h,o-z)
include 'param.h'
common/ivp1/time,dt,cc(15,jmax2,kmax2),ee(neq,jmax2,kmax2)
common/bfss4/rad,starm,pindex,jout(kmax2),jin(kmax2),ktop(jmax2)
common/bfss5/rho(jmax2,kmax2),drhor(jmax2,kmax2),
1 drhoz(jmax2,kmax2),angmo(jmax2)
data surface/0.0e00/
do i = 1 , neq
do j = 2 , jmax
c symmetry about equatorial plane
if (i.le.6) then
ee(i,j,1) = ee(i,j,3)
else
ee(i,j,1) = -ee(i,j,3)
ee(i,j,2) = 0.0
end if
c "top" of polytrope
if (ktop(j).eq.2) go to 100
k_s = ktop(j)
if (i.ge.3) ee(i,j,k_s) = surface
ee(i,j,k_s+1) = 2.0 * ee(i,j,k_s) - ee(i,j,k_s-1)
ee(i,j,k_s+1) = ee(i,j,k_s)
100 continue
end do
do k = 2 , kmax
c "outer" edge of torus
j_s = jout(k)
if (i.ge.3) ee(i,j_s,k) = surface
ee(i,j_s+1,k) = 2.0 * ee(i,j_s,k) - ee(i,j_s-1,k)
ee(i,j_s+1,k) = ee(i,j_s,k)
c "inner" edge of torus
j_s = jin(k)
if (i.ge.3) ee(i,j_s,k) = surface
ee(i,j_s-1,k) = 2.0 * ee(i,j_s,k) - ee(i,j_s+1,k)
ee(i,j_s-1,k) = ee(i,j_s,k)
end do
end do
return
end
subroutine equil(m_leg,scale,jrhomax,koji)
c
c***********************************************************************
c
c equilibrium values (cc array) for the coefficients
c
c***********************************************************************
c
implicit real*8 (a-h,o-z)
include 'param.h'
real*8 kesum,jsum
common/bfss4/rad,starm,pindex,jout(kmax2),jin(kmax2),ktop(jmax2)
common/bfss5/rho(jmax2,kmax2),drhor(jmax2,kmax2),
1 drhoz(jmax2,kmax2),angmo(jmax2)
common/bfss7/avquad(jmax2),davquad(jmax2)
common/poten2/delphi(2,jmax2,kmax2)
common/ivp1/time,dt,cc(15,jmax2,kmax2),ee(neq,jmax2,kmax2)
c potential solver common blocks
common/blok6/dtheta,cosign(lmax),sign(lmax),pi,grav
common/inside/tmass,enew,elost,edif,phichk,klocat
common/pois/phi3d(jmax2,kmax2,lmax)
common/grid/r(jmax2),z(kmax2),rhf(jmax1),zhf(kmax1),
1 g(jmax2),h(kmax2)
common/angular/angold(jmax2)
common/contour/kcontour(jmax2,10)
common/angm/angmom(jmax2),amassj(jmax2)
common/normal/delr,omegamax,wsum,totJ,toverw
pi = acos(-1.0)
twopi = 2.0*pi
fourpi = 4.0*pi
gamma = 1.0+1.0/pindex
gmin1 = gamma-1.0
gmin2 = gamma-2.0
gmin3 = gamma-3.0
do j = 2 , jmax1
do k = ktop(j) + 1 , kmax1
rho(j,k) = 0.0
end do
end do
do j = 2,jmax2
angmom(j) = 0.0
amassj(j) = 0.0
end do
call angquad
call thermo
c -- potcal(1,m): "1" = axisymmetric density
call potcal(1,m_leg,koji)
rad2 = rad*rad
rad3 = rad2*rad
volume = twopi*rad3
volsum = 0.0
smass = 0.0
wsum = 0.0
wstar = 0.0
kesum = 0.0
jsum = 0.0
rhomax = 0.0
jrhomax = 2
omegamax = 0.0
radmax = 0.0
do 1000 j = 2 , jmax
write(16,106) j,ktop(j),kcontour(j,1),kcontour(j,2),
& kcontour(j,3),kcontour(j,4),kcontour(j,5),
& kcontour(j,6)
write(17,106) j,jin(j),jout(j)
106 format(8i5)
po = rhf(j)/rad
deltapo = (r(j+1)-r(j))/rad
avq = angold(j)/rhf(j)**2
if (avq.ne.0.0) then
davq1 = (po/avq)*(avquad(j+1)-avquad(j))/deltapo
davq = davquad(j)
end if
if(rho(j,2).gt.rhomax) then
rhomax = rho(j,2)
jrhomax = j
omegamax = avq
radmax = rhf(j)
end if
velq = 0.5*(r(j+1)*avquad(j+1)+r(j)*avquad(j))
velq = angold(j)/rhf(j)
velqsq = velq*velq
if (j.ne.2) then
aq = avquad(j)
vq = aq*rhf(j)
else
aq = avq
vq = velq
end if
do 1100 k = 2 , kmax2
rhoq = rho(j,k)
if (rhoq .le. 0.0) go to 1100
deltaz = (z(k+1)-z(k))/rad
drhoqr = drhor(j,k)
drhoqz = drhoz(j,k)
weight = po*deltapo*deltaz
rhoqj = 0.5*(rho(j,k)+rho(j-1,k))
rhoqk = 0.5*(rho(j,k)+rho(j,k-1))
c.....coefficient array cc(m,j,k)
cc(1,j,k) = m_leg*avq
cc(2,j,k) = rhoq*(1.0+(rhf(j)/rhoq)*(rho(j+1,k)-
1 rho(j-1,k))/(rhf(j+1)-rhf(j-1)))/rhf(j)
cc(3,j,k) = m_leg*rhoq/rhf(j)
cc(4,j,k) = (rho(j,k+1)-rho(j,k-1))/(zhf(k+1)-zhf(k-1))
cc(12,j,k) = rhoq
cc(5,j,k) = gamma*gmin2*rhoqj**gmin3*drhoqr
cc(6,j,k) = m_leg*aq
cc(7,j,k) = gamma*rhoqj**gmin2
cc(13,j,k) = 1.0
cc(8,j,k) = m_leg*gamma*rhoq**gmin2/rhf(j)
cc(9,j,k) = avq*(2.0+davq)
cc(10,j,k) = m_leg/rhf(j)
cc(11,j,k) = gamma*gmin2*rhoqk**gmin3*drhoqz
cc(14,j,k) = gamma*rhoqk**gmin2
cc(15,j,k) = 1.0
c spheroid volume
volsum = volsum + weight
c spheroid mass
smass = smass + rhoq*weight
c rotational kinetic energy
kesum = kesum + 0.5*rhoq*velqsq*weight
c angular momentum
jsum = jsum + rhoq*velq*rhf(j)*weight
c gravitational potential energy
rjk = sqrt(rhf(j)**2+rhf(k)**2)
wsum = wsum + 0.25*rhoq*delphi(1,j,k)*weight
wstar = wstar - rhoq*(starm/rjk)*weight
1100 continue
angmom(j) = 2.0*jsum*volume
amassj(j) = 2.0*smass*volume
1000 continue
c
c calculate t/|w|
c
volsum = 2.0*volsum*volume
smass = 2.0*smass*volume
kesum = 2.0*kesum*volume
jsum = 2.0*jsum*volume
wsum = 2.0*wsum*volume
wstar = 2.0*wstar*volume
usum = 0.5*(-wsum-wstar-2.0*kesum)
toverw = kesum/abs(wsum+wstar)
totJ = jsum
c
c print the model parameters
c
write(6,1600) pindex,rad,toverw
1600 format (' n =',f5.2,' radius = ',1pe12.5,
1 ' T/|W| =',1p3e12.5)
write(6,1610) kesum,wsum,wstar,usum,jsum
1610 format (' T,W,U =',1p4e12.4,
1 ' J =',1pe12.4)
write(6,1800) m_leg
1800 format ( ' azimuthal mode number: ',i5/)
c
cirp = twopi/avquad(3)
write(6,2600) volsum/4.18879/rad3,smass
2600 format(' spheroid volume (4*pi*rad**3/3) and mass: '
1 ,1p2e12.5)
scale = 2.0*acos(-1.0)/omegamax
write(6,2700) jrhomax,radmax,rhomax,scale,omegamax
2700 format(' r(max): ',i5,1pe11.4,' rho(max): ',1pe11.4,
1 ' MIRP: ',1p2e11.4)
write(6,2701) jin(2),jout(2)
2701 format(' jin(2) =',1i4,' jout(2) =',1i4,/)
write(6,2750)
c do k = 2,kmax
c do j = 2,jmax
c write(47,498) j,k,rho(j,k)
c end do
c write(47,*)
c end do
c 498 format(2i5,1p1e12.5)
c
c write(2,*) jout,kout
c write(2,*) r(jout),starm
c write(2,96) ((rho(j,k),j=2,jmax1),k=2,kmax1)
c write(2,96) (angold(j),j=2,jmax1)
c 96 format(1p6e13.5)
2750 format(' j rhf(j) rho(j,2) avq
1 vortensity delphi(1,j,2)')
do j=2,jmax
