diff --git a/sources/interpolations.F90 b/sources/interpolations.F90
index a611165..4a17082 100644
--- a/sources/interpolations.F90
+++ b/sources/interpolations.F90
@@ -42,7 +42,8 @@ module interpolations
real(kind=8), dimension(:,:,:) , intent(in) :: q
real(kind=8), dimension(:,:,:,:,:), intent(out) :: qi
end subroutine
- subroutine reconstruct_iface(h, fc, fl, fr)
+ subroutine reconstruct_iface(positive, h, fc, fl, fr)
+ logical , intent(in) :: positive
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -76,7 +77,6 @@ module interpolations
! monotonicity preserving reconstruction coefficients
!
real(kind=8), save :: kappa = 1.0d+00
- real(kind=8), save :: kbeta = 1.0d+00
! number of ghost zones (required for compact schemes)
!
@@ -218,7 +218,6 @@ module interpolations
call get_parameter("eps" , eps )
call get_parameter("limo3_rad" , rad )
call get_parameter("kappa" , kappa )
- call get_parameter("kbeta" , kbeta )
call get_parameter("ppm_const" , ppm_const )
call get_parameter("central_weight" , cweight )
call get_parameter("cfl" , cfl )
@@ -978,20 +977,20 @@ module interpolations
!
! Arguments:
!
-! positive - the variable positivity flag;
-! h - the spatial step;
-! q - the variable array;
-! qi - the array of reconstructed interfaces (2 in each direction);
+! p - the variable positivity flag;
+! h - the spatial step;
+! q - the variable array;
+! qi - the array of reconstructed interfaces (2 in each direction);
!
!===============================================================================
!
- subroutine interfaces_dir(positive, h, q, qi)
+ subroutine interfaces_dir(p, h, q, qi)
use coordinates, only : nb, ne, nbl, neu
implicit none
- logical , intent(in) :: positive
+ logical , intent(in) :: p
real(kind=8), dimension(:) , intent(in) :: h
real(kind=8), dimension(:,:,:) , intent(in) :: q
real(kind=8), dimension(:,:,:,:,:), intent(out) :: qi
@@ -1025,23 +1024,23 @@ module interpolations
do k = nbl, neu
#endif /* NDIMS == 3 */
do j = nbl, neu
- call reconstruct(h(1), q(:,j,k), qi(:,j,k,1,1), qi(:,j,k,2,1))
+ call reconstruct(p, h(1), q(:,j,k), qi(:,j,k,1,1), qi(:,j,k,2,1))
end do ! j = nbl, neu
do i = nbl, neu
- call reconstruct(h(2), q(i,:,k), qi(i,:,k,1,2), qi(i,:,k,2,2))
+ call reconstruct(p, h(2), q(i,:,k), qi(i,:,k,1,2), qi(i,:,k,2,2))
end do ! i = nbl, neu
#if NDIMS == 3
end do ! k = nbl, neu
do j = nbl, neu
do i = nbl, neu
- call reconstruct(h(3), q(i,j,:), qi(i,j,:,1,3), qi(i,j,:,2,3))
+ call reconstruct(p, h(3), q(i,j,:), qi(i,j,:,1,3), qi(i,j,:,2,3))
end do ! i = nbl, neu
end do ! j = nbl, neu
#endif /* NDIMS == 3 */
! make sure the interface states are positive for positive variables
!
- if (positive) then
+ if (p) then
#if NDIMS == 3
do k = nbl, neu
@@ -1442,6 +1441,7 @@ module interpolations
!
! Arguments:
!
+! p - the flag indicating if the reconstructed variable is positivite;
! h - the spatial step; this is required for some reconstruction methods;
! f - the input vector of cell averaged values;
! fl - the left side state reconstructed for location (i+1/2);
@@ -1449,10 +1449,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct(h, f, fl, fr)
+ subroutine reconstruct(p, h, f, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: f
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -1461,7 +1462,7 @@ module interpolations
!
! reconstruct the states using the selected subroutine
!
