TALK=T;RUN(1,1)
   DISPLAY
     This case describes how the 'moving grid' method (see MOFOR
     entry in Encyclopedia, POLIS) is applied to simulation
     of a sphere falling through air. The 'moving grid' method is
     implemented by In-Form formulae written in the Q1 file.

     A sphere falls through air experiences a force in direction
     opposite to its motion. Terminal velocity is achieved when
     the drag force is equal in magnitude but opposite in direction
     to the gravity force propelling the sphere.

     In this case, the quadratic drag equation is used to calculate
     the drag force as follows.
        Fd = - 0.5 * rho * U**2.0 * A * Cd
     where Fd is the force of drag
           rho is the density of air
           U is the speed of the sphere
           A is the area of the projection of the sphere on a plane
             perpendicular to the direction of motion.
           Cd is the drag coefficient

     The velocity as a function of time for the sphere can be deriv$
ed
     as follows:

          U(t)= A1 * (EXP(A2*t)-1)/(EXP(A2*t)+1)

     where A1 = (2*M*G/rho*A*Cd)**0.5)
           A2 = ((2*rho*A*Cd*G)/M)**0.5

           where G is the gravity,9.81
                 M is the mass of the sphere

     The following terminal velcoty is asymptotically approached:

          Utm = (2*M*G/rho*A*Cd)**0.5

     The accelaration is given by the derivative of the velocity
     function with respect to time,

          a = 4*A1**2.0*A3*EXP(A2*t)/(EXP(A2*t)+1)**2.0

          where A3 is 0.5*rho*A*Cd/M

     The fluid used is air; the radius of the sphere is 1.0 and
     the drag coefficient, Cd used is 1.0

     This file contains a marco of commands which cause the
     Viewer when the Macro button is pressed to display the
     animation automatically. Note that the probe value of the
     last contour indicates the terminal velocity.

   ENDDIS
   VRV USE
   DOMAIN ON
  * Setting object visibility and painting status
   OBJECT SHOW TYPE BLOCKAGE
   OBJECT PAINT TYPE BLOCKAGE OFF
   OBJECT WIREFRAME TYPE BLOCKAGE OFF
   OBJECT SHOW TYPE OUTLET
   OBJECT PAINT TYPE OUTLET OFF
   OBJECT WIREFRAME TYPE OUTLET OFF
   VARIABLE  Pressure; CON ON
   VECTOR ON
   ANIMATE 1 20 1
   VARIABLE Velocity;vector on
   PAUSE
   ENDUSE
 ************************************************************
  Group 1. Run Title and Number
 ************************************************************
 ************************************************************
 
 TEXT(Falling sphere with air resistance      )
 
 ************************************************************
 ************************************************************
 
