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FLOSP2HL.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME FLOSP2HL
* Problem :
* *********
* A two-dimensional base flow problem in an inclined enclosure.
* Heat flux constant at y = +/- 1
* Low Reynold's number
* The flow is considered in a square of length 2, centered on the
* origin and aligned with the x-y axes. The square is divided into
* 4 n ** 2 sub-squares, each of length 1 / n. The differential
* equation is replaced by discrete nonlinear equations at each of
* the grid points.
* The differential equation relates the vorticity, temperature and
* a stream function.
*
* Source:
* J. N. Shadid
* "Experimental and computational study of the stability
* of Natural convection flow in an inclined enclosure",
* Ph. D. Thesis, University of Minnesota, 1989,
* problem SP2 (pp.128-130),
* SIF input: Nick Gould, August 1993.
* classification NQR2-MY-V-V
*IE M 1 $-PARAMETER n=27
*IE M 2 $-PARAMETER n=75
*IE M 5 $-PARAMETER n=363 original value
*IE M 8 $-PARAMETER n=867
*IE M 10 $-PARAMETER n=1323
IE M 15 $-PARAMETER n=2883
* Define the Rayleigh number. NB: This determines the difficulty
* of the problem.
RE RA 1.0D+3 $-PARAMETER Rayleigh number
* Set pi.
RF PI/4 ARCTAN 1.0
RM PI PI/4 4.0
* Define other problem parameters
RE AX 1.0
RM THETA PI 0.5
* Case 2. Constant heat flux at y = +/- 1
RE A1 1.0
RE A2 0.0
RE A3 -1.0
RE B1 1.0
RE B2 0.0
RE B3 -1.0
RE F1 1.0
RE F2 0.0
RE F3 0.0
RE G1 1.0
RE G2 0.0
RE G3 0.0
* Define a few helpful parameters
IA M-1 M -1
IM -M M -1
IM -M+1 M-1 -1
RI 1/H M
RM -1/H 1/H -1.0
RM 2/H 1/H 2.0
RM -2/H 1/H -2.0
RD H 1/H 1.0
R* H2 H H
R* 1/H2 1/H 1/H
RM -2/H2 1/H2 -2.0
RM 1/2H 1/H 0.5
RM -1/2H 1/H -0.5
R* AXX AX AX
R( SINTHETA SIN THETA
R( COSTHETA COS THETA
R* PI1 AX RA
R* PI1 PI1 COSTHETA
RM PI1 PI1 -0.5
RM -PI1 PI1 -1.0
R* PI2 AXX RA
R* PI2 PI2 SINTHETA
RM PI2 PI2 0.5
RM -PI2 PI2 -1.0
RM 2A1 A1 2.0
RM 2B1 B1 2.0
RM 2F1 F1 2.0
RM 2G1 G1 2.0
R/ 2F1/AX 2F1 AX
R/ 2G1/AX 2G1 AX
RM AX/2 AX 0.5
RM AXX/2 AXX 0.5
RM AXX/4 AXX 0.25
RM 2AX AX 2.0
RM 2AXX AXX 2.0
RD 2/AX AX 2.0
R/ 2/AXH 2/H AX
RM -2/AXH 2/AXH -1.0
R* PI1/2H PI1 1/2H
R* -PI1/2H PI1 -1/2H
R* PI2/2H PI2 1/2H
R* -PI2/2H PI2 -1/2H
R* 2A1/H 2A1 1/H
R* -2A1/H 2A1 -1/H
R* 2B1/H 2B1 1/H
R* -2B1/H 2B1 -1/H
R* 2F1/AXH 2F1/AX 1/H
R* -2F1/AXH 2F1/AX -1/H
R* 2G1/AXH 2G1/AX 1/H
R* -2G1/AXH 2G1/AX -1/H
R* AX/H2 AX 1/H2
RM -AX/H2 AX/H2 -1.0
RM AX/4H2 AX/H2 0.25
RM -AX/4H2 AX/H2 -0.25
R* AXX/H2 AXX 1/H2
RM -2AXX/H2 AXX/H2 -2.0
IE 1 1
IE 2 2
VARIABLES
* Define a vorticity(OM), temperature(PH) and stream function(PS)
* variable per discretized point in the square
DO J -M M
DO I -M M
X OM(I,J)
X PH(I,J)
X PS(I,J)
ND
GROUPS
* Define three equations per interior node
DO J -M+1 M-1
IA J+ J 1
IA J- J -1
DO I -M+1 M-1
IA I+ I 1
IA I- I -1
* The stream function equation(S) - linear (6.57a in the thesis).
