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calch.f90
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!==============================================================================
subroutine calch( s, n, r, h, dhds, dhdr, dhdsr, dhdrr )
!==============================================================================
!
! Compute the metrics for a curved wall.
! Set the functions xloc, yloc and arc for the parabolic cylinder.
!
! S. Scott Collis
!
! Revised: 9-23-96
!
!==============================================================================
implicit none
integer :: n, i
real :: s, r(n), h(n), dhds(n), dhdr(n), dhdsr(n), dhdrr(n)
real, external :: xloc, yloc
real :: xl, yl, th, bn1, bn2, dxdy, dydx, dxbds, dybds, dx, dy,&
ddxdx, ddydx, ddxdy, ddydy, d2dxdx2, d2dydx2, d2dxdy2, &
d2dydy2, dbn1, dbn2, d2xdy2, d2ydx2, d2xbds2, d2ybds2, &
d2bn1, d2bn2
real :: a(n), b(n), dads(n), dbds(n)
real, parameter :: zero = 0.0, pt5 = 0.5, one = 1.0, onept5 = 1.5, &
two = 2.0, twopt5 = 2.5, three = 3.0, &
infty = 1.0e30
!==============================================================================
! write(*,"('Caldh: s = ',e13.6)") s
if (s.eq.-one) then
h = one
dhdr = zero
dhds = zero
dhdrr = zero
dhdsr = zero
return
end if
xl = xloc( zero, s )
yl = yloc( xl )
th = atan2( one, yl )
bn1 = -sin(th)
bn2 = cos(th)
! write(*,"('Calch: ',8(e13.6,1x))") s, xl, yl, th, bn1, bn2
if (xl .eq. zero) then
dydx = infty
else
dydx = one / sqrt( two * xl )
end if
dxbds = one / sqrt(one + dydx**2)
if (xl .eq. zero) then
dxdy = zero
else
dxdy = sqrt( two * xl )
end if
dybds = one / sqrt( dxdy**2 + one )
if (xl .eq. zero) then
dx = zero
dy = one
ddxdx = infty
ddydx = zero
ddxdy = one
ddydy = zero
d2dxdx2 = infty
d2dydx2 = zero
d2dxdy2 = zero
d2dydy2 = zero
else
dx = yl
dy = one
ddxdx = one / yl
ddydx = zero
ddxdy = one
ddydy = zero
d2dxdx2 = -sqrt(two)/(two**2 * xl**onept5)
d2dydx2 = zero
d2dxdy2 = zero
d2dydy2 = zero
end if
if ( abs(bn1) .gt. abs(bn2) ) then
dbn1 = ( -ddydy/(dx**2 + dy**2)**pt5 + pt5*dy*(two*dx*ddxdy + &
two*dy*ddydy)/(dx**2 + dy**2)**onept5 ) * dybds
dbn2 = ( ddxdy/(dx**2 + dy**2)**pt5 - pt5*dx*(two*dx*ddxdy + &
two*dy*ddydy)/(dx**2 + dy**2)**onept5 ) * dybds
else
dbn1 = ( -ddydx/(dx**2 + dy**2)**pt5 + pt5*dy*(two*dx*ddxdx + &
two*dy*ddydx)/(dx**2 + dy**2)**onept5 ) * dxbds
dbn2 = ( ddxdx/(dx**2 + dy**2)**pt5 - pt5*dx*(two*dx*ddxdx + &
two*dy*ddydx)/(dx**2 + dy**2)**onept5 ) * dxbds
end if
if ( abs(bn1) .gt. abs(bn2) ) then
d2xdy2 = one
d2ybds2 = -(one + dxdy**2)**(-onept5) * dxdy * d2xdy2 * dybds
d2xbds2 = d2xdy2*(dybds)**2 + dxdy*d2ybds2
else
d2ydx2 = -one / ( two * sqrt(two) * xl**onept5 )
d2xbds2 = -(one + dydx**2)**(-onept5) * dydx * d2ydx2 * dxbds
d2ybds2 = d2ydx2*(dxbds)**2 + dydx*d2xbds2
end if
if ( abs(bn1) .gt. abs(bn2) ) then
d2bn1 = ((ddxdy*(dy*ddxdy-dx*ddydy)+dx*(dy*d2dxdy2-dx*d2dydy2))/ &
(dx**2+dy**2)**(onept5) - &
(three*dx*(dy*ddxdy-dx*ddydy)*(dx*ddxdy+dy*ddydy))/ &
(dx**2+dy**2)**(twopt5))*(dybds)**2 + &
(-ddydy/(dx**2 + dy**2)**pt5 + pt5*dy*(two*dx*ddxdy + &
two*dy*ddydy)/(dx**2 + dy**2)**onept5) * d2ybds2
d2bn2 = ((ddydy*(dy*ddxdy-dx*ddydy)+dy*(dy*d2dxdy2-dx*d2dydy2))/ &
(dx**2+dy**2)**(onept5) - &
(three*dy*(dy*ddxdy-dx*ddydy)*(dx*ddxdy+dy*ddydy))/ &
