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DRCAVTY1.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DRCAVTY1
* 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 problem is nonconvex.
* It differs from the problems DRCAVTY2 and DRCAVTY3 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 NQR2-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
* Considered nondimensional Reynolds number
RE RE 500.0 $-PARAMETER Reynolds number
IA M+2 M 2
RI RM+2 M+2
RD H RM+2 1.0
* 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
XE E(I,J) Y(I,J) 20.0
XE E(I,J) Y(I-1,J) -8.0 Y(I+1,J) -8.0
XE E(I,J) Y(I,J-1) -8.0 Y(I,J+1) -8.0
XE E(I,J) Y(I-1,J+1) 2.0 Y(I+1,J-1) 2.0
XE E(I,J) Y(I-1,J-1) 2.0 Y(I+1,J+1) 2.0
XE E(I,J) Y(I-2,J) 1.0 Y(I+2,J) 1.0
XE E(I,J) Y(I,J-2) 1.0 Y(I,J+2) 1.0
OD J
OD I
BOUNDS
FR DRCAVTY1 'DEFAULT'
* Bottom boundary
DO J -1 M+2
XX DRCAVTY1 Y(-1,J) 0.0
XX DRCAVTY1 Y(0,J) 0.0
OD J
* Left boundary
DO I 1 M
XX DRCAVTY1 Y(I,-1) 0.0
XX DRCAVTY1 Y(I,0) 0.0
OD I
* Right boundary
DO I 1 M
XX DRCAVTY1 Y(I,M+1) 0.0
XX DRCAVTY1 Y(I,M+2) 0.0
OD I
* Top boundary
DO J -1 M+2
ZX DRCAVTY1 Y(M+1,J) -H/2
ZX DRCAVTY1 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 USES
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 DRCAVTY1 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DRCAVTY1
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