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LUBRIF.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LUBRIF
* Problem :
* *********
* The elastodynamic lubrification problem by Kostreva.
* NB. This version has an error.
* See LUBRIFC for the correct formulation.
* Source:
* M.M. Kostreva,
* "Elasto-hydrodynamic lubrification: a non-linear
* complementarity problem",
* International Journal for Numerical Methods in Fluids,
* 4: 377-397, 1984.
* This problem is problem #5 in More's test set.
* SIF input: Ph. Toint, June 1990.
* classification QOR2-MN-V-V
* Number of discretized points per unit length
*IE NN 10 $-PARAMETER n = 151 original value
*IE NN 50 $-PARAMETER n = 751
IE NN 250 $-PARAMETER n = 3751
* Dimensionless pressure viscosity coefficient
RE ALPHA 1.838
* Dimensionless model parameter
RE LAMBDA 1.642
* Inlet point (do not change this)
RE XA -3.0
* Point far downstream (do not change this)
RE XF 2.0
* Number of discretized points -1
* ( for an interval of length XF - XA = 5.0 = 2.0 - (-3.0) )
IM N NN 5
* Constants
IE 0 0
IE 1 1
IE 2 2
IE 3 3
IE 4 4
RE PI 3.1415926535
* Computed parameters
IM 2N N 2
IA 2N-2 2N -2
IA 2N-1 2N -1
IA 2N+2 2N 2
RM -XA XA -1.0
R+ LEN XF -XA
RD 1/PI PI 1.0
RM 1/2PI 1/PI 0.5
RI RN N
RD 1/N RN 1.0
R* DX LEN 1/N
RD 1/DX DX 1.0
R* L/DX LAMBDA 1/DX
RM -L/DX L/DX -1.0
R* 1/DX2 1/DX 1/DX
RM -1/DX2 1/DX2 -1.0
R* DX/PI DX 1/PI
RM 2DX/PI DX/PI 2.0
RM DX/2 DX 0.5
VARIABLES
K
* Pressures
DO I 0 2N
DI I 2
X P(I)
ND
* Film thickness
DO J 1 2N-1
DI J 2
X H(J)
ND
* Discretized Reynolds operator values
DO I 2 2N-2
DI I 2
X R(I)
ND
GROUPS
* R(0) = 0
DO I 2 2N-2
DI I 2
ZE R(0) P(I) 2DX/PI
ND
ZE R(0) P(2N) DX/PI
* Complementarity equations: SUM_i p(i) * R(i) = 0
XN COMPL
* Definition of the R(i) via the Reynolds equation
DO I 2 2N-2
DI I 2
IA I-1 I -1
IA I+1 I 1
ZE DR(I) H(I+1) L/DX
ZE DR(I) H(I-1) -L/DX
XE DR(I) R(I) -1.0
ND
* Definition of the h(j)
* (uses integration by parts to avoid weak kernel singularity)
DO J 1 2N-1
DI J 2
IM -J J -1
XE DH(J) K 1.0 H(J) -1.0
DO I 2 2N
AE C(I) 0.0
OD I
RI RI-J -J
R* I-JDX RI-J DX/2
R( ALN ABS I-JDX
R( LN LOG ALN
R* T1 I-JDX LN
R* COEFF T1 1/2PI
A+ C(2) C(2) COEFF
IA I-J -J 2
RI RI-J I-J
R* I-JDX RI-J DX/2
R( ALN ABS I-JDX
R( LN LOG ALN
R* T1 I-JDX LN
R* COEFF T1 1/PI
A+ C(4) C(4) COEFF
DO I 4 2N-2
DI I 2
IA I-2 I -2
IA I+2 I 2
