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Andrey Klenin
LAKE
Commits
9b67413a
Commit
9b67413a
authored
3 years ago
by
Victor Stepanenko
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Reconstruction of horizonal concentration distribution in a mixed layer of a circular lake is added
parent
d60cf50a
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source/model/numerics_mod.f90
+143
-0
143 additions, 0 deletions
source/model/numerics_mod.f90
source/model/phys_func.f90
+20
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20 additions, 0 deletions
source/model/phys_func.f90
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0 deletions
source/model/numerics_mod.f90
+
143
−
0
View file @
9b67413a
...
...
@@ -350,4 +350,147 @@ y(1:N) = x(1:N)
deallocate
(
x
)
END
SUBROUTINE
SMOOTHER_CONSERV
!************************************************************************
!* *
!* Program to calculate the first kind modified Bessel function of *
!* integer order N, for any REAL X, using the function BESSI(N,X). *
!* *
!* -------------------------------------------------------------------- *
!* *
!* SAMPLE RUN: *
!* *
!* (Calculate Bessel function for N=2, X=0.75). *
!* *
!* Bessel function of order 2 for X = 0.7500: *
!* *
!* Y = 0.73666878E-01 *
!* *
!* -------------------------------------------------------------------- *
!* Reference: From Numath Library By Tuan Dang Trong in Fortran 77. *
!* *
!* F90 Release 1.2 By J-P Moreau, Paris. *
!* (www.jpmoreau.fr) *
!* *
!* Version 1.1: corected value of P4 in BESSIO (P4=1.2067492 and not *
!* 1.2067429) Aug. 2011. *
!* Version 2: all variables are declared. *
!************************************************************************
!PROGRAM TBESSI
!
! IMPLICIT NONE
! REAL*8 BESSI, X, Y
! INTEGER N
!
! N=2
! X=0.75D0
!
! Y = BESSI(N,X)
!
! write(*,10) N, X
! write(*,20) Y
!
! stop
!
!10 format (/' Bessel Function of order ',I2,' for X=',F8.4,':')
!20 format(/' Y = ',E15.8/)
!
!END
! ----------------------------------------------------------------------
! Auxiliary Bessel functions for N=0, N=1
FUNCTION
BESSI0
(
X
)
IMPLICIT
NONE
REAL
*
8
X
,
BESSI0
,
Y
,
P1
,
P2
,
P3
,
P4
,
P5
,
P6
,
P7
,
&
&
Q1
,
Q2
,
Q3
,
Q4
,
Q5
,
Q6
,
Q7
,
Q8
,
Q9
,
AX
,
BX
DATA
P1
,
P2
,
P3
,
P4
,
P5
,
P6
,
P7
/
1.D0
,
3.5156229D0
,
3.0899424D0
,
1.2067492D0
,
&
&
0.2659732D0
,
0.360768D-1
,
0.45813D-2
/
DATA
Q1
,
Q2
,
Q3
,
Q4
,
Q5
,
Q6
,
Q7
,
Q8
,
Q9
/
0.39894228D0
,
0.1328592D-1
,
&
&
0.225319D-2
,
-0.157565D-2
,
0.916281D-2
,
-0.2057706D-1
,
&
&
0.2635537D-1
,
-0.1647633D-1
,
0.392377D-2
/
IF
(
ABS
(
X
)
.LT.
3.75D0
)
THEN
Y
=
(
X
/
3.75D0
)
**
2
BESSI0
=
P1
+
Y
*
(
P2
+
Y
*
(
P3
+
Y
*
(
P4
+
Y
*
(
P5
+
Y
*
(
P6
+
Y
*
P7
)))))
ELSE
AX
=
ABS
(
X
)
Y
=
3.75D0
/
AX
BX
=
EXP
(
AX
)/
SQRT
(
AX
)
AX
=
Q1
+
Y
*
(
Q2
+
Y
*
(
Q3
+
Y
*
(
Q4
+
Y
*
(
Q5
+
Y
*
(
Q6
+
Y
*
(
Q7
+
Y
*
(
Q8
+
Y
*
Q9
)))))))
BESSI0
=
AX
*
BX
ENDIF
RETURN
END
! ----------------------------------------------------------------------
FUNCTION
BESSI1
(
X
)
IMPLICIT
NONE
REAL
*
8
X
,
BESSI1
,
Y
,
P1
,
P2
,
P3
,
P4
,
P5
,
P6
,
P7
,
&
&
Q1
,
Q2
,
Q3
,
Q4
,
Q5
,
Q6
,
Q7
,
Q8
,
Q9
,
AX
,
BX
DATA
P1
,
P2
,
P3
,
P4
,
P5
,
P6
,
P7
/
0.5D0
,
0.87890594D0
,
0.51498869D0
,
&
&
0.15084934D0
,
0.2658733D-1
,
0.301532D-2
,
0.32411D-3
/
DATA
Q1
,
Q2
,
Q3
,
Q4
,
Q5
,
Q6
,
Q7
,
Q8
,
Q9
/
0.39894228D0
,
-0.3988024D-1
,
&
&
-0.362018D-2
,
0.163801D-2
,
-0.1031555D-1
,
0.2282967D-1
,
&
&
-0.2895312D-1
,
0.1787654D-1
,
-0.420059D-2
/
IF
(
ABS
(
X
)
.LT.