dhdr=(avquad(j+1)*r(j+1)**2-avquad(j-1)*r(j-1)**2)/
1 (r(j+1)-r(j-1))
if (r(j).ne.0.0) then
ep=(2.0*avquad(j)/r(j))*dhdr
else
ep=0.0
end if
if(rho(j,2).ne.0.0) then
vortensity=rho(j,2)/dhdr*rhf(j)
else
vortensity=0.0
end if
if(ep.gt.0.0) ep=sqrt(ep)/m_leg
avq=avquad(j)
write(6,2800) j,rhf(j),rho(j,2),avq,vortensity,delphi(1,j,2)
2800 format(i5,1p6e14.5)
end do
rewind(47)
do k = 2,jmax
do j = 2,kmax
write(47,499) j,k,rho(j,k)
end do
write(47,*)
end do
499 format(2i5,1p1e12.5)
return
end
subroutine perturbation(m_leg,jrhomax,koji)
c
c***********************************************************************
c
c initial perturbation
c
c***********************************************************************
c
implicit real*8 (a-h,o-z)
include 'param.h'
c
common/bfss4/rad,starm,pindex,jout(kmax2),jin(kmax2),ktop(jmax2)
common/bfss5/rho(jmax2,kmax2),drhor(jmax2,kmax2),
1 drhoz(jmax2,kmax2),angmo(jmax2)
common/bfss7/avquad(jmax2),davquad(jmax2)
common/poten2/delphi(2,jmax2,kmax2)
common/ivp1/time,dt,cc(15,jmax2,kmax2),ee(neq,jmax2,kmax2)
c potential solver common blocks
common/blok6/dtheta,cosign(lmax),sign(lmax),pi,grav
common/inside/tmass,enew,elost,edif,phichk,klocat
common/pois/phi3d(jmax2,kmax2,lmax)
common/grid/r(jmax2),z(kmax2),rhf(jmax1),zhf(kmax1),
1 g(jmax2),h(kmax2)
common/stardelta/starq(2,2),starphi(2,jmax2,kmax2)
dimension cyl(jmax1)
c
data time / 0.0 /
pi = acos(-1.0)
twopi = 2.0*pi
cyl(1)=0.0
delta=twopi*(r(3)-r(2))
do j=2,jmax1
dcyl=0.0
dvol=delta*(r(j+1)**2-r(j)**2)
do k=2,kmax1
dcyl=dcyl+rho(j,k)*dvol
end do
cyl(j)=cyl(j-1)+dcyl
end do
do j=1,jmax1
cyl(j)=cyl(j)/cyl(jmax1)
end do
read(5,*) jump,tstart
if(jump.eq.1) then
read (11) ee
time = tstart
else
call angquad
delta = twopi / (jout(2)-jin(2))
do 2000 j = jin(2) , jout(2)
do 2000 k = 2 , kmax
rhoamp = 0.0
vamp = 0.0
vphi = 0.0
if (rho(j,k).gt.0.0) then
rhoamp = 1.0e-16 * rand(1)
end if
phase = twopi*rand(j+k)
c
c ----------------------------------------------------------------
c turn on Gaussian pulse
c
c if(m_leg.eq.1 .and. rho(j,k).gt.0.0) then
c rhoamp = 1.0e-10*(rho(j,k)/rhf(j))
c phase = twopi*cyl(j)
c vphi = -rhoamp*(avquad(j)*rhf(j)/rho(j,k))
c end if
c
c Gaussian pulse
c
jgo = 0
if (jgo.eq.1) then
jpulse = 173
jwidth = 6
jpulse = 70
jwidth = 3
jpulse = 89
jwidth = 3
gaussian = ((j-jpulse)/jwidth)**2
rhoamp = 1.0e-02 * exp(-gaussian)
gaussian = ((k-2)/jwidth)**2
rhoamp = rhoamp * exp(-gaussian)
phase = twopi/8.0
end if
weight1 = cos(phase)
weight2 = sin(phase)
ee(1,j,k) = rhoamp * weight1
ee(2,j,k) = rhoamp * weight2
ee(3,j,k) = vamp * weight1
ee(4,j,k) = vamp * weight2
ee(5,j,k) = vphi * weight1
ee(6,j,k) = vphi * weight2
ee(7,j,k) = vamp * weight1
ee(8,j,k) = vamp * weight2
2000 continue
c.....boundary conditions
call boundary(jrhomax)
end if
c....center-of-mass and momentum conservation