(dx**2+dy**2)**(twopt5))*(dybds)**2 + &
(ddxdy/(dx**2 + dy**2)**pt5 - pt5*dx*(two*dx*ddxdy + &
two*dy*ddydy)/(dx**2 + dy**2)**onept5) * d2ybds2
else
d2bn1 = ((ddxdx*(dy*ddxdx-dx*ddydx)+dx*(dy*d2dxdx2-dx*d2dydx2))/ &
(dx**2+dy**2)**(onept5) - &
(three*dx*(dy*ddxdx-dx*ddydx)*(dx*ddxdx+dy*ddydx))/ &
(dx**2+dy**2)**(twopt5))*(dxbds)**2 + &
(-ddydx/(dx**2 + dy**2)**pt5 + pt5*dy*(two*dx*ddxdx + &
two*dy*ddydx)/(dx**2 + dy**2)**onept5) * d2xbds2
d2bn2 = ((ddydx*(dy*ddxdx-dx*ddydx)+dy*(dy*d2dxdx2-dx*d2dydx2))/ &
(dx**2+dy**2)**(onept5) - &
(three*dy*(dy*ddxdx-dx*ddydx)*(dx*ddxdx+dy*ddydx))/ &
(dx**2+dy**2)**(twopt5))*(dxbds)**2 + &
(ddxdx/(dx**2 + dy**2)**pt5 - pt5*dx*(two*dx*ddxdx + &
two*dy*ddydx)/(dx**2 + dy**2)**onept5) * d2xbds2
end if
!.... now form the actual metric and metric derivatives
a = dxbds + r * dbn1
b = dybds + r * dbn2
h = sqrt( a**2 + b**2 )
dads = d2xbds2 + r * d2bn1
dbds = d2ybds2 + r * d2bn2
dhds = ( a * dads + b * dbds ) / h
dhdr = ( a * dbn1 + b * dbn2 ) / h
dhdrr = ( -dhdr**2 + dbn1**2 + dbn2**2 ) / h
dhdsr = -dhds / h**2 * ( a * dbn1 + b * dbn2 ) + &
( dads * dbn1 + a * d2bn1 + dbds * dbn2 + b * d2bn2 ) / h
! do i = 1, n
! write(70,10) r(i), h(i), dhds(i), dhdr(i), dhdsr(i), dhdrr(i)
! end do
10 format(8(1pe13.6,1x))
return
end
!==============================================================================
function xloc(x, ds)
!==============================================================================
implicit none
real :: xloc, x, ds
real, external :: rtflsp, func
real :: darc, x1
common /distance/ darc, x1
!==============================================================================
darc = ds
x1 = x
xloc = rtflsp(func, x1, x1 + 2.0 * ds, 1.0d-12)
return
end
!==============================================================================
function yloc(x)
!==============================================================================
! For a parabolic cylinder
!==============================================================================
implicit none
real :: yloc, x
!==============================================================================
yloc = sqrt( 2.0 * x )
return
end
!==============================================================================
function func(x)
!==============================================================================
implicit none
real :: func, x
real, external :: arc
real :: darc, x1
common /distance/ darc, x1
!==============================================================================
func = darc - arc(x1,x)
return
end
!==============================================================================
function arc(x1,x2)
!==============================================================================
! For a parabolic cylinder
!==============================================================================
implicit none
real :: arc, x1, x2, xi1, xi2
!==============================================================================
xi1 = sqrt(x1)
xi2 = sqrt(x2)
arc = sqrt(2.0)*0.5*xi2*sqrt(1.0+2.0*xi2**2) + &
0.5*log(sqrt(2.0)*xi2 + sqrt(1.0+2.0*xi2**2))
arc = arc - ( sqrt(2.0)*0.5*xi1*sqrt(1.0+2.0*xi1**2) + &
0.5*log(sqrt(2.0)*xi1 + sqrt(1.0+2.0*xi1**2)) )
return
end