- call reconstruct_states(h, f(:), fl(:), fr(:))
+ call reconstruct_states(p, h, f(:), fl(:), fr(:))
! correct the reconstruction near extrema by clipping them in order to improve
! the stability of scheme
@@ -1485,10 +1486,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_tvd(h, fc, fl, fr)
+ subroutine reconstruct_tvd(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -1553,10 +1555,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_weno3(h, fc, fl, fr)
+ subroutine reconstruct_weno3(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -1675,10 +1678,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_limo3(h, fc, fl, fr)
+ subroutine reconstruct_limo3(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -1818,10 +1822,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_ppm(h, fc, fl, fr)
+ subroutine reconstruct_ppm(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -2002,10 +2007,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_weno5z(h, fc, fl, fr)
+ subroutine reconstruct_weno5z(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -2159,10 +2165,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_weno5yc(h, fc, fl, fr)
+ subroutine reconstruct_weno5yc(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -2317,10 +2324,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_weno5ns(h, fc, fl, fr)
+ subroutine reconstruct_weno5ns(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -2503,12 +2511,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_crweno5z(h, fc, fl, fr)
+ subroutine reconstruct_crweno5z(p, h, fc, fl, fr)
use algebra, only : tridiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -2878,12 +2887,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_crweno5yc(h, fc, fl, fr)
+ subroutine reconstruct_crweno5yc(p, h, fc, fl, fr)
use algebra, only : tridiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -3256,12 +3266,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_crweno5ns(h, fc, fl, fr)
+ subroutine reconstruct_crweno5ns(p, h, fc, fl, fr)
use algebra, only : tridiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -3647,10 +3658,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_mp5(h, fc, fl, fr)
+ subroutine reconstruct_mp5(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -3676,7 +3688,7 @@ module interpolations
u(n-1) = sum(ce3(:) * fc(n-2:n))
u(n ) = fc(n )
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -3694,7 +3706,7 @@ module interpolations
u(n-1) = sum(ce3(:) * fi(n-2:n))
u(n ) = fi(n )
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -3724,10 +3736,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_mp7(h, fc, fl, fr)
+ subroutine reconstruct_mp7(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -3755,7 +3768,7 @@ module interpolations
u(n-1) = sum(ce3(:) * fc(n-2:n))
u(n ) = fc(n )
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -3775,7 +3788,7 @@ module interpolations
u(n-1) = sum(ce3(:) * fi(n-2:n))
u(n ) = fi(n )
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -3805,10 +3818,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_mp9(h, fc, fl, fr)
+ subroutine reconstruct_mp9(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -3838,7 +3852,7 @@ module interpolations
u(n-1) = sum(ce3(:) * fc(n-2:n))
u(n ) = fc(n )
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -3860,7 +3874,7 @@ module interpolations
u(n-1) = sum(ce3(:) * fi(n-2:n))
u(n ) = fi(n )
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -3902,12 +3916,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_crmp5(h, fc, fl, fr)
+ subroutine reconstruct_crmp5(p, h, fc, fl, fr)
use algebra, only : tridiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -3958,7 +3973,7 @@ module interpolations
call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -3983,7 +3998,7 @@ module interpolations
call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -4014,12 +4029,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_crmp7(h, fc, fl, fr)
+ subroutine reconstruct_crmp7(p, h, fc, fl, fr)
use algebra, only : tridiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -4072,7 +4088,7 @@ module interpolations
call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -4099,7 +4115,7 @@ module interpolations
call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -4130,12 +4146,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_crmp9(h, fc, fl, fr)
+ subroutine reconstruct_crmp9(p, h, fc, fl, fr)
use algebra, only : pentadiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -4196,7 +4213,7 @@ module interpolations
call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -4225,7 +4242,7 @@ module interpolations
call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -4260,12 +4277,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_ocmp5(h, fc, fl, fr)
+ subroutine reconstruct_ocmp5(p, h, fc, fl, fr)
use algebra, only : tridiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -4327,7 +4345,7 @@ module interpolations
call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -4352,7 +4370,7 @@ module interpolations
call tridiag(n, a(1:n), b(1:n), c(1:n), r(1:n), u(1:n))
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -4387,12 +4405,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_ocmp7(h, fc, fl, fr)
+ subroutine reconstruct_ocmp7(p, h, fc, fl, fr)
use algebra, only : pentadiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -4466,7 +4485,7 @@ module interpolations
call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -4493,7 +4512,7 @@ module interpolations
call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -4528,12 +4547,13 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_ocmp9(h, fc, fl, fr)
+ subroutine reconstruct_ocmp9(p, h, fc, fl, fr)
use algebra, only : pentadiag
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -4611,7 +4631,7 @@ module interpolations
call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
fl(1:n) = u(1:n)
@@ -4640,7 +4660,7 @@ module interpolations
call pentadiag(n, e(:), c(:), d(:), a(:), b(:), r(:), u(:))
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
fr(1:n-1) = u(n-1:1:-1)
@@ -4773,10 +4793,11 @@ module interpolations
!