 IRUNN = 1 ;LIBREF = 0
 ************************************************************
  Group 2. Time dependence
 STEADY = F
    * Set overall time and no. of steps
 TFIRST =0. ;TLAST =4.
 FSTEP = 1 ;LSTEP = 80
 TFRAC(1)=0.0125 ;TFRAC(2)=0.025
 TFRAC(3)=0.0375 ;TFRAC(4)=0.05
 TFRAC(5)=0.0625 ;TFRAC(6)=0.075
 TFRAC(7)=0.0875 ;TFRAC(8)=0.1
 TFRAC(9)=0.1125 ;TFRAC(10)=0.125
 TFRAC(11)=0.1375 ;TFRAC(12)=0.15
 TFRAC(13)=0.1625 ;TFRAC(14)=0.175
 TFRAC(15)=0.1875 ;TFRAC(16)=0.2
 TFRAC(17)=0.2125 ;TFRAC(18)=0.225
 TFRAC(19)=0.2375 ;TFRAC(20)=0.25
 TFRAC(21)=0.2625 ;TFRAC(22)=0.275
 TFRAC(23)=0.2875 ;TFRAC(24)=0.3
 TFRAC(25)=0.3125 ;TFRAC(26)=0.325
 TFRAC(27)=0.3375 ;TFRAC(28)=0.35
 TFRAC(29)=0.3625 ;TFRAC(30)=0.375
 TFRAC(31)=0.3875 ;TFRAC(32)=0.4
 TFRAC(33)=0.4125 ;TFRAC(34)=0.425
 TFRAC(35)=0.4375 ;TFRAC(36)=0.45
 TFRAC(37)=0.4625 ;TFRAC(38)=0.475
 TFRAC(39)=0.4875 ;TFRAC(40)=0.5
 TFRAC(41)=0.5125 ;TFRAC(42)=0.525
 TFRAC(43)=0.5375 ;TFRAC(44)=0.55
 TFRAC(45)=0.5625 ;TFRAC(46)=0.575
 TFRAC(47)=0.5875 ;TFRAC(48)=0.6
 TFRAC(49)=0.6125 ;TFRAC(50)=0.625
 TFRAC(51)=0.6375 ;TFRAC(52)=0.65
 TFRAC(53)=0.6625 ;TFRAC(54)=0.675
 TFRAC(55)=0.6875 ;TFRAC(56)=0.7
 TFRAC(57)=0.7125 ;TFRAC(58)=0.725
 TFRAC(59)=0.7375 ;TFRAC(60)=0.75
 TFRAC(61)=0.7625 ;TFRAC(62)=0.775
 TFRAC(63)=0.7875 ;TFRAC(64)=0.8
 TFRAC(65)=0.8125 ;TFRAC(66)=0.825
 TFRAC(67)=0.8375 ;TFRAC(68)=0.85
 TFRAC(69)=0.8625 ;TFRAC(70)=0.875
 TFRAC(71)=0.8875 ;TFRAC(72)=0.9
 TFRAC(73)=0.9125 ;TFRAC(74)=0.925
 TFRAC(75)=0.9375 ;TFRAC(76)=0.95
 TFRAC(77)=0.9625 ;TFRAC(78)=0.975
 TFRAC(79)=0.9875 ;TFRAC(80)=1.
 ************************************************************
  Group 3. X-Direction Grid Spacing
 CARTES = T
 NX = 18
 XULAST =4.
 XFRAC(1)=0.05 ;XFRAC(2)=0.1
 XFRAC(3)=0.15 ;XFRAC(4)=0.2
 XFRAC(5)=0.25 ;XFRAC(6)=0.305556
 XFRAC(7)=0.361111 ;XFRAC(8)=0.416667
 XFRAC(9)=0.472222 ;XFRAC(10)=0.527778
 XFRAC(11)=0.583333 ;XFRAC(12)=0.638889
 XFRAC(13)=0.694444 ;XFRAC(14)=0.75
 XFRAC(15)=0.8125 ;XFRAC(16)=0.875
 XFRAC(17)=0.9375 ;XFRAC(18)=1.
 ************************************************************
  Group 4. Y-Direction Grid Spacing
 NY = 18
 YVLAST =4.
 YFRAC(1)=0.05 ;YFRAC(2)=0.1
 YFRAC(3)=0.15 ;YFRAC(4)=0.2
 YFRAC(5)=0.25 ;YFRAC(6)=0.305556
 YFRAC(7)=0.361111 ;YFRAC(8)=0.416667
