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DRCAV1LQ.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DRCAV1LQ
* Problem :
* *********
* This system of nonlinear equations models the stream function
* corresponding to an incompressible fluid flow in a driven cavity
* (after elimination of the vorticity). The system is solved in the
* least-squares sense. The nonlinear system formulation is problem DRCAVTY1.
* The problem is nonconvex.
* It differs from the problems DRCAV2LQ and DRCAV3LQ by the value
* chosen for the Reynolds number.
* Source:
* P.N. Brown and Y. Saad,
* "Hybrid Krylov Methods for Nonlinear Systems of Equations",
* SIAM J. Sci. Stat. Comput. 11, pp. 450-481, 1990.
* The boundary conditions have been set according to
* I.E. Kaporin and O. Axelsson,
* "On a class of nonlinear equation solvers based on the residual norm
* reduction over a sequence of affine subspaces",
* SIAM J, Sci. Comput. 16(1), 1995.
* SIF input: Ph. Toint, Jan 1995.
* classification OXR2-MY-V-V
* Discretization mesh: n = (M+3)**2 - fixed variables
*IE M 10 $-PARAMETER n = 100 original value
*IE M 31 $-PARAMETER n = 961
IE M 63 $-PARAMETER n = 3969
*IE M 100 $-PARAMETER n = 10000
IA M+2 M 2
RI RM+2 M+2
RD H RM+2 1.0
* Considered nondimensional Reynolds number
RE RE 500.0 $-PARAMETER Reynolds number
* Useful constants
IE -1 -1
IE 0 0
IE 1 1
IA M+1 M 1
RM H/2 H 0.5
RM -H/2 H/2 -1.0
RM RE/4 RE 0.25
RM -RE/4 RE/4 -1.0
VARIABLES
DO I -1 M+2
DO J -1 M+2
X Y(I,J)
OD J
OD I
GROUPS
DO I 1 M
IA I-2 I -2
IA I-1 I -1
IA I+1 I 1
IA I+2 I 2
DO J 1 M
IA J-2 J -2
IA J-1 J -1
IA J+1 J 1
IA J+2 J 2
XN E(I,J) Y(I,J) 20.0
XN E(I,J) Y(I-1,J) -8.0 Y(I+1,J) -8.0
XN E(I,J) Y(I,J-1) -8.0 Y(I,J+1) -8.0
XN E(I,J) Y(I-1,J+1) 2.0 Y(I+1,J-1) 2.0
XN E(I,J) Y(I-1,J-1) 2.0 Y(I+1,J+1) 2.0
XN E(I,J) Y(I-2,J) 1.0 Y(I+2,J) 1.0
XN E(I,J) Y(I,J-2) 1.0 Y(I,J+2) 1.0
OD J
OD I
BOUNDS
FR DRCAV1LQ 'DEFAULT'
* Bottom boundary
DO J -1 M+2
XX DRCAV1LQ Y(-1,J) 0.0
XX DRCAV1LQ Y(0,J) 0.0
OD J
* Left boundary
DO I 1 M
XX DRCAV1LQ Y(I,-1) 0.0
XX DRCAV1LQ Y(I,0) 0.0
OD I
* Right boundary
DO I 1 M
XX DRCAV1LQ Y(I,M+1) 0.0
XX DRCAV1LQ Y(I,M+2) 0.0
OD I
* Top boundary
DO J -1 M+2
ZX DRCAV1LQ Y(M+1,J) -H/2
ZX DRCAV1LQ Y(M+2,J) H/2
OD J
ELEMENT TYPE
EV IPR A1 A2
EV IPR B1 B2
EV IPR B3 B4
EV IPR B5 B6
EV IPR B7 B8
IV IPR AA BB
ELEMENT USES
XT 'DEFAULT' IPR
DO I 1 M
IA I-2 I -2
IA I-1 I -1
IA I+1 I 1
IA I+2 I 2
DO J 1 M
IA J-2 J -2
IA J-1 J -1
IA J+1 J 1
IA J+2 J 2
ZV X(I,J) A1 Y(I,J+1)
ZV X(I,J) A2 Y(I,J-1)
ZV X(I,J) B1 Y(I-2,J)
ZV X(I,J) B2 Y(I-1,J-1)
ZV X(I,J) B3 Y(I-1,J+1)
ZV X(I,J) B4 Y(I-1,J)
ZV X(I,J) B5 Y(I+1,J)
ZV X(I,J) B6 Y(I+1,J-1)
ZV X(I,J) B7 Y(I+1,J+1)
ZV X(I,J) B8 Y(I+2,J)
ZV Z(I,J) A1 Y(I+1,J)
ZV Z(I,J) A2 Y(I-1,J)
ZV Z(I,J) B1 Y(I,J-2)
ZV Z(I,J) B2 Y(I-1,J-1)
ZV Z(I,J) B3 Y(I+1,J-1)
ZV Z(I,J) B4 Y(I,J-1)
ZV Z(I,J) B5 Y(I,J+1)
ZV Z(I,J) B6 Y(I-1,J+1)
ZV Z(I,J) B7 Y(I+1,J+1)
ZV Z(I,J) B8 Y(I,J+2)
OD J
OD I
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 1 M
DO J 1 M
ZE E(I,J) X(I,J) RE/4
ZE E(I,J) Z(I,J) -RE/4
OD J
OD I
OBJECT BOUND
LO DRCAV1LQ 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DRCAV1LQ
INDIVIDUALS
T IPR
R AA A1 1.0 A2 -1.0
R BB B1 1.0 B2 1.0
R BB B3 1.0 B4 -4.0
R BB B5 4.0 B6 -1.0
R BB B7 -1.0 B8 -1.0
F AA * BB
G AA BB
G BB AA
H AA BB 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS DRCAV1LQ
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA