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C *******************************************************************
C ** THIS FORTRAN CODE IS INTENDED TO ILLUSTRATE POINTS MADE IN **
C ** THE TEXT. TO OUR KNOWLEDGE IT WORKS CORRECTLY. HOWEVER IT IS **
C ** THE RESPONSIBILITY OF THE USER TO TEST IT, IF IT IS USED IN A **
C ** RESEARCH APPLICATION. **
C *******************************************************************
C *******************************************************************
C ** FICHE F.30. CONSTANT-NPH MD - EXTENDED SYSTEM METHOD **
C *******************************************************************
PROGRAM ANDERS
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES
C *******************************************************************
C ** CONSTANT-NPH MOLECULAR DYNAMICS BY ANDERSEN'S METHOD. **
C ** **
C ** THE MODIFIED EQUATIONS OF MOTION ARE AS FOLLOWS: **
C ** R2 = F/M + (R/3)[V2/V - (2/3)*(V1/V)**2] **
C ** V2 = ( PRES - PRESUR ) / MP **
C ** WHERE R,R1,R2 ARE THE ATOM POSITIONS AND THEIR DERIVATIVES, **
C ** V,V1,V2 ARE THE VOLUME AND ITS DERIVATIVE, AND MP IS THE **
C ** MASS OF THE PISTON SURROUNDING THE BOX. PRES IS THE **
C ** CALCULATED PRESSURE, AND PRESUR THE REQUIRED PRESSURE. **
C ** WE SOLVE THESE EQUATIONS BY A GEAR 4-VALUE METHOD FOR SECOND **
C ** ORDER DIFFERENTIAL EQUATIONS. FOLLOWING BROWN AND CLARKE, WE **
C ** USE UNSCALED DISTANCE VARIABLES WHICH ARE REDUCED BY SIGMA. **
C ** **
C ** REFERENCES: **
C ** **
C ** ANDERSEN, J. CHEM. PHYS. 72, 283, 1980. **
C ** HAILE AND GRABEN, J. CHEM. PHYS., 73, 2412, 1980. **
C ** BROWN AND CLARKE, MOLEC. PHYS., 51, 1243, 1984. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF MOLECULES **
C ** REAL DT TIMESTEP **
C ** REAL MP PISTON MASS **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL RX1(N),RY1(N),RZ1(N) FIRST DERIVATIVES **
C ** REAL RX2(N),RY2(N),RZ2(N) SECOND DERIVATIVES **
C ** REAL RX3(N),RY3(N),RZ3(N) THIRD DERIVATIVES **
C ** REAL VOL,VOL1,VOL2,VOL3 VOLUME AND DERIVATIVES **
C ** REAL FX(N),FY(N),FZ(N) TOTAL FORCES **
C ** **
C ** ROUTINES REFERENCED **
C ** **
C ** SUBROUTINE READCN ( CNFILE ) **
C ** READS IN CONFIGURATION AND BOX VARIABLES **
C ** SUBROUTINE FORCE ( RCUT, V, W ) **
C ** CALCULATES FORCES, POTENTIAL, AND VIRIAL **
C ** SUBROUTINE KINET ( K ) **
C ** CALCULATES KINETIC ENERGY **
C ** SUBROUTINE PREDIC ( DT ) **
C ** PREDICTOR ROUTINE FOR CONFIGURATION AND BOX VARIABLES **
C ** SUBROUTINE CORREC ( DT ) **
C ** CORRECTOR ROUTINE FOR CONFIGURATION AND BOX VARIABLES **
C ** SUBROUTINE WRITCN ( CNFILE ) **