 YFRAC(9)=0.472222 ;YFRAC(10)=0.527778
 YFRAC(11)=0.583333 ;YFRAC(12)=0.638889
 YFRAC(13)=0.694444 ;YFRAC(14)=0.75
 YFRAC(15)=0.8125 ;YFRAC(16)=0.875
 YFRAC(17)=0.9375 ;YFRAC(18)=1.
 ************************************************************
  Group 5. Z-Direction Grid Spacing
 PARAB = F
 NZ = 31
 ZWLAST =10.
 ZFRAC(1)=0.030769 ;ZFRAC(2)=0.061538
 ZFRAC(3)=0.092308 ;ZFRAC(4)=0.123077
 ZFRAC(5)=0.153846 ;ZFRAC(6)=0.184615
 ZFRAC(7)=0.215385 ;ZFRAC(8)=0.246154
 ZFRAC(9)=0.276923 ;ZFRAC(10)=0.307692
 ZFRAC(11)=0.338462 ;ZFRAC(12)=0.369231
 ZFRAC(13)=0.4 ;ZFRAC(14)=0.433333
 ZFRAC(15)=0.466667 ;ZFRAC(16)=0.5
 ZFRAC(17)=0.533333 ;ZFRAC(18)=0.566667
 ZFRAC(19)=0.6 ;ZFRAC(20)=0.633333
 ZFRAC(21)=0.666667 ;ZFRAC(22)=0.7
 ZFRAC(23)=0.733333 ;ZFRAC(24)=0.766667
 ZFRAC(25)=0.8 ;ZFRAC(26)=0.833333
 ZFRAC(27)=0.866667 ;ZFRAC(28)=0.9
 ZFRAC(29)=0.933333 ;ZFRAC(30)=0.966667
 ZFRAC(31)=1.
 ************************************************************
  Group 6. Body-Fitted Coordinates
 ************************************************************
  Group 7. Variables: STOREd,SOLVEd,NAMEd
 ONEPHS = T
 NAME(1)=P1 ;NAME(3)=U1
 NAME(5)=V1 ;NAME(7)=W1
 NAME(148)=E1 ;NAME(149)=VLSQ
 NAME(150)=PRPS
    * Y in SOLUTN argument list denotes:
    * 1-stored 2-solved 3-whole-field
    * 4-point-by-point 5-explicit 6-harmonic averaging 
 SOLUTN(P1,Y,Y,Y,N,N,Y)
 SOLUTN(U1,Y,Y,N,N,N,Y)
 SOLUTN(V1,Y,Y,Y,N,N,Y)
 SOLUTN(W1,Y,Y,Y,N,N,Y)
 SOLUTN(E1,Y,N,N,N,N,N)
 SOLUTN(VLSQ,Y,N,N,N,N,Y)
 SOLUTN(PRPS,Y,N,N,N,N,Y)
 PRPS = 150
 ************************************************************
  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(P1,Y,Y,Y,N,Y,Y)
 TERMS(U1,Y,Y,Y,Y,Y,Y)
 TERMS(V1,Y,Y,Y,Y,Y,Y)
 TERMS(W1,Y,Y,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.
 RADIA =0. ;RADIB =0.
 ENUL =1.0E-05 ;ENUT =0.
 PRNDTL(U1)=1. ;PRNDTL(V1)=1.
 PRNDTL(W1)=1.
 PRT(U1)=1. ;PRT(V1)=1.
 PRT(W1)=1.
 CP1 =1005. ;CP2 =1.
 ************************************************************
  Group 10.Inter-Phase Transfer Processes
 ************************************************************
  Group 11.Initial field variables (PHIs)
 FIINIT(P1)=1.0E-10 ;FIINIT(U1)=1.0E-10
 FIINIT(V1)=1.0E-10 ;FIINIT(W1)=1.0E-10
 FIINIT(E1)=1.0E-10 ;FIINIT(VLSQ)=1.0E-10
 FIINIT(PRPS)=-1.
 