I+ I-J I -J
RI RI-J I-J
R* I-JDX RI-J DX/2
R( ALN ABS I-JDX
R( LN LOG ALN
R* T1 I-JDX LN
R* COEFF T1 1/PI
A+ C(I+2) C(I+2) COEFF
RM -COEFF COEFF -1.0
A+ C(I-2) C(I-2) -COEFF
OD I
I+ I-J 2N -J
RI RI-J I-J
R* I-JDX RI-J DX/2
R( ALN ABS I-JDX
R( LN LOG ALN
R* T1 I-JDX LN
R* COEFF T1 1/2PI
RM -COEFF COEFF -1.0
A+ C(2N-2) C(2N-2) -COEFF
DO I 2 2N-2
DI I 2
ZE DH(J) P(I) C(I)
ND
CONSTANTS
* R(0)
X LUBRIF R(0) 1.0
* Definition of h(j)
DO J 1 2N-1
DI J 2
RI RJ J
R* JDX RJ DX/2
R+ XJ XA JDX
R* XJSQ XJ XJ
RA XJSQ+1 XJSQ 1.0
AM RHS XJSQ+1 -1.0
Z LUBRIF DH(J) RHS
ND
BOUNDS
XR LUBRIF K
DO I 2 2N-2
DI I 2
XU LUBRIF P(I) 3.0
XL LUBRIF P(I) 0.0
ND
DO I 1 2N-1
DI I 2
XR LUBRIF H(I)
ND
XX LUBRIF P(0) 0.0
XX LUBRIF P(2N) 0.0
START POINT
XV LUBRIF 'DEFAULT' 0.0
I+ 2NN NN NN
IM 4NN NN 4
DO I 2 4NN
DI I 2
RI RI I
R* IDX RI DX/2
R+ XI XA IDX
RM LIN XI 0.02
RA PI0 LIN 0.06
Z LUBRIF P(I) PI0
ND
IA 4NN+2 4NN 2
IM 8NN NN 8
DO I 4NN+2 8NN
DI I 2
RI RI I
R* IDX RI DX/2
R+ XI XA IDX
R* XISQ XI XI
RM -XISQ XISQ -1.0
RA 1-XISQ -XISQ 1.0
R( PI0 SQRT 1-XISQ
Z LUBRIF P(I) PI0
ND
IA 8NN+2 8NN 2
DO I 8NN+2 2N
DI I 2
X LUBRIF P(I) 0.0
ND
DO J 1 2N-1
DI J 2
RI RJ J
R* JDX RJ DX/2
R+ XJ XA JDX
R* XJSQ XJ XJ
Z LUBRIF H(J) XJSQ
ND
ELEMENT TYPE
EV REY PA PB
EV REY H
EP REY A
EV 2PR P R
ELEMENT USES
* Elements for the Reynolds equations
DO J 1 2N-1
DI J 2
IA I+ J 1
IA I- J -1
XT ER(J) REY
ZV ER(J) PA P(I-)
ZV ER(J) H P(I+)
ZV ER(J) PB H(J)
ZP ER(J) A ALPHA
ND
* Elements for the complementarity conditions
DO I 2 2N-2
DI I 2
XT EC(I) 2PR
ZV EC(I) P P(I)
ZV EC(I) R R(I)
ND
GROUP USES
* Complementarity
DO I 2 2N-2
DI I 2
XE COMPL EC(I)
ND
* Reynolds equations
DO I 2 2N-2
DI I 2
IA I-1 I -1
IA I+1 I 1
ZE DR(I) ER(I-1) 1/DX2
ZE DR(I) ER(I+1) -1/DX2
ND
OBJECT BOUND
LO LUBRIF 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LUBRIF
TEMPORARIES
R PAMPB
R HCB
R HSQ
R T1
R T2
R EARG
R E
R HA
M EXP
INDIVIDUALS
T 2PR
F P * R
G P R
G R P
H P R 1.0
T REY
A HA - 0.5 * A
A EARG HA * ( PA + PB )
A E EXP( EARG )
A PAMPB PA - PB
A T1 PAMPB * HA + 1.0
A T2 PAMPB * HA - 1.0
A HSQ H * H
A HCB HSQ * H
F PAMPB * HCB * E
G PA T1 * HCB * E
G PB T2 * HCB * E
G H 3.0 * PAMPB * HSQ * E
H PA PA HCB * E * HA * ( T1 + 1.0)
H PA PB HCB * E * HA * ( T1 - 1.0)
H PA H 3.0 * T1 * HSQ * E
H PB PB HCB * E * HA * ( T2 - 1.0)
H PB H 3.0 * T2 * HSQ * E
H H H 6.0 * H * PAMPB * E
ENDATA