```
TALK=T;RUN(1,1)
PHOTON USE
AUTOPLOT
file
phi 5

cl
msg U1 DIFFUSION OF A FREE VORTEX
msg Velocity (U1) profile
msg Green line --- PHOENICS solution
msg crosses ---   analytical solution
da 1 u1;da 1 uana
col9 1;blb4 2

msg press  to end
pause
end
END_USE
DISPLAY

The case considered is 1d radial diffusion of a free vortex with
fixed-value boundary conditions at the axis and outer boundary.
The predictions show a 20% discrepancy with the analytical
solution in the core of the vortex. However, the view is taken
that a pure free vortex will never be encountered in practice,
but rather a combined vortex will be observed  in which a forced
vortex is present in the core and a free vortex outside this
region. For this case PHOENICS procures exact agreement with the
analytical solution as demonstrated by case 830 below.

ENDDIS
************************************************************
Group 1. Run Title and Number
************************************************************
************************************************************

TEXT(1D U1 Diffusion Of A Free Vortex        )

************************************************************
************************************************************

IRUNN = 1 ;LIBREF = 14
************************************************************
Group 2. Time dependence
************************************************************
Group 3. X-Direction Grid Spacing
CARTES = F
NX = 1
XULAST =1.0E-03
XFRAC(1)=1.
************************************************************
Group 4. Y-Direction Grid Spacing
NY = 20
YVLAST =1.
YFRAC(1)=0.05 ;YFRAC(2)=0.1
YFRAC(3)=0.15 ;YFRAC(4)=0.2
YFRAC(5)=0.25 ;YFRAC(6)=0.3
YFRAC(7)=0.35 ;YFRAC(8)=0.4
YFRAC(9)=0.45 ;YFRAC(10)=0.5
YFRAC(11)=0.55 ;YFRAC(12)=0.6
YFRAC(13)=0.65 ;YFRAC(14)=0.7
YFRAC(15)=0.75 ;YFRAC(16)=0.8
YFRAC(17)=0.85 ;YFRAC(18)=0.9
YFRAC(19)=0.95 ;YFRAC(20)=1.
************************************************************
Group 5. Z-Direction Grid Spacing
PARAB = F
NZ = 1
ZWLAST =1.
ZFRAC(1)=1.
************************************************************
Group 6. Body-Fitted Coordinates
************************************************************
Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS = T
NAME(3)=U1 ;NAME(150)=UANA
* Y in SOLUTN argument list denotes:
* 1-stored 2-solved 3-whole-field
* 4-point-by-point 5-explicit 6-harmonic averaging
SOLUTN(U1,Y,Y,N,N,N,Y)
SOLUTN(UANA,Y,N,N,N,N,Y)
************************************************************
Group 8. Terms & Devices
* Y in TERMS argument list denotes:
* 1-built-in source 2-convection 3-diffusion 4-transient
* 5-first phase variable 6-interphase transport
TERMS(U1,Y,N,Y,Y,Y,Y)
DIFCUT =0.5 ;ZDIFAC =1.
GALA = F ;ADDDIF = F
ISOLX = -1 ;ISOLY = -1 ;ISOLZ = -1
************************************************************
Group 9. Properties used if PRPS is not
stored, and where PRPS = -1.0 if it is!
RHO1 =1. ;TMP1 =0.
EL1 =0.
TSURR =0. ;TEMP0 =0.
PRESS0 =0.
DVO1DT =0. ;DRH1DP =0.
EMISS =0. ;SCATT =0.
ENUL =1. ;ENUT =0.
PRNDTL(U1)=1.
PRT(U1)=1.
CP1 =1. ;CP2 =1.
************************************************************
Group 10.Inter-Phase Transfer Processes
************************************************************
Group 11.Initial field variables (PHIs)
FIINIT(U1)=0.025 ;FIINIT(UANA)=1.0E-10

PATCH(IN1 ,INIVAL, 1, 1, 1, 1, 1, 1, 1, 1)
INIT(IN1 ,UANA,0. ,1. )

PATCH(IN2 ,INIVAL, 1, 1, 2, 2, 1, 1, 1, 1)
INIT(IN2 ,UANA,0. ,0.333333 )

PATCH(IN3 ,INIVAL, 1, 1, 3, 3, 1, 1, 1, 1)
INIT(IN3 ,UANA,0. ,0.2 )

PATCH(IN4 ,INIVAL, 1, 1, 4, 4, 1, 1, 1, 1)
INIT(IN4 ,UANA,0. ,0.142857 )

PATCH(IN5 ,INIVAL, 1, 1, 5, 5, 1, 1, 1, 1)
INIT(IN5 ,UANA,0. ,0.111111 )

PATCH(IN6 ,INIVAL, 1, 1, 6, 6, 1, 1, 1, 1)