 PATCH(^OB2 ,INIVAL, 2, 0, 0, 0, 0, 0, 1, 1)
 INIT(^OB2 ,PRPS,0. ,198. )
 INIADD = F
 FSWEEP = 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(IN ,LOW , 1, 18, 1, 18, 1, 1, 1, 80)
 COVAL(IN ,P1 ,In-Form:source - see Grp 19)
 COVAL(IN ,W1 ,In-Form:source - see Grp 19)
 
 PATCH(ACEL ,PHASEM, 1, 18, 1, 18, 1, 31, 1, 80)
 COVAL(ACEL ,W1 ,In-Form:source - see Grp 19)
 
 PATCH(OB1 ,HIGH , 1, 18, 1, 18, 31, 31, 1, 80)
 COVAL(OB1 ,P1 ,1000. ,0. )
 COVAL(OB1 ,U1 ,0. ,0. )
 COVAL(OB1 ,V1 ,0. ,0. )
 COVAL(OB1 ,W1 ,0. ,0. )
 XCYCLE = F
 EGWF = T
 WALLCO = GRND2
 ************************************************************
  Group 14. Downstream Pressure For PARAB
 ************************************************************
  Group 15. Terminate Sweeps
 LSWEEP = 20 ;ISWC1 = 1
 LITHYD = 1 ;LITFLX = 1 ;LITC = 1 ;ITHC1 = 1
 SELREF = T
 RESFAC =1.0E-03
 ************************************************************
  Group 16. Terminate Iterations
 LITER(P1)=250 ;LITER(U1)=10
 LITER(V1)=10 ;LITER(W1)=10
 ENDIT(P1)=1.0E-03 ;ENDIT(U1)=1.0E-03
 ENDIT(V1)=1.0E-03 ;ENDIT(W1)=1.0E-03
 ************************************************************
  Group 17. Relaxation
 RELAX(P1,LINRLX,1.)
 RELAX(U1,FALSDT,1.)
 RELAX(V1,FALSDT,1.)
 RELAX(W1,FALSDT,1.)
 RELAX(E1,LINRLX,1.)
 RELAX(VLSQ,LINRLX,1.)
 RELAX(PRPS,LINRLX,1.)
 OVRRLX =0.
 EXPERT = F ;NNORSL = F
 ************************************************************
  Group 18. Limits
 VARMAX(P1)=1.0E+10 ;VARMIN(P1)=-1.0E+10
 VARMAX(U1)=1.0E+06 ;VARMIN(U1)=-1.0E+06
 VARMAX(V1)=1.0E+06 ;VARMIN(V1)=-1.0E+06
 VARMAX(W1)=1.0E+06 ;VARMIN(W1)=-1.0E+06
 VARMAX(E1)=1.0E+10 ;VARMIN(E1)=-1.0E+10
 VARMAX(VLSQ)=1.0E+10 ;VARMIN(VLSQ)=-1.0E+10
 VARMAX(PRPS)=1.0E+10 ;VARMIN(PRPS)=-1.0E+10
 ************************************************************
  Group 19. Data transmitted to GROUND
 NAMSAT =MOSG
 CALFOR = T
 IDISPB = 1 ;IDISPC = 100
 ISG62 = 1
 SPEDAT(SET,GXMONI,TRANSIENT,L,F)
 SPEDAT(SET,SOURCE,R1!IN,C,=5.114685*(EXP(3.836014*TIM)-1)/(EXP(3.$)
 SPEDAT(SET,SOURCE,R1!IN,C,836014*TIM)+1)*RHO1)
 SPEDAT(SET,SOURCE,W1!IN,C,=5.114685*(EXP(3.836014*TIM)-1)/(EXP(3.$)
 SPEDAT(SET,SOURCE,W1!IN,C,836014*TIM)+1)!ONLYMS)
 SPEDAT(SET,SOURCE,W1!ACEL,C,=4*9.81*EXP(3.836014*(TIM-0.025))/(EX$)
 SPEDAT(SET,SOURCE,W1!ACEL,C,P(3.836014*(TIM-0.025))+1)^2.0)
 SPEDAT(SET,STORED,E1,C,=4*9.81*EXP(3.836014*(TIM-0.025))/(EXP(3.8$)
 SPEDAT(SET,STORED,E1,C,36014*(TIM-0.025))+1)^2.0!ZSLFIN)
 SPEDAT(SET,DRAG,MOMCENX,R,0.)
 SPEDAT(SET,DRAG,MOMCENY,R,0.)
 SPEDAT(SET,DRAG,MOMCENZ,R,0.)
 SPEDAT(SET,OBJNAM,!OB1,C,B2)
 SPEDAT(SET,OBJTYP,!OB1,C,OUTLET)
 SPEDAT(SET,ARATIO,!OB1,R,1.)
 SPEDAT(SET,OBJNAM,^OB2,C,B3)
 SPEDAT(SET,OBJTYP,^OB2,C,BLOCKAGE)
 SPEDAT(SET,B3,MATERIAL,R,198.)
 SPEDAT(SET,FACETDAT,NUMOBJ,I,2)
 SPEDAT(SET,MATERIAL,198,L,T)
 RG( 1) =2.
 ************************************************************
  Group 20. Preliminary Printout
 DISTIL = T ;NULLPR = F
 NDST = 0
 DSTTOL =1.0E-02
 EX(P1)=1.545 ;EX(U1)=0.1283
 EX(V1)=0.1283 ;EX(W1)=5.154
 EX(E1)=0. ;EX(VLSQ)=0.
 EX(PRPS)=0.
 ************************************************************
  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(P1,Y,N,Y,Y,Y,Y)
 OUTPUT(U1,Y,N,Y,Y,Y,Y)
 OUTPUT(V1,Y,N,Y,Y,Y,Y)
 OUTPUT(W1,Y,N,Y,Y,Y,Y)
 OUTPUT(E1,Y,N,Y,N,N,N)
 OUTPUT(VLSQ,N,N,Y,N,N,N)
 OUTPUT(PRPS,N,N,Y,N,N,N)
 ************************************************************
  Group 22. Monitor Print-Out
 IXMON = 9 ;IYMON = 9 ;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
 NTPRIN = -1 ;ISTPRF = 1 ;ISTPRL = 100000
 NXPRIN = -1 ;IXPRF = 1 ;IXPRL = 10000
 NYPRIN = -1 ;IYPRF = 1 ;IYPRL = 10000
 NZPRIN = -1 ;IZPRF = 1 ;IZPRL = 10000
 XZPR = F ;YZPR = T
 IPLTF = 1 ;IPLTL = -1 ;NPLT = -1
 ISWPRF = 1 ;ISWPRL = 100000
 ITABL = 3 ;IPROF = 1
 ABSIZ =0.5 ;ORSIZ =0.4
 NTZPRF = 1 ;NCOLPF = 50
 ICHR = 2 ;NCOLCO = 45 ;NROWCO = 20
   No PATCHes yet used for this Group
 ************************************************************
  Group 24. Dumps For Restarts
 SAVE = T ;NOWIPE = F
 NSAVE =CHAM
 IDISPA = 2 ;IDISPB = 1 ;IDISPC = 100
 CSG1    ='M'
STOP