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fd_temporal.f90
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!==============================================================================
subroutine fd_temporal(name, ind)
!==============================================================================
!
! Driver for temporal parallel stability solver using finite difference
!
! Uses Carpenter's third order closure for the boundaries
!
! Revised: 12-12-95
!==============================================================================
use stuff
use material
use stencils
implicit none
integer i, j, k, ix, ier, ind
integer i0, idof, j0, jdof
real vm(ny,ndof,nx), isign, perf
real, external :: EPICG
character(80) name
real eta(ny), y(ny), deta(ny), d2eta(ny)
real A(ny,ndof,ndof), B(ny,ndof,ndof), C(ny,ndof,ndof)
real D(ny,ndof,ndof), G(ny,ndof,ndof)
real Vxx(ny,ndof,ndof), Vxy(ny,ndof,ndof), Vyy(ny,ndof,ndof)
real Vxz(ny,ndof,ndof), Vyz(ny,ndof,ndof), Vzz(ny,ndof,ndof)
real g1vm(ny,ndof), g2vm(ny,ndof), g3vm(ny,ndof)
real g11vm(ny,ndof), g12vm(ny,ndof), g13vm(ny,ndof)
real g21vm(ny,ndof), g22vm(ny,ndof), g23vm(ny,ndof)
real g31vm(ny,ndof), g32vm(ny,ndof), g33vm(ny,ndof)
real gum(ny,nsd,nsd), grhom(ny,nsd), gtm(ny,nsd), gpm(ny,nsd)
real divum(ny), g1divum(ny), g2divum(ny), g3divum(ny)
real rhom(ny), u1m(ny), u2m(ny), u3m(ny), tm(ny), pm(ny)
real rmu(ny), dmu(ny), d2mu(ny)
real rlm(ny), dlm(ny), d2lm(ny)
real con(ny), dcon(ny), d2con(ny)
real g1mu(ny), g2mu(ny), g3mu(ny)
real g1lm(ny), g2lm(ny), g3lm(ny)
real g1con(ny), g2con(ny), g3con(ny)
real g1dmu(ny), g2dmu(ny), g3dmu(ny)
real g1dlm(ny), g2dlm(ny), g3dlm(ny)
real g1dcon(ny), g2dcon(ny), g3dcon(ny)
real S1jj(ny), S2jj(ny), S3jj(ny), S(ny,nsd,nsd)
real fact
complex Dh(ny,ndof,ndof), Ah(ny,ndof,ndof), Bh(ny,ndof,ndof)
complex :: scale
complex A0(ndof*ny,ndof*ny), B0(ndof*ny,ndof*ny), C0(ndof*ny,ndof*ny)
complex evec(ndof*ny,ndof*ny), alp(ndof*ny), bet(ndof*ny)
complex omg(ndof*ny), cs(ndof*ny)
real temp1(ndof*ny), temp2(ndof*ny)
integer index(ndof*ny)
!.... stuff for LAPACK eigensolver
integer info, lwork
complex, allocatable :: work(:)
real, allocatable :: rwork(:)
integer, allocatable :: ipiv(:)
! logical :: Navier = .true. ! Viscosity
!==============================================================================
!.... initialize the gradients
g1vm = zero
g2vm = zero
g3vm = zero
g11vm = zero
g12vm = zero
g13vm = zero
g21vm = zero
g22vm = zero
g23vm = zero
g31vm = zero
g32vm = zero
g33vm = zero
!.... grid
call ogengrid(y, eta, deta, d2eta)
!.... read the mean field
if (ider) then
write(*,*) 'Using internal derivatives'
call getmean(vm, y, eta, ny, ind)
else
call getmean2(vm, y, eta, g2vm, g22vm, ny, ind)
end if
!.... loop over the streamwise stations