INIT(IN6 ,UANA,0. ,0.090909 )

PATCH(IN7 ,INIVAL, 1, 1, 7, 7, 1, 1, 1, 1)
INIT(IN7 ,UANA,0. ,0.076923 )

PATCH(IN8 ,INIVAL, 1, 1, 8, 8, 1, 1, 1, 1)
INIT(IN8 ,UANA,0. ,0.066667 )

PATCH(IN9 ,INIVAL, 1, 1, 9, 9, 1, 1, 1, 1)
INIT(IN9 ,UANA,0. ,0.058824 )

PATCH(IN10 ,INIVAL, 1, 1, 10, 10, 1, 1, 1, 1)
INIT(IN10 ,UANA,0. ,0.052632 )

PATCH(IN11 ,INIVAL, 1, 1, 11, 11, 1, 1, 1, 1)
INIT(IN11 ,UANA,0. ,0.047619 )

PATCH(IN12 ,INIVAL, 1, 1, 12, 12, 1, 1, 1, 1)
INIT(IN12 ,UANA,0. ,0.043478 )

PATCH(IN13 ,INIVAL, 1, 1, 13, 13, 1, 1, 1, 1)
INIT(IN13 ,UANA,0. ,0.04 )

PATCH(IN14 ,INIVAL, 1, 1, 14, 14, 1, 1, 1, 1)
INIT(IN14 ,UANA,0. ,0.037037 )

PATCH(IN15 ,INIVAL, 1, 1, 15, 15, 1, 1, 1, 1)
INIT(IN15 ,UANA,0. ,0.034483 )

PATCH(IN16 ,INIVAL, 1, 1, 16, 16, 1, 1, 1, 1)
INIT(IN16 ,UANA,0. ,0.032258 )

PATCH(IN17 ,INIVAL, 1, 1, 17, 17, 1, 1, 1, 1)
INIT(IN17 ,UANA,0. ,0.030303 )

PATCH(IN18 ,INIVAL, 1, 1, 18, 18, 1, 1, 1, 1)
INIT(IN18 ,UANA,0. ,0.028571 )

PATCH(IN19 ,INIVAL, 1, 1, 19, 19, 1, 1, 1, 1)
INIT(IN19 ,UANA,0. ,0.027027 )

PATCH(IN20 ,INIVAL, 1, 1, 20, 20, 1, 1, 1, 1)
INIT(IN20 ,UANA,0. ,0.025641 )
FSWEEP = 1
IURINI = 1
NAMFI =CHAM
************************************************************
Group 12. Patchwise adjustment of terms
Patches for this group are printed with those
for Group 13.
Their names begin either with GP12 or &
************************************************************
Group 13. Boundary & Special Sources

PATCH(INNER ,CELL , 1, 1, 1, 1, 1, 1, 1, 1)
COVAL(INNER ,U1 , FIXVAL ,0.025 )

PATCH(OUTER ,NORTH , 1, 1, 20, 20, 1, 1, 1, 1)
COVAL(OUTER ,U1 , FIXVAL ,0.025 )
IURVAL = 1
XCYCLE = F
EGWF = T
WALLCO = GRND2
************************************************************
Group 14. Downstream Pressure For PARAB
************************************************************
Group 15. Terminate Sweeps
LSWEEP = 4 ;ISWC1 = 1
LITHYD = 1 ;LITFLX = 1 ;LITC = 1 ;ITHC1 = 1
SELREF = T
RESFAC =1.0E-04
************************************************************
Group 16. Terminate Iterations
LITER(U1)=10
ENDIT(U1)=1.0E-03
************************************************************
Group 17. Relaxation
RELAX(U1,FALSDT,1.)
RELAX(UANA,LINRLX,1.)
OVRRLX =0.
EXPERT = F ;NNORSL = F
************************************************************
Group 18. Limits
VARMAX(U1)=1.0E+06 ;VARMIN(U1)=-1.0E+06
VARMAX(UANA)=1.0E+10 ;VARMIN(UANA)=-1.0E+10
************************************************************
Group 19. Data transmitted to GROUND
PARSOL = F
ISG62 = 1
************************************************************
Group 20. Preliminary Printout
************************************************************
Group 21. Print-out of Variables
INIFLD = F ;SUBWGR = F
* Y in OUTPUT argument list denotes:
* 1-field 2-correction-eq. monitor 3-selective dumping
* 4-whole-field residual 5-spot-value table 6-residual table
OUTPUT(U1,Y,N,Y,Y,Y,Y)
OUTPUT(UANA,Y,N,Y,N,N,N)
************************************************************
Group 22. Monitor Print-Out
IXMON = 1 ;IYMON = 6 ;IZMON = 1
NPRMON = 100000 ;NPRMNT = 1 ;TSTSWP = 1
UWATCH = T ;USTEER = T
HIGHLO = F
************************************************************
Group 23.Field Print-Out & Plot Control
NPRINT = 100000 ;NUMCLS = 5
NYPRIN = 1 ;IYPRF = 1 ;IYPRL = 10000
IPLTF = 1 ;IPLTL = -1 ;NPLT = -1
ISWPRF = 1 ;ISWPRL = 100000
ITABL = 2 ;IPROF = 1
ABSIZ =0.5 ;ORSIZ =0.4
NTZPRF = 1 ;NCOLPF = 50
ICHR = 2 ;NCOLCO = 45 ;NROWCO = 20

PATCH(LONGPLOT,PROFIL, 1, 1, 1, 20, 1, 1, 1, 1)
PLOT(LONGPLOT,U1 ,0. ,0. )
************************************************************
Group 24. Dumps For Restarts
SAVE = T ;NOWIPE = F
NSAVE =CHAM
STOP
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