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CHEMRCTA.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CHEMRCTA
* Problem :
* *********
* The tubular chemical reactor model problem by Poore, using a
* finite difference approximation to the steady state solutions.
* Source: Problem 8, eqs (8.6)--(8.9) in
* J.J. More',
* "A collection of nonlinear model problems"
* Proceedings of the AMS-SIAM Summer seminar on the Computational
* Solution of Nonlinear Systems of Equations, Colorado, 1988.
* Argonne National Laboratory MCS-P60-0289, 1989.
* SIF input: Ph. Toint, Dec 1989.
* minor correction by Ph. Shott, Jan 1995 and F Ruediger, Mar 1997.
* classification NOR2-MN-V-V
* The axial coordinate interval is [0,1]
* Number of discretized point for the interval [0,1].
* The number of variables is 2N.
*IE N 5 $-PARAMETER n = 10
*IE N 25 $-PARAMETER n = 50
*IE N 50 $-PARAMETER n = 100
*IE N 250 $-PARAMETER n = 500 original value
*IE N 500 $-PARAMETER n = 1000
IE N 2500 $-PARAMETER n = 5000
* Problem's constants
* Mass Peclet number
RE PEM 1.0 $-PARAMETER
* Heat Peclet number
RE PEH 5.0 $-PARAMETER
* Damkholer number
RE D 0.135 $-PARAMETER
* Heat of the reaction
RE B 0.5 $-PARAMETER
* Heat transfer coefficient
RE BETA 2.0 $-PARAMETER
* Activation energy
RE GAMMA 25.0 $-PARAMETER
* Constants
IE 1 1
IE 2 2
RE 1.0 1.0
* Discretization definition
IA N-1 N -1
RI 1/H N-1
RM -1/H 1/H -1.0
R/ H 1.0 1/H
R* 1/H2 1/H 1/H
* Constant coefficients in the equations
* 1) concentration equations
RM -D D -1.0
R/ 1/PEM 1.0 PEM
R* 1/H2PEM 1/PEM 1/H2
RM -1/H2PM 1/H2PEM -1.0
R* HPEM PEM H
RM -HPEM HPEM -1.0
R+ -2/H2PM -1/H2PM -1/H2PM
RM CU1 -HPEM 1.0
R+ CUI-1 1/H2PEM 1/H
R+ CUI -2/H2PM -1/H
* 2) temperature equations
R* BD B D
RM -BETA BETA -1.0
R/ 1/PEH 1.0 PEH
R* 1/H2PEH 1/PEH 1/H2
RM -1/H2PH 1/H2PEH -1.0
R* HPEH PEH H
RM -HPEH HPEH -1.0
R+ -2/H2PH -1/H2PH -1/H2PH
RM CT1 -HPEH 1.0
R+ CTI-1 1/H2PEH 1/H
R+ CTI -2/H2PH -1/H
R+ CTI CTI -BETA
VARIABLES
* Temperature at the discretized points.
DO I 1 N
X T(I)
ND
* Concentration at the discretized points.
DO I 1 N
X U(I)
ND
GROUPS
* First equations in s = 0 (i=1)
* 1) concentration
XE GU(1) U(1) -1.0
ZE GU(1) U(2) CU1
* 2) temperature
XE GT(1) T(1) -1.0
ZE GT(1) T(2) CT1
* Middle equations (1<i<n)
DO I 2 N-1
IA I-1 I -1
IA I+1 I 1
* 1) concentration
ZE GU(I) U(I-1) CUI-1
ZE GU(I) U(I) CUI
ZE GU(I) U(I+1) 1/H2PEM
* 2) temperature
ZE GT(I) T(I) BETA
ZE GT(I) T(I-1) CTI-1
ZE GT(I) T(I) CTI
ZE GT(I) T(I+1) 1/H2PEH
ND
* Last equations in s = 1 (i=n)
* 1) concentration
XE GU(N) U(N-1) -1.0
XE GU(N) U(N) 1.0
* 2) temperature
XE GT(N) T(N-1) -1.0
XE GT(N) T(N) 1.0
CONSTANTS
Z CHEMRCTA GU(1) -HPEM
Z CHEMRCTA GT(1) -HPEH
BOUNDS
* temperature and concentration are nonnegative
DO I 1 N
XL CHEMRCTA T(I) 0.0000001
ND
START POINT
XV CHEMRCTA 'DEFAULT' 1.0
ELEMENT TYPE
* Weighted reaction rate
EV REAC U T
EP REAC G
ELEMENT USES
XT 'DEFAULT' REAC
DO I 2 N-1
ZV EU(I) U U(I)
ZV EU(I) T T(I)
ZP EU(I) G GAMMA
ZV ET(I) U U(I)
ZV ET(I) T T(I)
ZP ET(I) G GAMMA
ND
GROUP USES
DO I 2 N-1
ZE GU(I) EU(I) -D
ZE GT(I) ET(I) BD
ND
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CHEMRCTA
TEMPORARIES
R DADT
R D2ADT2
R EX
R UEX
M EXP
INDIVIDUALS
* Weighted reaction rate (Arrhenius cinetics)
T REAC
A DADT G / ( T * T )
A D2ADT2 - 2.0 * DADT / T
A EX EXP( G - G / T )
A UEX EX * U
F UEX
G U EX
G T UEX * DADT
H U T EX * DADT
H T T UEX * ( DADT * DADT + D2ADT2 )
ENDATA