3.75D0
)
THEN
Y
=
(
X
/
3.75D0
)
**
2
BESSI1
=
X
*
(
P1
+
Y
*
(
P2
+
Y
*
(
P3
+
Y
*
(
P4
+
Y
*
(
P5
+
Y
*
(
P6
+
Y
*
P7
))))))
ELSE
AX
=
ABS
(
X
)
Y
=
3.75D0
/
AX
BX
=
EXP
(
AX
)/
SQRT
(
AX
)
AX
=
Q1
+
Y
*
(
Q2
+
Y
*
(
Q3
+
Y
*
(
Q4
+
Y
*
(
Q5
+
Y
*
(
Q6
+
Y
*
(
Q7
+
Y
*
(
Q8
+
Y
*
Q9
)))))))
BESSI1
=
AX
*
BX
ENDIF
RETURN
END
! ----------------------------------------------------------------------
! ----------------------------------------------------------------------
FUNCTION
BESSI
(
N
,
X
)
!
! This subroutine calculates the first kind modified Bessel function
! of integer order N, for any REAL X. We use here the classical
! recursion formula, when X > N. For X < N, the Miller's algorithm
! is used to avoid overflows.
! REFERENCE:
! C.W.CLENSHAW, CHEBYSHEV SERIES FOR MATHEMATICAL FUNCTIONS,
! MATHEMATICAL TABLES, VOL.5, 1962.
!
IMPLICIT
NONE
INTEGER
,
PARAMETER
::
IACC
=
40
REAL
*
8
,
PARAMETER
::
BIGNO
=
1.D10
,
BIGNI
=
1.D-10
INTEGER
N
,
M
,
J
REAL
*
8
X
,
BESSI
,
TOX
,
BIM
,
BI
,
BIP
!,BESSI0,BESSI1
IF
(
N
.EQ.
0
)
THEN
BESSI
=
BESSI0
(
X
)
RETURN
ENDIF
IF
(
N
.EQ.
1
)
THEN
BESSI
=
BESSI1
(
X
)
RETURN
ENDIF
IF
(
X
.EQ.
0.D0
)
THEN
BESSI
=
0.D0
RETURN
ENDIF
TOX
=
2.D0
/
X
BIP
=
0.D0
BI
=
1.D0
BESSI
=
0.D0
M
=
2
*
((
N
+
INT
(
SQRT
(
FLOAT
(
IACC
*
N
)))))
DO
12
J
=
M
,
1
,
-1
BIM
=
BIP
+
DFLOAT
(
J
)
*
TOX
*
BI
BIP
=
BI
BI
=
BIM
IF
(
ABS
(
BI
)
.GT.
BIGNO
)
THEN
BI
=
BI
*
BIGNI
BIP
=
BIP
*
BIGNI
BESSI
=
BESSI
*
BIGNI
ENDIF
IF
(
J
.EQ.
N
)
BESSI
=
BIP
12
CONTINUE
BESSI
=
BESSI
*
BESSI0
(
X
)/
BI
RETURN
END
END
MODULE
NUMERICS
This diff is collapsed.
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source/model/phys_func.f90
+
20
−
0
View file @
9b67413a
...
...
@@ -1985,5 +1985,25 @@ END FUNCTION FP_THETA
if
(
firstcall
)
firstcall
=
.false.
END
SUBROUTINE
DIFFMIN_HS
!> Function HORIZCONC returns a value of dissolved concentration in the mixed layer
!! at distance r from center of circular lake; according to
!! (DelSontro et al., Ecosystems, 2018) extended by inclusion of linear sink term
FUNCTION
HORIZCONC
(
Caver
,
r
,
rL
,
kdiff
,
kexch
,
ksink
,
hML
)
result
(
Cr
)
use
NUMERICS
,
only
:
BESSI
!Bessel function
implicit
none
!Input/output variables
real
(
kind
=
ireals
),
intent
(
in
)
::
Caver
!> horizontally averaged concentration in the ML
real
(
kind
=
ireals
),
intent
(
in
)
::
r
!> distance form lake center, m
real
(
kind
=
ireals
),
intent
(
in
)
::
rL
!> lake radius, m
real
(
kind
=
ireals
),
intent
(
in
)
::
kdiff
!> effective diffusion coefficient in horizontal, m**2/s
real
(
kind
=
ireals
),
intent
(
in
)
::
kexch
!> gas exchange koefficient with the atmosphere (piston velocity), m/s
real
(
kind
=
ireals
),
intent
(
in
)
::
ksink
!> the rate of concentration sink in the ML, s**(-1)
real
(
kind
=
ireals
),
intent
(
in
)
::
hML
!> mixed-layer (ML) depth
real
(
kind
=
ireals
)
::
Cr
!> concentration at the distance r from lake center
!Local variables
real
(
kind
=
ireals
)
::
x
x
=
sqrt
((
kexch
/
hML
+
ksink
)/
kdiff
)
Cr
=
0.5
*
Caver
*
rL
*
BESSI
(
0_4
,
x
*
r
)/
BESSI
(
1_4
,
x
*
rL
)
END
FUNCTION
HORIZCONC
END
MODULE
PHYS_FUNC
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