do ix = 1, nx
write (*,*)
write (*,*) 'F O R M I N G E I G E N S Y S T E M'
!.... initialize
G = zero
A = zero
B = zero
C = zero
D = zero
Vxx = zero
Vxy = zero
Vyy = zero
Vxz = zero
Vyz = zero
Vzz = zero
rhom = vm(:,1,ix)
u1m = vm(:,2,ix)
u2m = vm(:,3,ix)
u3m = vm(:,4,ix)
tm = vm(:,5,ix)
pm = one / (gamma * Ma**2) * rhom * tm
if (ider) then
!.... Compute first derivatives of mean field
call grad(ndof, nx, ny, nz, vm, g1vm, g2vm, g3vm, ix, one, dy, one)
!.... Compute second derivatives of mean field
call grad(ndof, nx, ny, nz, g1vm, g11vm, g12vm, g13vm, &
ix, one, dy, one)
call grad(ndof, nx, ny, nz, g2vm, g21vm, g22vm, g23vm, &
ix, one, dy, one)
call grad(ndof, nx, ny, nz, g3vm, g31vm, g32vm, g33vm, &
ix, one, dy, one)
!.... transform the gradients to physical space
do k = 1, ndof
g22vm(:,k) = g22vm(:,k) * deta**2 + g2vm(:,k) * d2eta
g2vm(:,k) = g2vm(:,k) * deta
end do
end if
!.... write out the mean field and its gradients
open(10,file='rho.out')
do j = 1, ny
write (10,13) y(j), vm(j,1,ix), g2vm(j,1), g22vm(j,1)
end do
close(10)
open(10,file='u.out')
do j = 1, ny
write (10,13) y(j), vm(j,2,ix), g2vm(j,2), g22vm(j,2)
end do
close(10)
open(10,file='v.out')
do j = 1, ny
write (10,13) y(j), vm(j,3,ix), g2vm(j,3), g22vm(j,3)
end do
close(10)
open(10,file='w.out')
do j = 1, ny
write (10,13) y(j), vm(j,4,ix), g2vm(j,4), g22vm(j,4)
end do
close(10)
open(10,file='t.out')
do j = 1, ny
write (10,13) y(j), vm(j,5,ix), g2vm(j,5), g22vm(j,5)
end do
close(10)
13 format(4(1pe20.13,1x))
!.... initialize gradient of mean velocity
gum(:,1,1) = g1vm(:,2)
gum(:,1,2) = g2vm(:,2)
gum(:,1,3) = g3vm(:,2)
gum(:,2,1) = g1vm(:,3)
gum(:,2,2) = g2vm(:,3)
gum(:,2,3) = g3vm(:,3)
gum(:,3,1) = g1vm(:,4)
gum(:,3,2) = g2vm(:,4)
gum(:,3,3) = g3vm(:,4)
divum = gum(:,1,1) + gum(:,2,2) + gum(:,3,3)
!.... initialize gradient of rho and T in the mean
grhom(:,1) = g1vm(:,1)
grhom(:,2) = g2vm(:,1)
grhom(:,3) = g3vm(:,1)
gtm(:,1) = g1vm(:,5)
gtm(:,2) = g2vm(:,5)
gtm(:,3) = g3vm(:,5)
fact = one / (gamma * Ma**2)
gpm(:,1) = fact * ( grhom(:,1) * tm + rhom * gtm(:,1) )
gpm(:,2) = fact * ( grhom(:,2) * tm + rhom * gtm(:,2) )
gpm(:,3) = fact * ( grhom(:,3) * tm + rhom * gtm(:,3) )
!.... compute the gradient of the divergence of um
g1divum = g11vm(:,2) + g12vm(:,3)
g2divum = g12vm(:,2) + g22vm(:,3)
g3divum = zero
!.... compute some stuff that is useful for the viscous terms
do i = 1, nsd
do j = 1, nsd
S(:,i,j) = pt5 * ( gum(:,i,j) + gum(:,j,i) )
end do
end do
S1jj = pt5 * ( g11vm(:,2) + g11vm(:,2) + g22vm(:,2) + &
g12vm(:,3) + g33vm(:,2) + g13vm(:,4) )
S2jj = pt5 * ( g11vm(:,3) + g21vm(:,2) + g22vm(:,3) + &
g22vm(:,3) + g33vm(:,3) + g23vm(:,4) )
S3jj = pt5 * ( g11vm(:,4) + g31vm(:,2) + g22vm(:,4) + &
g32vm(:,3) + g33vm(:,4) + g33vm(:,4) )