C ** WRITES OUT CONFIGURATION AND BOX VARIABLES **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N)
REAL RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N)
REAL VOL, VOL1, VOL2, VOL3, DPRES
INTEGER STEP, NSTEP, IPRINT
REAL ACV, ACK, ACE, ACP, ACT, ACH, ACD
REAL ACVSQ, ACKSQ, ACESQ, ACPSQ, ACTSQ, ACHSQ, ACDSQ
REAL AVV, AVK, AVE, AVP, AVT, AVH, AVD
REAL FLV, FLK, FLE, FLP, FLT, FLH, FLD
REAL DT, DENS, TEMP, RCUT, PRES, PRESUR, NORM
REAL K, V, W, E, H, HAM
REAL KN, VN, EN, HN, HAMN
REAL SR3, SR9, VLRC, WLRC, VLRC0, WLRC0, PI, MP
CHARACTER TITLE*80, CNFILE*30
REAL FREE
PARAMETER ( FREE = 3.0 )
PARAMETER ( PI = 3.1415927 )
C *******************************************************************
WRITE(*,'(1H1, '' **** PROGRAM ANDERS **** '')')
WRITE(*,'(//1X,'' MOLECULAR DYNAMICS OF LENNARD-JONES ATOMS'')')
WRITE(*,'(1X, '' CONSTANT-NPH ALGORITHM OF ANDERSEN '')')
C ** BASIC SIMULATION PARAMETERS **
WRITE(*,'('' ENTER RUN TITLE '')')
READ (*,'(A)') TITLE
WRITE(*,'('' ENTER CONFIGURATION FILENAME '')')
READ (*,'(A)') CNFILE
WRITE(*,'('' ENTER NUMBER OF STEPS '')')
READ (*,*) NSTEP
WRITE(*,'('' ENTER INTERVAL BETWEEN PRINTS '')')
READ (*,*) IPRINT
WRITE(*,'('' ENTER THE FOLLOWING IN L-J REDUCED UNITS '')')
WRITE(*,'('' ENTER TIMESTEP '')')
READ (*,*) DT
WRITE(*,'('' ENTER POTENTIAL CUTOFF '')')
READ (*,*) RCUT
WRITE(*,'('' ENTER DESIRED PRESSURE '')')
READ (*,*) PRESUR
WRITE(*,'('' ENTER PISTON MASS PARAMETER, M '')')
READ (*,*) MP
WRITE(*,'(//1X,A)') TITLE
WRITE(*,'('' CONFIGURATION FILENAME '',A)') CNFILE
WRITE(*,'('' NUMBER OF STEPS = '',I6 )') NSTEP
WRITE(*,'('' PRINT INTERVAL = '',I6 )') IPRINT
WRITE(*,'('' TIMESTEP = '',F10.5)') DT
WRITE(*,'('' POTENTIAL CUTOFF = '',F10.5)') RCUT
WRITE(*,'('' DESIRED PRES. = '',F10.5)') PRESUR
WRITE(*,'('' M PARAMETER = '',F10.5)') MP
C ** READCN MUST READ IN INITIAL CONFIGURATION **
C ** AND ASSIGN VALUES TO BOX AND ITS DERIVATIVES **
CALL READCN ( CNFILE )
DENS = REAL ( N ) / VOL
WRITE(*,'('' INITIAL DENS. = '',F10.5)') DENS
IF ( IPRINT .LE. 0 ) IPRINT = NSTEP + 1
C ** PREPARE FACTORS FOR LONG-RANGE CORRECTIONS **
C ** NB: SPECIFIC TO LENNARD-JONES POTENTIAL **
SR3 = ( 1.0 / RCUT ) ** 3
SR9 = SR3 ** 3
VLRC0 = 8.0 * PI * REAL ( N ) * SR9 / 9.0
: - 8.0 * PI * REAL ( N ) * SR3 / 3.0
WLRC0 = 32.0 * PI * REAL ( N ) * SR9 / 9.0
: - 16.0 * PI * REAL ( N ) * SR3 / 3.0
C ** ZERO ACCUMULATORS **
ACV = 0.0
ACK = 0.0
ACE = 0.0
ACP = 0.0
ACT = 0.0
ACH = 0.0
ACD = 0.0
ACVSQ = 0.0
ACKSQ = 0.0
ACESQ = 0.0
ACPSQ = 0.0
ACTSQ = 0.0
ACHSQ = 0.0
ACDSQ = 0.0
FLV = 0.0
FLK = 0.0
FLE = 0.0
FLP = 0.0
FLT = 0.0
FLH = 0.0
FLD = 0.0
WRITE(*,'(//1X,''**** START OF DYNAMICS ****'')')
WRITE(*,10001)