!===============================================================================
!
- subroutine reconstruct_gp(h, fc, fl, fr)
+ subroutine reconstruct_gp(p, h, fc, fl, fr)
implicit none
+ logical , intent(in) :: p
real(kind=8) , intent(in) :: h
real(kind=8), dimension(:), intent(in) :: fc
real(kind=8), dimension(:), intent(out) :: fl, fr
@@ -4814,7 +4835,7 @@ module interpolations
! apply the monotonicity preserving limiting
!
- call mp_limiting(fc(:), u(:))
+ call mp_limiting(p, n, fc(:), u(:))
! copy the interpolation to the respective vector
!
@@ -4848,7 +4869,7 @@ module interpolations
! apply the monotonicity preserving limiting
!
- call mp_limiting(fi(:), u(:))
+ call mp_limiting(p, n, fi(:), u(:))
! copy the interpolation to the respective vector
!
@@ -5325,93 +5346,118 @@ module interpolations
! subroutine MP_LIMITING:
! ----------------------
!
-! Subroutine applies the monotonicity preserving (MP) limiter to a vector of
-! high order reconstructed interface values.
+! Subroutine applies the monotonicity preserving (MP) limitation to
+! the interface states reconstructed using a high order upwind
+! interpolation.
!
! Arguments:
!
-! qc - the vector of cell-centered values;
-! qi - the vector of interface values obtained from the high order
-! interpolation as input and its monotonicity limited values as output;
+! p - the logical flag indicating if the variable is positive;
+! n - the length of vector u and q;
+! u - the vector of centered cell-integrated values;
+! q - the vector of interface values obtained from the high order
+! interpolation to which the limitation is applied;
!
! References:
!
! [1] Suresh, A. & Huynh, H. T.,
! "Accurate Monotonicity-Preserving Schemes with Runge-Kutta
! Time Stepping"
-! Journal on Computational Physics,
-! 1997, vol. 136, pp. 83-99,
-! http://dx.doi.org/10.1006/jcph.1997.5745
-! [2] He, ZhiWei, Li, XinLiang, Fu, DeXun, & Ma, YanWen,
-! "A 5th order monotonicity-preserving upwind compact difference
-! scheme",
-! Science China Physics, Mechanics and Astronomy,
-! Volume 54, Issue 3, pp. 511-522,
-! http://dx.doi.org/10.1007/s11433-010-4220-x
+! Journal on Computational Physics, 1997, 136, 83-99,
+! https://doi.org/10.1006/jcph.1997.5745
+! [2] Myeong-Hwan Ahn1, Duck-Joo Lee,
+! "Modified Monotonicity Preserving Constraints for High-Resolution
+! Optimized Compact Scheme",
+! Journal of Scientific Computing, 2020, 83:34,
+! https://doi.org/10.1007/s10915-020-01221-0
!
!===============================================================================
!
- subroutine mp_limiting(qc, qi)
+ subroutine mp_limiting(p, n, u, q)
implicit none
- real(kind=8), dimension(:), intent(in) :: qc
- real(kind=8), dimension(:), intent(inout) :: qi
+ logical , intent(in) :: p
+ integer , intent(in) :: n
+ real(kind=8), dimension(n), intent(in) :: u
+ real(kind=8), dimension(n), intent(inout) :: q
- integer :: n, i, im1, ip1, ip2
- real(kind=8) :: dq, ds, dc0, dc4, dm1, dp1, dml, dmr
+ integer :: i, im2, im1, ip1, ip2
+ real(kind=8) :: du, dm, dc, dp, dc4, dmm, dmp, di, de, bt
real(kind=8) :: qlc, qmd, qmp, qmn, qmx, qul
- real(kind=8), dimension(0:size(qc)+2) :: dm
+ real(kind=8), dimension(n) :: d
+ real(kind=8), dimension(2) :: umn, umx
!-------------------------------------------------------------------------------
!