ZE S(I,J) OM(I,J) -2/H2
ZE S(I,J) OM(I+,J) 1/H2
ZE S(I,J) OM(I-,J) 1/H2
ZE S(I,J) OM(I,J) -2AXX/H2
ZE S(I,J) OM(I,J+) AXX/H2
ZE S(I,J) OM(I,J-) AXX/H2
ZE S(I,J) PH(I+,J) -PI1/2H
ZE S(I,J) PH(I-,J) PI1/2H
ZE S(I,J) PH(I,J+) -PI2/2H
ZE S(I,J) PH(I,J-) PI2/2H
* The vorticity equation(V) - linear (6.57b in the thesis).
ZE V(I,J) PS(I,J) -2/H2
ZE V(I,J) PS(I+,J) 1/H2
ZE V(I,J) PS(I-,J) 1/H2
ZE V(I,J) PS(I,J) -2AXX/H2
ZE V(I,J) PS(I,J+) AXX/H2
ZE V(I,J) PS(I,J-) AXX/H2
ZE V(I,J) OM(I,J) AXX/4
* The thermal energy equation(E) - quadratic (6.57c in the thesis).
ZE E(I,J) PH(I,J) -2/H2
ZE E(I,J) PH(I+,J) 1/H2
ZE E(I,J) PH(I-,J) 1/H2
ZE E(I,J) PH(I,J) -2AXX/H2
ZE E(I,J) PH(I,J+) AXX/H2
ZE E(I,J) PH(I,J-) AXX/H2
ND
* Boundary conditions on the temperature.
DO K -M M
ZE T(K,M) PH(K,M) 2A1/H
ZE T(K,M) PH(K,M-1) -2A1/H
ZE T(K,M) PH(K,M) A2
ZE T(K,-M) PH(K,-M+1) 2B1/H
ZE T(K,-M) PH(K,-M) -2B1/H
ZE T(K,-M) PH(K,-M) B2
ZE T(M,K) PH(M,K) 2F1/AXH
ZE T(M,K) PH(M-1,K) -2F1/AXH
ZE T(M,K) PH(M,K) F2
ZE T(-M,K) PH(-M+1,K) 2G1/AXH
ZE T(-M,K) PH(-M,K) -2G1/AXH
ZE T(-M,K) PH(-M,K) G2
* Boundary conditions on the vorticity. NB: Steady state assumed
ZE V(K,M) PS(K,M) -2/H
ZE V(K,M) PS(K,M-1) 2/H
ZE V(K,-M) PS(K,-M+1) 2/H
ZE V(K,-M) PS(K,-M) -2/H
ZE V(M,K) PS(M,K) -2/AXH
ZE V(M,K) PS(M-1,K) 2/AXH
ZE V(-M,K) PS(-M+1,K) 2/AXH
ZE V(-M,K) PS(-M,K) -2/AXH
ND
CONSTANTS
DO K -M M
Z FLOSP2HL T(K,M) A3
Z FLOSP2HL T(K,-M) B3
Z FLOSP2HL T(M,K) F3
Z FLOSP2HL T(-M,K) G3
ND
BOUNDS
FR FLOSP2HL 'DEFAULT'
* Boundary conditions on the stream functions.
DO K -M M
XX FLOSP2HL PS(K,-M) 1.0
XX FLOSP2HL PS(-M,K) 1.0
XX FLOSP2HL PS(K,M) 1.0
XX FLOSP2HL PS(M,K) 1.0
ND
ELEMENT TYPE
EV PROD PSIM PSIP
EV PROD PHIM PHIP
IV PROD PSIDIF PHIDIF
ELEMENT USES
DO J -M+1 M-1
IA J+ J 1
IA J- J -1
DO I -M+1 M-1
IA I+ I 1
IA I- I -1
XT E(I,J) PROD
ZV E(I,J) PSIP PS(I,J+)
ZV E(I,J) PSIM PS(I,J-)
ZV E(I,J) PHIP PH(I+,J)
ZV E(I,J) PHIM PH(I-,J)
XT F(I,J) PROD
ZV F(I,J) PSIP PS(I+,J)
ZV F(I,J) PSIM PS(I-,J)
ZV F(I,J) PHIP PH(I,J+)
ZV F(I,J) PHIM PH(I,J-)
ND
GROUP USES
DO J -M+1 M-1
DO I -M+1 M-1
ZE E(I,J) E(I,J) -AX/4H2
ZE E(I,J) F(I,J) AX/4H2
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS FLOSP2HL
INDIVIDUALS
T PROD
R PSIDIF PSIP 1.0 PSIM -1.0
R PHIDIF PHIP 1.0 PHIM -1.0
F PSIDIF * PHIDIF
G PSIDIF PHIDIF
G PHIDIF PSIDIF
H PSIDIF PHIDIF 1.0
ENDATA