C *******************************************************************
C ** MAIN LOOP STARTS **
C *******************************************************************
DO 1000 STEP = 1, NSTEP
C ** IMPLEMENT ALGORITHM **
CALL PREDIC ( DT )
CALL FORCE ( RCUT, V, W )
CALL KINET ( K )
C ** INCLUDE LONG-RANGE CORRECTIONS IN ALGORITHM **
KN = K / REAL ( N )
DENS = REAL ( N ) / VOL
WLRC = WLRC0 * DENS
TEMP = 2.0 * KN / FREE
PRES = DENS * TEMP + ( W + WLRC ) / VOL
DPRES = ( PRES - PRESUR ) / MP
CALL CORREC ( DT )
C ** CALCULATE INSTANTANEOUS VALUES **
C ** INCLUDING LONG-RANGE CORRECTIONS **
DENS = REAL ( N ) / VOL
VLRC = VLRC0 * DENS
WLRC = WLRC0 * DENS
V = V + VLRC
W = W + WLRC
E = K + V
VN = V / REAL ( N )
EN = E / REAL ( N )
TEMP = 2.0 * KN / FREE
PRES = DENS * TEMP + W / VOL
H = E + PRES * VOL + 0.5 * MP * VOL1 ** 2
HAM = E + PRESUR * VOL + 0.5 * MP * VOL1 ** 2
HN = H / REAL ( N )
HAMN = HAM / REAL ( N )
C ** INCREMENT ACCUMULATORS **
ACE = ACE + EN
ACK = ACK + KN
ACV = ACV + VN
ACP = ACP + PRES
ACH = ACH + HN
ACD = ACD + DENS
ACESQ = ACESQ + EN ** 2
ACKSQ = ACKSQ + KN ** 2
ACVSQ = ACVSQ + VN ** 2
ACPSQ = ACPSQ + PRES ** 2
ACHSQ = ACHSQ + HN ** 2
ACDSQ = ACDSQ + DENS ** 2
C ** OPTIONALLY PRINT INFORMATION **
IF ( MOD ( STEP, IPRINT ) .EQ. 0 ) THEN
WRITE(*,'(1X,I8,9(2X,F10.5))')
: STEP, EN, HN, KN, VN, PRES, TEMP, DENS, HAMN, VOL
ENDIF
1000 CONTINUE
C *******************************************************************
C ** MAIN LOOP ENDS **
C *******************************************************************
WRITE(*,'(/1X,''**** END OF DYNAMICS **** ''//)')
C ** WRITE OUT FINAL CONFIGURATION **
C ** INCLUDING VOL,VOL1,VOL2,VOL3 **
CALL WRITCN ( CNFILE )
C ** WRITE OUT FINAL AVERAGES **
NORM = REAL ( NSTEP )
AVE = ACE / NORM
AVK = ACK / NORM
AVV = ACV / NORM
AVP = ACP / NORM
AVH = ACH / NORM
AVD = ACD / NORM
ACESQ = ( ACESQ / NORM ) - AVE ** 2
ACKSQ = ( ACKSQ / NORM ) - AVK ** 2
ACVSQ = ( ACVSQ / NORM ) - AVV ** 2
ACPSQ = ( ACPSQ / NORM ) - AVP ** 2
ACHSQ = ( ACHSQ / NORM ) - AVH ** 2
ACDSQ = ( ACDSQ / NORM ) - AVD ** 2
IF ( ACESQ .GT. 0.0 ) FLE = SQRT ( ACESQ )
IF ( ACKSQ .GT. 0.0 ) FLK = SQRT ( ACKSQ )
IF ( ACVSQ .GT. 0.0 ) FLV = SQRT ( ACVSQ )
IF ( ACPSQ .GT. 0.0 ) FLP = SQRT ( ACPSQ )
IF ( ACHSQ .GT. 0.0 ) FLH = SQRT ( ACHSQ )
IF ( ACDSQ .GT. 0.0 ) FLD = SQRT ( ACDSQ )
AVT = AVK / 1.5
FLT = FLK / 1.5
WRITE(*,'('' AVERAGES'',7(2X,F10.5))')
: AVE, AVH, AVK, AVV, AVP, AVT, AVD
WRITE(*,'('' FLUCTS '',7(2X,F10.5))')
: FLE, FLH, FLK, FLV, FLP, FLT, FLD
STOP
10001 FORMAT(//1X,'TIMESTEP ..ENERGY.. .ENTHALPY. ..KINETIC.',
: ' ..POTENT.. .PRESSURE. ..TEMPER.. ..DENSITY.',
: ' ...HAMIL.. ..VOLUME..')