- n = size(qc)
+ d(1 ) = 0.0d+00
+ d(2:n) = u(2:n) - u(1:n-1)
- dm(0 ) = 0.0d+00
- dm(1 ) = 0.0d+00
- dm(2:n) = qc(2:n) - qc(1:n-1)
- dm(n+1) = 0.0d+00
- dm(n+2) = 0.0d+00
+ im2 = 1
+ im1 = 1
+ ip1 = 2
+ ip2 = 3
- do i = 1, n - 1
+ do i = 1, n
- ip1 = i + 1
+ du = kappa * d(i)
- if (dm(i) * dm(ip1) >= 0.0d+00) then
- dq = kappa * dm(i)
- else
- dq = kbeta * dm(i)
- end if
+ qmp = u(i) + minmod(d(ip1), du)
- qmp = qc(i) + minmod(dm(ip1), dq)
- ds = (qi(i) - qc(i)) * (qi(i) - qmp)
+ if ((q(i) - u(i)) * (q(i) - qmp) > eps) then
- if (ds > eps) then
+ dm = d(i ) - d(im1)
+ dc = d(ip1) - d(i )
+ dp = d(ip2) - d(ip1)
+ dc4 = 4.0d+00 * dc
- im1 = i - 1
- ip2 = i + 2
+ dmp = minmod4(dc4 - dp, 4.0d+00 * dp - dc, dc, dp)
+ dmm = minmod4(dc4 - dm, 4.0d+00 * dm - dc, dc, dm)
- dm1 = dm(i ) - dm(im1)
- dc0 = dm(ip1) - dm(i )
- dp1 = dm(ip2) - dm(ip1)
- dc4 = 4.0d+00 * dc0
+ qul = u(i) + du
+ qmd = u(i) + 5.0d-01 * (d(ip1) - dmp )
+ qlc = u(i) + 5.0d-01 * (d(i ) + 8.0d+00 * dmm / 3.0d+00)
- dml = 0.5d+00 * minmod4(dc4 - dm1, 4.0d+00 * dm1 - dc0, dc0, dm1)
- dmr = 0.5d+00 * minmod4(dc4 - dp1, 4.0d+00 * dp1 - dc0, dc0, dp1)
+ umn(1) = min(u(im1), u(ip1))
+ umn(2) = min(u(im2), u(ip2))
+ umx(1) = max(u(im1), u(ip1))
+ umx(2) = max(u(im2), u(ip2))
- qmd = qc(i) + 0.5d+00 * dm(ip1) - dmr
- qul = qc(i) + dq
- qlc = qc(i) + 0.5d+00 * dq + dml
+ if ((u(i) > umx(1) .and. umx(1) > umx(2) .and. &
+ u(im2) <= u(ip1) .and. u(im1) >= u(ip2)) .or. &
+ (u(i) < umn(1) .and. umn(1) < umn(2) .and. &
+ u(im2) >= u(ip1) .and. u(im1) <= u(ip2))) then
- qmx = max(min(qc(i), qc(ip1), qmd), min(qc(i), qul, qlc))
- qmn = min(max(qc(i), qc(ip1), qmd), max(qc(i), qul, qlc))
+ bt = 2.0d+00 * u(i)
+ di = (u(im1) + u(ip1)) - bt
+ de = (u(im2) + u(ip2)) - bt
+ bt = di / de
+ if (bt > 3.0d-01) qlc = u(im2)
- qi(i) = median(qi(i), qmn, qmx)
+ end if
+
+ qmx = max(min(u(i), u(ip1), qmd), min(u(i), qul, qlc))
+ qmn = min(max(u(i), u(ip1), qmd), max(u(i), qul, qlc))
+
+ if (p .and. qmn <= 0.0d+00) then
+ if (d(i) <= 0.0d+00 .and. d(ip1) >= 0.0d+00) then
+ qmn = u(i) * u(ip1) / (u(i) + u(ip1))
+ else
+ qmn = max(eps, min(u(i), u(ip1)))
+ end if
+ end if
+
+ q(i) = median(q(i), qmn, qmx)
end if
- end do ! i = 1, n - 1
+ im2 = im1
+ im1 = i
+ ip1 = ip2
+ ip2 = min(ip2 + 1, n)
+
+ end do
!-------------------------------------------------------------------------------
!