call angquad
xc = 0.0
yc = 0.0
vxc = 0.0
vyc = 0.0
do j = jin(2),jout(2)
rdr = rhf(j)*(r(j+1)-r(j))
do k = 2,kmax1
if(rho(j,k).le.0.0) go to 9100
volc = twopi*rdr*(z(k+1)-z(k))
xc = xc+ee(1,j,k)*rhf(j)*volc
yc = yc+ee(2,j,k)*rhf(j)*volc
vxc = vxc+ee(1,j,k)*avquad(j)*rhf(j)*volc
vyc = vyc+ee(2,j,k)*avquad(j)*rhf(j)*volc
9100 continue
end do
end do
if(jump.eq.1) then
if(m_leg.eq.1) read(21) starq
else
starq(1,1)=xc
starq(1,2)=yc
starq(2,1)=-vyc/starm
starq(2,2)=+vxc/starm
end if
return
end
subroutine evolve(m_leg,scale,jrhomax,koji,angpow)
c
c ********************************************
c * *
c * solves Initial Value Problem (IVP) *
c * *
c ********************************************
c
implicit real*8 (a-h,o-z)
include 'param.h'
c
common/bfss4/rad,starm,pindex,jout(kmax2),jin(kmax2),ktop(jmax2)
common/bfss5/rho(jmax2,kmax2),drhor(jmax2,kmax2),
1 drhoz(jmax2,kmax2),angmo(jmax2)
common/bfss7/avquad(jmax2),davquad(jmax2)
common/poten2/delphi(2,jmax2,kmax2)
common/ivp1/time,dt,cc(15,jmax2,kmax2),ee(neq,jmax2,kmax2)
common/contour/kcontour(jmax2,10)
common/angular/angold(jmax2)
common/tstep/tstepPower,max_steps
common/phasesh/pshiftr
common/dens/rhog(jmax2,kmax2)
common/angm/angmom(jmax2),amassj(jmax2)
common/winteg/wintg(2,jmax2,kmax2),wintstr(3,jmax2,kmax2),
1 djay(jmax2,kmax2),torque(jmax2)
common/phase/phase(jmax2),wphs(2,jmax2,kmax2)
common/efns/amp4(jmax2),wamp(jmax2)
common/totals/etot(jmax2),strtot(jmax2)
common/wintegN/wintgN(2,jmax2,kmax2),wintstrN(3,jmax2,kmax2)
c potential solver common blocks
common/blok6/dtheta,cosign(lmax),sign(lmax),pi,grav
common/inside/tmass,enew,elost,edif,phichk,klocat
common/pois/phi3d(jmax2,kmax2,lmax)
common/grid/r(jmax2),z(kmax2),rhf(jmax1),zhf(kmax1),
1 g(jmax2),h(kmax2)
common/stardelta/starq(2,2),starphi(2,jmax2,kmax2)
common/stardelta1/starold(2,2),deltastar(2,2)
c
dimension dqdr(neq),dedt(neq,jmax2,kmax2),eeold(neq,jmax2,kmax2),
1 delee(neq,jmax2,kmax2),rk(4),rt(4)
dimension star_step(2,2)
common/norm/rnorm(jmax1)
common/normal/delr,omegamax,wsum,totJ,toverw
c
c...Fourth-order Runge-Kutta coefficients
c
data rk/0.16666667,0.3333333,0.3333333,0.16666667/
data rt/0.5,0.5,1.0,1.0/
c
pi = acos(-1.0)
twopi = 2.0*pi
raddeg = 360.0/twopi
scal = (rad/float(jmax-2))**2.0
deltar = rad/float(jmax-2)
omegam = 2.0*pi/scale
c
c...time step controls
c
dt = 0.00002*scale
tmin = 0.002*scale * 0.5**tstepPower
tmax = 0.010*scale * 0.5**tstepPower
do 3000 m_s = 1 , max_steps
c.....initialize work arrays
do i = 1 , neq
do j = 1 , jmax2
do k = 1 , kmax2
delee(i,j,k) = 0.0
eeold(i,j,k) = ee(i,j,k)
end do
end do
end do
do j = 1 , 2
do k = 1 , 2
star_step(j,k) = 0.0
starold(j,k) = starq(j,k)
end do
end do
do 2000 n_rk = 1 , 4
c.....boundary conditions
call boundary(jrhomax)
c.....perturbed gravitational potential