!.... compute mean material properties
call getmat(tm*te, rmu, rlm, con, dmu, d2mu, &
dlm, d2lm, dcon, d2con)
!.... nondimensionalize
rmu = rmu / rmue
dmu = dmu * Te / rmue
d2mu = d2mu * Te**2 / rmue
con = con / cone
dcon = dcon * Te / cone
d2con = d2con * Te**2 / cone
rlm = rlm / rlme
dlm = dlm * Te / rlme
d2lm = d2lm * Te**2 / rlme
!.... compute gradients of viscosity using chain-rule
g1mu = dmu * gtm(:,1)
g2mu = dmu * gtm(:,2)
g3mu = dmu * gtm(:,3)
g1dmu = d2mu * gtm(:,1)
g2dmu = d2mu * gtm(:,2)
g3dmu = d2mu * gtm(:,3)
!.... compute gradients of conductivity using chain-rule
g1con = dcon * gtm(:,1)
g2con = dcon * gtm(:,2)
g3con = dcon * gtm(:,3)
g1dcon = d2con * gtm(:,1)
g2dcon = d2con * gtm(:,2)
g3dcon = d2con * gtm(:,3)
!.... compute gradients of bulk viscosity using chain-rule
g1lm = dlm * gtm(:,1)
g2lm = dlm * gtm(:,2)
g3lm = dlm * gtm(:,3)
g1dlm = d2lm * gtm(:,1)
g2dlm = d2lm * gtm(:,2)
g3dlm = d2lm * gtm(:,3)
!==============================================================================
!.... Continuity equation
G(:,1,1) = one
A(:,1,1) = u1m
A(:,1,2) = rhom
B(:,1,1) = u2m
B(:,1,3) = rhom
C(:,1,1) = u3m
C(:,1,4) = rhom
D(:,1,1) = divum
D(:,1,2) = grhom(:,1)
D(:,1,3) = grhom(:,2)
D(:,1,4) = grhom(:,3)
!.... Momentum equation -- x_1 (convective + pressure)
G(:,2,2) = rhom
A(:,2,1) = tm/(gamma * Ma**2)
A(:,2,2) = rhom * u1m
A(:,2,5) = rhom/(gamma * Ma**2)
B(:,2,2) = rhom * u2m
C(:,2,2) = rhom * u3m
D(:,2,1) = u1m * gum(:,1,1) + u2m * gum(:,1,2) + u3m * gum(:,1,3) &
+ gtm(:,1) / (gamma * Ma**2)
D(:,2,2) = rhom * gum(:,1,1)
D(:,2,3) = rhom * gum(:,1,2)
D(:,2,4) = rhom * gum(:,1,3)
D(:,2,5) = grhom(:,1) / (gamma * Ma**2)
!.... (viscous lambda)
if (Navier) then
fact = rlme / (rmue * Re)
A(:,2,2) = A(:,2,2) - fact * g1lm
A(:,2,5) = A(:,2,5) - fact * dlm * divum
B(:,2,3) = B(:,2,3) - fact * g1lm
C(:,2,4) = C(:,2,4) - fact * g1lm
D(:,2,5) = D(:,2,5) - fact * ( g1dlm * divum + dlm * g1divum )
Vxx(:,2,2) = fact * rlm
Vxy(:,2,3) = fact * rlm
Vxz(:,2,4) = fact * rlm
!.... (viscous mu)
fact = one / Re
A(:,2,2) = A(:,2,2) - fact * two * g1mu
A(:,2,3) = A(:,2,3) - fact * g2mu
A(:,2,4) = A(:,2,4) - fact * g3mu
A(:,2,5) = A(:,2,5) - fact * dmu * two * S(:,1,1)
B(:,2,2) = B(:,2,2) - fact * g2mu
B(:,2,5) = B(:,2,5) - fact * dmu * two * S(:,1,2)
C(:,2,2) = C(:,2,2) - fact * g3mu
C(:,2,5) = C(:,2,5) - fact * dmu * two * S(:,1,3)
D(:,2,5) = D(:,2,5) - fact * two * ( g1dmu * S(:,1,1) + &
g2dmu * S(:,1,2) + g3dmu * S(:,1,3) + &
dmu * S1jj )
Vxx(:,2,2) = Vxx(:,2,2) + fact * two * rmu
Vxy(:,2,3) = Vxy(:,2,3) + fact * rmu
Vyy(:,2,2) = Vyy(:,2,2) + fact * rmu
Vxz(:,2,4) = Vxz(:,2,4) + fact * rmu
Vzz(:,2,2) = Vzz(:,2,2) + fact * rmu
end if
!.... Momentum equation -- x_2 (convective + pressure)
G(:,3,3) = rhom
A(:,3,3) = rhom * u1m