END
SUBROUTINE FORCE ( RCUT, V, W )
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES
C *******************************************************************
C ** LENNARD-JONES FORCE ROUTINE IN REDUCED UNITS **
C ** **
C ** THE POTENTIAL IS V(R) = 4*((1/R)**12-(1/R)**6) **
C ** WE INCLUDE SPHERICAL CUTOFF AND MINIMUM IMAGING IN CUBIC BOX. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF MOLECULES **
C ** REAL RX(N),RY(N),RZ(N) MOLECULAR POSITIONS **
C ** REAL FX(N),FY(N),FZ(N) MOLECULAR FORCES **
C ** REAL VOL SIMULATION VOLUME **
C ** REAL BOX SIMULATION BOX LENGTH **
C ** REAL RCUT PAIR POTENTIAL CUTOFF **
C ** REAL V POTENTIAL ENERGY **
C ** REAL W VIRIAL FUNCTION **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N)
REAL RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N)
REAL VOL, VOL1, VOL2, VOL3, DPRES
INTEGER I, J
REAL RCUT, V, W, BOX
REAL BOXINV, RCUTSQ
REAL RXI, RYI, RZI, RXIJ, RYIJ, RZIJ, RIJSQ
REAL FXI, FYI, FZI, FXIJ, FYIJ, FZIJ
REAL SR2, SR6, SR12, VIJ, WIJ, FIJ
C *******************************************************************
C ** USEFUL QUANTITIES **
BOX = VOL ** ( 1.0 / 3.0 )
BOXINV = 1.0 / BOX
RCUTSQ = RCUT ** 2
C ** ZERO FORCES, POTENTIAL, VIRIAL **
DO 100 I = 1, N
FX(I) = 0.0
FY(I) = 0.0
FZ(I) = 0.0
100 CONTINUE
V = 0.0
W = 0.0
C ** OUTER LOOP BEGINS **
DO 200 I = 1, N - 1
RXI = RX(I)
RYI = RY(I)
RZI = RZ(I)
FXI = FX(I)
FYI = FY(I)
FZI = FZ(I)
C ** INNER LOOP BEGINS **
DO 199 J = I + 1, N
RXIJ = RXI - RX(J)
RYIJ = RYI - RY(J)
RZIJ = RZI - RZ(J)
RXIJ = RXIJ - ANINT ( RXIJ * BOXINV ) * BOX
RYIJ = RYIJ - ANINT ( RYIJ * BOXINV ) * BOX
RZIJ = RZIJ - ANINT ( RZIJ * BOXINV ) * BOX
RIJSQ = RXIJ ** 2 + RYIJ ** 2 + RZIJ ** 2
IF ( RIJSQ .LT. RCUTSQ ) THEN
SR2 = 1.0 / RIJSQ
SR6 = SR2 * SR2 * SR2
VIJ = SR6 * ( SR6 - 1.0 )
V = V + VIJ
WIJ = SR6 * ( SR6 - 0.5 )
W = W + WIJ
FIJ = WIJ * SR2
FXIJ = FIJ * RXIJ
FYIJ = FIJ * RYIJ
FZIJ = FIJ * RZIJ
FXI = FXI + FXIJ
FYI = FYI + FYIJ
FZI = FZI + FZIJ
FX(J) = FX(J) - FXIJ
FY(J) = FY(J) - FYIJ
FZ(J) = FZ(J) - FZIJ
ENDIF
199 CONTINUE
C ** INNER LOOP ENDS **
FX(I) = FXI
FY(I) = FYI
FZ(I) = FZI
200 CONTINUE
C ** OUTER LOOP ENDS **
C ** MULTIPLY RESULTS BY NUMERICAL FACTORS **
DO 300 I = 1, N
FX(I) = FX(I) * 48.0
FY(I) = FY(I) * 48.0
FZ(I) = FZ(I) * 48.0
300 CONTINUE
V = V * 4.0
W = W * 48.0 / 3.0
RETURN
END
SUBROUTINE KINET ( K )
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES
C *******************************************************************