call potcal(2,m_leg,koji)
c.....time derivatives
do 1000 j = 2 , jmax
do 1100 k = 2 , kcontour(j,6)
if(rho(j,k).le.0.0) go to 1100
call derivs(m_leg,dqdr,j,k)
do i = 1 , neq
dedt(i,j,k) = dqdr(i)
end do
1100 continue
1000 continue
c....calculate intermediate values
do 1500 j = 2 , jmax
do 1500 k = 2 , kcontour(j,6)
if(rho(j,k).le.0.0) go to 1500
do i = 1 , neq
delta = dt*dedt(i,j,k)
delee(i,j,k) = delee(i,j,k)+rk(n_rk)*delta
ee(i,j,k) = eeold(i,j,k)+rt(n_rk)*delta
end do
1500 continue
do 1600 j = 1 , 2
do 1600 k = 1 , 2
delta = deltastar(j,k)
star_step(j,k) = star_step(j,k)+rk(n_rk)*delta
starq(j,k) = starold(j,k)+rt(n_rk)*delta
1600 continue
2000 continue
c.....update variables using Runge-Kutta algorithm
do i = 1 , neq
do j = 2 , jmax
do k = 2 , kcontour(j,6)
if (rho(j,k).gt.0) then
ee(i,j,k) = eeold(i,j,k)+delee(i,j,k)
end if
end do
end do
end do
do j = 1 , 2
do k = 1 , 2
starq(j,k) = starold(j,k)+star_step(j,k)
end do
end do
c.....boundary conditions
call boundary(jrhomax)
c.....advance time
time = time + dt
c.....new time step
stepmin = 1.0e+15
jmin = 0
kmin = 0
do j = jin(2)+1,jout(2)-1
do k = 3 , kcontour(j,6)-1
if(rho(j,k).le.0.0) go to 2500
amp = (ee(1,j,k)**2+ee(2,j,k)**2)
famp = (dedt(1,j,k)**2+dedt(2,j,k)**2)
if(amp.ne.0.0 .and. famp.ne.0.0) then
tstep = sqrt(amp/famp)
else
tstep = stepmin
end if
if(tstep.lt.stepmin) then
stepmin = tstep
jmin = j
kmin = k
end if
2500 continue
end do
end do
stepmin = 0.4*stepmin
dt = dmax1(stepmin,tmin)
dt = dmin1(dt,tmax)
write(42,2510) time,dt,stepmin,jmin,kmin
2510 format(1p3e12.5,2i6)
c.....print density at representative radii
kout = 2
jpr = jin(kout) + 2
r1 = rho(jpr,kout)
amp1 = sqrt(ee(1,jpr,kout)**2+ee(2,jpr,kout)**2)/r1
phase1 = atan(ee(2,jpr,kout)/ee(1,jpr,kout))
if(ee(1,jpr,kout).lt.0.0) phase1=phase1+pi
if(phase1.lt.0.0) phase1=phase1+twopi
jpr = (jin(kout)+jout(kout))/2
r2 = rho(jpr,kout)
amp2 = sqrt(ee(1,jpr,kout)**2+ee(2,jpr,kout)**2)/r2
phase2 =atan(ee(2,jpr,kout)/ee(1,jpr,kout))
if(ee(1,jpr,kout).lt.0.0) phase2=phase2+pi
if(phase2.lt.0.0) phase2=phase2+twopi
jpr = jout(kout)-2
r3 = rho(jpr,kout)
amp3 = sqrt(ee(1,jpr,kout)**2+ee(2,jpr,kout)**2)/r3
phase3 = atan(ee(2,jpr,kout)/ee(1,jpr,kout))
if(ee(1,jpr,kout).lt.0.0) phase3=phase3+pi
if(phase3.lt.0.0) phase3=phase3+twopi
write(22,3150) time,amp1,phase1*raddeg,amp2,phase2*raddeg,
1 amp3,phase3*raddeg
jnorm = jrhomax
th = time*(avquad(jnorm)/2.0/acos(-1.0))
write(23,3150) th,amp1,phase1*raddeg,amp2,phase2*raddeg,
1 amp3,phase3*raddeg
flush(23)
ckz...calculate growth rates in kojima units
if(th.eq.0.0) then
amp1old = 0.0
amp2old = 0.0
amp3old = 0.0
thOld = th
phase1Old = 0.0
phase2Old = 0.0
phase3Old = 0.0
end if
if(m_s.lt.500) then
mergeCount = 1
mergeIter = 0
end if
rewind(50)
if(mod(m_s,100).eq.0) then
amp1New = amp1
amp2New = amp2
amp3New = amp3