B(:,3,1) = tm/(gamma * Ma**2)
B(:,3,3) = rhom * u2m
B(:,3,5) = rhom/(gamma * Ma**2)
C(:,3,3) = rhom * u3m
D(:,3,1) = u1m * gum(:,2,1) + u2m * gum(:,2,2) + u3m * gum(:,2,3) &
+ gtm(:,2) / (gamma * Ma**2)
D(:,3,2) = rhom * gum(:,2,1)
D(:,3,3) = rhom * gum(:,2,2)
D(:,3,4) = rhom * gum(:,2,3)
D(:,3,5) = grhom(:,2) / (gamma * Ma**2)
!.... (viscous lambda)
if (Navier) then
fact = rlme / (rmue * Re)
A(:,3,2) = A(:,3,2) - fact * g2lm
B(:,3,3) = B(:,3,3) - fact * g2lm
B(:,3,5) = B(:,3,5) - fact * dlm * divum
C(:,3,4) = C(:,3,4) - fact * g2lm
D(:,3,5) = D(:,3,5) - fact * ( g2dlm * divum + dlm * g2divum )
Vxy(:,3,2) = fact * rlm
Vyy(:,3,3) = fact * rlm
Vyz(:,3,4) = fact * rlm
!.... (viscous mu)
fact = one / Re
A(:,3,3) = A(:,3,3) - fact * g1mu
A(:,3,5) = A(:,3,5) - fact * dmu * two * S(:,2,1)
B(:,3,2) = B(:,3,2) - fact * g1mu
B(:,3,3) = B(:,3,3) - fact * two * g2mu
B(:,3,4) = B(:,3,4) - fact * g3mu
B(:,3,5) = B(:,3,5) - fact * dmu * two * S(:,2,2)
C(:,3,3) = C(:,3,3) - fact * g3mu
C(:,3,5) = C(:,3,5) - fact * dmu * two * S(:,2,3)
D(:,3,5) = D(:,3,5) - fact * two * ( g1dmu * S(:,2,1) + &
g2dmu * S(:,2,2) + g3dmu * S(:,2,3) + &
dmu * S2jj )
Vxx(:,3,3) = Vxx(:,3,3) + fact * rmu
Vxy(:,3,2) = Vxy(:,3,2) + fact * rmu
Vyy(:,3,3) = Vyy(:,3,3) + fact * two * rmu
Vyz(:,3,4) = Vyz(:,3,4) + fact * rmu
Vzz(:,3,3) = Vzz(:,3,3) + fact * rmu
end if
!.... Momentum equation -- x_3 (convective + pressure)
G(:,4,4) = rhom
A(:,4,4) = rhom * u1m
B(:,4,4) = rhom * u2m
C(:,4,1) = tm/(gamma * Ma**2)
C(:,4,4) = rhom * u3m
C(:,4,5) = rhom/(gamma * Ma**2)
D(:,4,1) = u1m * gum(:,3,1) + u2m * gum(:,3,2) + u3m * gum(:,3,3) &
+ gtm(:,3) / (gamma * Ma**2)
D(:,4,2) = rhom * gum(:,3,1)
D(:,4,3) = rhom * gum(:,3,2)
D(:,4,4) = rhom * gum(:,3,3)
D(:,4,5) = grhom(:,3) / (gamma * Ma**2)
!.... (viscous lambda)
if (Navier) then
fact = rlme / (rmue * Re)
A(:,4,2) = A(:,4,2) - fact * g3lm
B(:,4,3) = B(:,4,3) - fact * g3lm
C(:,4,4) = C(:,4,4) - fact * g3lm
C(:,4,5) = C(:,4,5) - fact * dlm * divum
D(:,4,5) = D(:,4,5) - fact * ( g3dlm * divum + dlm * g3divum )
Vxz(:,4,2) = fact * rlm
Vyz(:,4,3) = fact * rlm
Vzz(:,4,4) = fact * rlm
!.... (viscous mu)
fact = one / Re
A(:,4,4) = A(:,4,4) - fact * g1mu
A(:,4,5) = A(:,4,5) - fact * dmu * two * S(:,3,1)
B(:,4,4) = B(:,4,4) - fact * g2mu
B(:,4,5) = B(:,4,5) - fact * dmu * two * S(:,3,2)
C(:,4,2) = C(:,4,2) - fact * g1mu
C(:,4,3) = C(:,4,3) - fact * g2mu
C(:,4,4) = C(:,4,4) - fact * two * g3mu
C(:,4,5) = C(:,4,5) - fact * dmu * two * S(:,3,3)
D(:,4,5) = D(:,4,5) - fact * two * ( g1dmu * S(:,3,1) + &
g2dmu * S(:,3,2) + g3dmu * S(:,3,3) + &
dmu * S3jj )
Vxx(:,4,4) = Vxx(:,4,4) + fact * rmu
Vyy(:,4,4) = Vyy(:,4,4) + fact * rmu
Vxz(:,4,2) = Vxz(:,4,2) + fact * rmu
Vyz(:,4,3) = Vyz(:,4,3) + fact * rmu
Vzz(:,4,4) = Vzz(:,4,4) + fact * two * rmu