C ** ROUTINE TO COMPUTE KINETIC ENERGY. **
C ** **
C ** MOMENTUM AND VELOCITY ARE RELATED THROUGH THE FOLLOWING **
C ** DIFFERENTIAL EQUATION: P = R1 - V1*R/3.0/V **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N)
REAL RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N)
REAL VOL, VOL1, VOL2, VOL3, DPRES
REAL K, V1V3, PX, PY, PZ
INTEGER I
C *******************************************************************
K = 0.0
V1V3 = VOL1 / VOL / 3.0
DO 1000 I = 1, N
PX = RX1(I) - RX(I) * V1V3
PY = RY1(I) - RY(I) * V1V3
PZ = RZ1(I) - RZ(I) * V1V3
K = K + PX ** 2 + PY ** 2 + PZ ** 2
1000 CONTINUE
K = 0.5 * K
RETURN
END
SUBROUTINE READCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES
C *******************************************************************
C ** SUBROUTINE TO READ IN INITIAL CONFIGURATION FROM UNIT 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N)
REAL RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N)
REAL VOL, VOL1, VOL2, VOL3, DPRES
CHARACTER CNFILE*(*)
INTEGER CNUNIT, NN
PARAMETER ( CNUNIT = 10 )
C ******************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE,
: STATUS = 'OLD', FORM = 'UNFORMATTED' )
READ ( CNUNIT ) NN, VOL, VOL1, VOL2, VOL3
IF ( NN .NE. N ) STOP 'INCORRECT VALUE OF N'
READ ( CNUNIT ) RX, RY, RZ
READ ( CNUNIT ) RX1, RY1, RZ1
READ ( CNUNIT ) RX2, RY2, RZ2
READ ( CNUNIT ) RX3, RY3, RZ3
CLOSE ( UNIT = CNUNIT )
RETURN
END
SUBROUTINE WRITCN ( CNFILE )
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES
C *******************************************************************
C ** ROUTINE TO WRITE OUT FINAL CONFIGURATION TO UNIT 10 **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N)
REAL RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N)
REAL VOL, VOL1, VOL2, VOL3, DPRES
CHARACTER CNFILE*(*)
INTEGER CNUNIT
PARAMETER ( CNUNIT = 10 )
C *******************************************************************
OPEN ( UNIT = CNUNIT, FILE = CNFILE,
: STATUS = 'OLD', FORM = 'UNFORMATTED' )
WRITE ( CNUNIT ) N, VOL, VOL1, VOL2, VOL3
WRITE ( CNUNIT ) RX, RY, RZ
WRITE ( CNUNIT ) RX1, RY1, RZ1
WRITE ( CNUNIT ) RX2, RY2, RZ2
WRITE ( CNUNIT ) RX3, RY3, RZ3
CLOSE ( UNIT = CNUNIT )
RETURN
END
SUBROUTINE PREDIC ( DT )
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES
C *******************************************************************
C ** STANDARD TAYLOR SERIES PREDICTORS **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N)
REAL RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N)