end if
!.... Energy equation (Advection + pressure)
G(:,5,1) = -gamma1 * tm / gamma
G(:,5,5) = rhom / gamma
A(:,5,1) = -gamma1 * u1m * tm / gamma
A(:,5,5) = rhom * u1m / gamma
B(:,5,1) = -gamma1 * u2m * tm / gamma
B(:,5,5) = rhom * u2m / gamma
C(:,5,1) = -gamma1 * u3m * tm / gamma
C(:,5,5) = rhom * u3m / gamma
D(:,5,1) = one/gamma * ( u1m * gtm(:,1) + u2m * gtm(:,2) + &
u3m * gtm(:,3) )
D(:,5,2) = rhom * gtm(:,1) - gamma1 * Ma**2 * gpm(:,1)
D(:,5,3) = rhom * gtm(:,2) - gamma1 * Ma**2 * gpm(:,2)
D(:,5,4) = rhom * gtm(:,3) - gamma1 * Ma**2 * gpm(:,3)
D(:,5,5) = -gamma1/gamma * ( u1m * grhom(:,1) + u2m * grhom(:,2) + &
u3m * grhom(:,3) )
if (Navier) then
!.... diffusion
fact = one / (Pr * Re)
A(:,5,5) = A(:,5,5) - fact * (g1con + dcon * gtm(:,1))
B(:,5,5) = B(:,5,5) - fact * (g2con + dcon * gtm(:,2))
C(:,5,5) = C(:,5,5) - fact * (g3con + dcon * gtm(:,3))
D(:,5,5) = D(:,5,5) - fact * (g1dcon * gtm(:,1) + &
g2dcon * gtm(:,2) + g3dcon * gtm(:,3) + &
dcon * ( g11vm(:,5) + g22vm(:,5) + &
g33vm(:,5) ) )
Vxx(:,5,5) = fact * con
Vyy(:,5,5) = fact * con
Vzz(:,5,5) = fact * con
!.... dissipation (lambda)
fact = gamma1 * Ma**2 * rlme / (Re * rmue)
A(:,5,2) = A(:,5,2) - fact * two * rlm * divum
B(:,5,3) = B(:,5,3) - fact * two * rlm * divum
C(:,5,4) = C(:,5,4) - fact * two * rlm * divum
D(:,5,5) = D(:,5,5) - fact * dlm * divum * divum
!.... dissipation (mu)
fact = two * gamma1 * Ma**2 / Re
A(:,5,2) = A(:,5,2) - fact * two * rmu * S(:,1,1)
A(:,5,3) = A(:,5,3) - fact * two * rmu * S(:,2,1)
A(:,5,4) = A(:,5,4) - fact * two * rmu * S(:,3,1)
B(:,5,2) = B(:,5,2) - fact * two * rmu * S(:,1,2)
B(:,5,3) = B(:,5,3) - fact * two * rmu * S(:,2,2)
B(:,5,4) = B(:,5,4) - fact * two * rmu * S(:,3,2)
C(:,5,2) = C(:,5,2) - fact * two * rmu * S(:,1,3)
C(:,5,3) = C(:,5,3) - fact * two * rmu * S(:,2,3)
C(:,5,4) = C(:,5,4) - fact * two * rmu * S(:,3,3)
D(:,5,5) = D(:,5,5) - fact * dmu * ( S(:,1,1)**2 + &
S(:,1,2)**2 + S(:,1,3)**2 + S(:,2,1)**2 + &
S(:,2,2)**2 + S(:,2,3)**2 + S(:,3,1)**2 + &
S(:,3,2)**2 + S(:,3,3)**2)
end if
!==============================================================================
!.... form the equations
Dh = D + im * alpha * A + im * beta * C &
+ alpha**2 * Vxx + alpha * beta * Vxz + beta**2 * Vzz
Ah = A - two * im * alpha * Vxx - im * beta * Vxz
Bh = B - im * alpha * Vxy - im * beta * Vyz
!.... account for the mapping
do idof = 1, ndof
do jdof = 1, ndof
Bh(:,idof,jdof) = Bh(:,idof,jdof) * deta - Vyy(:,idof,jdof) * d2eta
Vyy(:,idof,jdof) = Vyy(:,idof,jdof) * deta**2
end do
end do
!.... initialize
A0 = zero
B0 = zero
evec = zero
alp = zero
bet = zero
!.... B0
do idof = 1, ndof-1
B0(idof,idof) = im * one ! continuity and no-slip BC
end do
i = 1
idof = ndof
i0 = (i-1)*ndof
do jdof = 1, ndof
B0(i0+idof,i0+jdof) = im * G(i,idof,jdof) ! energy
end do
do idof = 1, ndof
do jdof = 1, ndof
do i = 2, ny-1
i0 = (i-1)*ndof
B0(i0+idof,i0+jdof) = im * G(i,idof,jdof)
end do
end do
end do
i0 = (ny-1)*ndof
do idof = 1, ndof
B0(i0+idof,i0+idof) = im * one ! zero dist.
end do
!.... A0
i = 1
i0 = (i-1)*ndof
idof = 1 ! continuity at the wall
do jdof = 1, ndof
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = Dh(i,idof,jdof) + &
(gg1/dy) * Bh(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (gg2/dy) * Bh(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (gg3/dy) * Bh(i,idof,jdof)
j0 = (i+2)*ndof
A0(i0+idof,j0+jdof) = (gg4/dy) * Bh(i,idof,jdof)
j0 = (i+3)*ndof
A0(i0+idof,j0+jdof) = (gg5/dy) * Bh(i,idof,jdof)
j0 = (i+4)*ndof
A0(i0+idof,j0+jdof) = (gg6/dy) * Bh(i,idof,jdof)
end do
i = 1
i0 = (i-1)*ndof
idof = ndof ! energy equation at the wall
do jdof = 1, ndof-1
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = Dh(i,idof,jdof) + &
(gg1/dy) * Bh(i,idof,jdof) - &
dd1/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (gg2/dy) * Bh(i,idof,jdof) - &
dd2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (gg3/dy) * Bh(i,idof,jdof) - &
dd3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+2)*ndof
A0(i0+idof,j0+jdof) = (gg4/dy) * Bh(i,idof,jdof) - &
dd4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+3)*ndof
A0(i0+idof,j0+jdof) = (gg5/dy) * Bh(i,idof,jdof) - &
dd5/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+4)*ndof
A0(i0+idof,j0+jdof) = (gg6/dy) * Bh(i,idof,jdof)
end do
jdof = ndof !.... adiabatic contraint
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = Dh(i,idof,jdof) &
-dd1/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = -dd2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = -dd3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+2)*ndof
A0(i0+idof,j0+jdof) = -dd4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+3)*ndof
A0(i0+idof,j0+jdof) = -dd5/(dy*dy) * Vyy(i,idof,jdof)
do idof = 1, ndof
do jdof = 1, ndof
i = 2
i0 = (i-1)*ndof
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (gh1/dy) * Bh(i,idof,jdof) - &
db1/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = (gh2/dy) * Bh(i,idof,jdof) + &
Dh(i,idof,jdof) - &
db2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (gh3/dy) * Bh(i,idof,jdof) - &
db3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (gh4/dy) * Bh(i,idof,jdof) - &
db4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+2)*ndof
A0(i0+idof,j0+jdof) = (gh5/dy) * Bh(i,idof,jdof) - &
db5/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+3)*ndof
A0(i0+idof,j0+jdof) = (gh6/dy) * Bh(i,idof,jdof)
i = 3
i0 = (i-1)*ndof
j0 = (i-3)*ndof
A0(i0+idof,j0+jdof) = (gi1/dy) * Bh(i,idof,jdof) - &
da1/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (gi2/dy) * Bh(i,idof,jdof) - &