REAL VOL, VOL1, VOL2, VOL3, DPRES
REAL DT
INTEGER I
REAL C1, C2, C3
C *******************************************************************
C1 = DT
C2 = C1 * DT / 2.0
C3 = C2 * DT / 3.0
DO 100 I = 1, N
RX(I) = RX(I) + C1*RX1(I) + C2*RX2(I) + C3*RX3(I)
RY(I) = RY(I) + C1*RY1(I) + C2*RY2(I) + C3*RY3(I)
RZ(I) = RZ(I) + C1*RZ1(I) + C2*RZ2(I) + C3*RZ3(I)
RX1(I) = RX1(I) + C1*RX2(I) + C2*RX3(I)
RY1(I) = RY1(I) + C1*RY2(I) + C2*RY3(I)
RZ1(I) = RZ1(I) + C1*RZ2(I) + C2*RZ3(I)
RX2(I) = RX2(I) + C1*RX3(I)
RY2(I) = RY2(I) + C1*RY3(I)
RZ2(I) = RZ2(I) + C1*RZ3(I)
100 CONTINUE
VOL = VOL + C1*VOL1 + C2*VOL2 + C3*VOL3
VOL1 = VOL1 + C1*VOL2 + C2*VOL3
VOL2 = VOL2 + C1*VOL3
RETURN
END
SUBROUTINE CORREC ( DT )
COMMON / BLOCK1 / RX, RY, RZ, RX1, RY1, RZ1,
: RX2, RY2, RZ2, RX3, RY3, RZ3,
: FX, FY, FZ
COMMON / BLOCK2 / VOL, VOL1, VOL2, VOL3, DPRES
C *******************************************************************
C ** GEAR CORRECTOR ALGORITHM. **
C ** **
C ** FOR TIMESTEP-SCALED VARIABLES, GEAR COEFFICIENTS WOULD BE AS **
C ** FOLLOWS (4-VALUE METHOD, 2ND-ORDER D.E.): 1/6, 5/6, 1, 1/3. **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL RX(N), RY(N), RZ(N)
REAL RX1(N), RY1(N), RZ1(N)
REAL RX2(N), RY2(N), RZ2(N)
REAL RX3(N), RY3(N), RZ3(N)
REAL FX(N), FY(N), FZ(N)
REAL VOL, VOL1, VOL2, VOL3, DPRES
REAL DT
INTEGER I
REAL C1, C2, C3, COEFF0, COEFF1, COEFF3
REAL CORV, CORRX, CORRY, CORRZ, VFAC
REAL RX2I, RY2I, RZ2I
REAL GEAR0, GEAR1, GEAR3
PARAMETER ( GEAR0 = 1.0 / 6.0,
: GEAR1 = 5.0 / 6.0,
: GEAR3 = 1.0 / 3.0 )
C *******************************************************************
C1 = DT
C2 = C1 * DT / 2.0
C3 = C2 * DT / 3.0
COEFF0 = GEAR0 * C2
COEFF1 = GEAR1 * C2 / C1
COEFF3 = GEAR3 * C2 / C3
VFAC = ( ( VOL2 / VOL ) - 2.0 * ( VOL1 / VOL ) ** 2 / 3.0 )
: / 3.0
DO 400 I = 1, N
RX2I = FX(I) + VFAC * RX(I)
RY2I = FY(I) + VFAC * RY(I)
RZ2I = FZ(I) + VFAC * RZ(I)
CORRX = RX2I - RX2(I)
CORRY = RY2I - RY2(I)
CORRZ = RZ2I - RZ2(I)
RX(I) = RX(I) + COEFF0 * CORRX
RY(I) = RY(I) + COEFF0 * CORRY
RZ(I) = RZ(I) + COEFF0 * CORRZ
RX1(I) = RX1(I) + COEFF1 * CORRX
RY1(I) = RY1(I) + COEFF1 * CORRY
RZ1(I) = RZ1(I) + COEFF1 * CORRZ
RX2(I) = RX2I
RY2(I) = RY2I
RZ2(I) = RZ2I
RX3(I) = RX3(I) + COEFF3 * CORRX
RY3(I) = RY3(I) + COEFF3 * CORRY
RZ3(I) = RZ3(I) + COEFF3 * CORRZ
400 CONTINUE
CORV = DPRES - VOL2
VOL = VOL + COEFF0 * CORV
VOL1 = VOL1 + COEFF1 * CORV
VOL2 = DPRES
VOL3 = VOL3 + COEFF3 * CORV
RETURN
END
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