da2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = (gi3/dy) * Bh(i,idof,jdof) + &
Dh(i,idof,jdof) - &
da3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (gi4/dy) * Bh(i,idof,jdof) - &
da4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (gi5/dy) * Bh(i,idof,jdof) - &
da5/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+2)*ndof
A0(i0+idof,j0+jdof) = (gi6/dy) * Bh(i,idof,jdof)
i = 4
i0 = (i-1)*ndof
j0 = (i-4)*ndof
A0(i0+idof,j0+jdof) = (gj1/dy) * Bh(i,idof,jdof)
j0 = (i-3)*ndof
A0(i0+idof,j0+jdof) = (gj2/dy) * Bh(i,idof,jdof) - &
da1/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (gj3/dy) * Bh(i,idof,jdof) - &
da2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = (gj4/dy) * Bh(i,idof,jdof) + &
Dh(i,idof,jdof) - &
da3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (gj5/dy) * Bh(i,idof,jdof) - &
da4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (gj6/dy) * Bh(i,idof,jdof) - &
da5/(dy*dy) * Vyy(i,idof,jdof)
do i = 5, ny-4
i0 = (i-1)*ndof
j0 = (i-3)*ndof
A0(i0+idof,j0+jdof) = (ga1/dy) * Bh(i,idof,jdof) - &
(da1)/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (ga2/dy) * Bh(i,idof,jdof) - &
(da2)/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = Dh(i,idof,jdof) - &
(da3)/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (ga3/dy) * Bh(i,idof,jdof) - &
(da4)/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (ga4/dy) * Bh(i,idof,jdof) - &
(da5)/(dy*dy) * Vyy(i,idof,jdof)
end do
i = ny-3
i0 = (i-1)*ndof
j0 = (i-3)*ndof
A0(i0+idof,j0+jdof) = (-gj6/dy) * Bh(i,idof,jdof) - &
da1/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (-gj5/dy) * Bh(i,idof,jdof) - &
da2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = (-gj4/dy) * Bh(i,idof,jdof) + &
Dh(i,idof,jdof) - &
da3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (-gj3/dy) * Bh(i,idof,jdof) + &
da4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (-gj2/dy) * Bh(i,idof,jdof) + &
da5/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+2)*ndof
A0(i0+idof,j0+jdof) = (-gj1/dy) * Bh(i,idof,jdof)
i = ny-2
i0 = (i-1)*ndof
j0 = (i-4)*ndof
A0(i0+idof,j0+jdof) = (-gi6/dy) * Bh(i,idof,jdof)
j0 = (i-3)*ndof
A0(i0+idof,j0+jdof) = (-gi5/dy) * Bh(i,idof,jdof) - &
da1/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (-gi4/dy) * Bh(i,idof,jdof) - &
da2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = (-gi3/dy) * Bh(i,idof,jdof) + &
Dh(i,idof,jdof) - &
da3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (-gi2/dy) * Bh(i,idof,jdof) + &
da4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i+1)*ndof
A0(i0+idof,j0+jdof) = (-gi1/dy) * Bh(i,idof,jdof) - &
da5/(dy*dy) * Vyy(i,idof,jdof)
i = ny-1
i0 = (i-1)*ndof
j0 = (i-5)*ndof
A0(i0+idof,j0+jdof) = (-gh6/dy) * Bh(i,idof,jdof)
j0 = (i-4)*ndof
A0(i0+idof,j0+jdof) = (-gh5/dy) * Bh(i,idof,jdof) - &
db5/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-3)*ndof
A0(i0+idof,j0+jdof) = (-gh4/dy) * Bh(i,idof,jdof) - &
db4/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (-gh3/dy) * Bh(i,idof,jdof) - &
db3/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = (-gh2/dy) * Bh(i,idof,jdof) + &
Dh(i,idof,jdof) - &
db2/(dy*dy) * Vyy(i,idof,jdof)
j0 = (i)*ndof
A0(i0+idof,j0+jdof) = (-gh1/dy) * Bh(i,idof,jdof) - &
db1/(dy*dy) * Vyy(i,idof,jdof)
end do
end do
if (.false.) then ! zero-disturbance
i = ny
i0 = (i-1)*ndof
idof = 1 ! continuity in the FS
do jdof = 1, ndof
j0 = (i-6)*ndof
A0(i0+idof,j0+jdof) = (-gg6/dy) * Bh(i,idof,jdof)
j0 = (i-5)*ndof
A0(i0+idof,j0+jdof) = (-gg5/dy) * Bh(i,idof,jdof)
j0 = (i-4)*ndof
A0(i0+idof,j0+jdof) = (-gg4/dy) * Bh(i,idof,jdof)
j0 = (i-3)*ndof
A0(i0+idof,j0+jdof) = (-gg3/dy) * Bh(i,idof,jdof)
j0 = (i-2)*ndof
A0(i0+idof,j0+jdof) = (-gg2/dy) * Bh(i,idof,jdof)
j0 = (i-1)*ndof
A0(i0+idof,j0+jdof) = Dh(i,idof,jdof) + &
(-gg1/dy) * Bh(i,idof,jdof)
end do
end if
write (*,*)
write (*,*) 'S O L V I N G E I G E N S Y S T E M'
!.... IMSL generalized complex eigensolver
! CALL GVCCG (ndof*ny, A0, ndof*ny, B0, ndof*ny, &
! alp, bet, evec, ndof*ny)
!.... Lapack generalized complex eigensolver
! lwork = 8*ndof*ny
! allocate (work(lwork), rwork(lwork), STAT=ier)
! if (ier .ne. 0) then
! write(*,*) 'Error allocating work space'
! call exit(1)
! end if
! call CGEGV ( 'N', 'V', ndof*ny, A0, ndof*ny, B0, ndof*ny, &
! alp, bet, evec, ndof*ny, evec, ndof*ny, &
! work, lwork, rwork, info )
! write (*,*) 'Info = ', info
! deallocate (work, rwork)
!.... compute the frequency (temporal)
! where (bet .ne. 0)
! omg = alp / bet
! elsewhere
! omg = zero
! end where
!.... IMSL regular complex eigensolver
! call LINCG (ndof*ny, B0, ndof*ny, B0, ndof*ny)
! call MCRCR (ndof*ny, ndof*ny, B0, ndof*ny, &
! ndof*ny, ndof*ny, A0, ndof*ny, &
! ndof*ny, ndof*ny, C0, ndof*ny)
! call EVCCG (ndof*ny, C0, ndof*ny, omg, evec, ndof*ny)
!.... Lapack regular complex eigensolver
allocate(ipiv(ndof*ny), STAT=ier)
if (ier .ne. 0) then
write(*,*) 'Error allocating pivots'
call exit(1)
end if
#ifdef CRAY
call CGESV( ndof*ny, ndof*ny, B0, ndof*ny, ipiv, A0, ndof*ny, info )
if (info.ne.0) then
write(*,*) 'Error in CGESV'
call exit(1)
end if
#else
call ZGESV( ndof*ny, ndof*ny, B0, ndof*ny, ipiv, A0, ndof*ny, info )
if (info.ne.0) then
write(*,*) 'Error in ZGESV'
call exit(1)
end if
#endif
deallocate(ipiv)
lwork = 2*ndof*ny
allocate (work(lwork), rwork(2*ndof*ny), STAT=ier)
if (ier .ne. 0) then
write(*,*) 'Error allocating work space'
call exit(1)
end if
#ifdef CRAY
call CGEEV('N', 'V', ndof*ny, A0, ndof*ny, omg, evec, ndof*ny, &
evec, ndof*ny, work, lwork, rwork, info)
#else