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CG.f
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executable file
·1074 lines (967 loc) · 43.8 KB
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C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE CG_PDF(ETA,NETA,MFMEAN,MFVAR,PDF)
IMPLICIT NONE
INCLUDE 'formats.h'
INTEGER NETA,IETA
DOUBLE PRECISION MFMEAN,MFVAR,MFMEAN_G,MFVAR_G
DOUBLE PRECISION ETA(NETA),PDF(NETA)
DOUBLE PRECISION G(NETA-2),GM1,GM2,ETA_TEMP(NETA-2)
DOUBLE PRECISION BOUND,DUM
INTEGER STATUS
DOUBLE PRECISION AG,AREA,A1A2FLAG,A1,A2,FRAC
DOUBLE PRECISION MFMEANPASS
COMMON/MFMEANBLOK/MFMEANPASS
DOUBLE PRECISION MFVARPASS
COMMON/MFVARBLOK/MFVARPASS
DOUBLE PRECISION NORMDIST,CDFNORMDIST,TRAP
EXTERNAL NORMDIST,CDFNORMDIST,TRAP
LOGICAL CHECK
INTEGER NNLEQ,LDFJAC,INFO,LWA,IFLAG
PARAMETER(NNLEQ = 2,LWA = (NNLEQ*(NNLEQ+13))/2+1,
$ LDFJAC = NNLEQ)
DOUBLE PRECISION FNORM
DOUBLE PRECISION X(NNLEQ),FVEC(NNLEQ),FJAC(NNLEQ,NNLEQ),WA(LWA)
DOUBLE PRECISION ENORM,DPMPAR
EXTERNAL FCGPDF
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
INTEGER I_TWO,I_FOUR
COMMON/INTCONSTANTS/I_TWO,I_FOUR
INTEGER NLS_METH
COMMON/NONLINEARSOLVERVARS1/NLS_METH
DOUBLE PRECISION NLS_TOL
COMMON/NONLINEARSOLVERVARS2/NLS_TOL
C FIND THE MEAN AND VARIANCE OF THE CGPDF
CALL FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
C G
DO IETA = 2,NETA-1
G(IETA-1) = NORMDIST(ETA(IETA),MFMEAN_G,MFVAR_G)
ETA_TEMP(IETA-1) = ETA(IETA)
ENDDO
C STRENGTH OF DELTA FUNCTION AT 0
C GM1 = INT_-INF^0 [G(ETA)DETA]
GM1 = CDFNORMDIST(D_ZERO,MFMEAN_G,MFVAR_G)
C CALL CDFNOR(1,GM1,DUM,D_ZERO,MFMEAN_G,DSQRT(MFVAR_G),STATUS,BOUND)
C STRENGTH OF DELTA FUNCTION AT 1
C GM2 = INT_1^+INF [G(ETA)DETA]
C USE THE FACT THAT INT_-INF^+INF[G(ETA)DETA] = 1
C INT_-INF^1[G(ETA)DETA] + INT_1^+INF[G(ETA)DETA] = 1 =>
C GM2 = INT_1^+INF[G(ETA)DETA] = 1 - INT_-INF^1[G(ETA)DETA]
GM2 = D_ONE - CDFNORMDIST(D_ONE,MFMEAN_G,MFVAR_G)
C CALL CDFNOR(1,GM2,DUM,D_ONE,MFMEAN_G,DSQRT(MFVAR_G),STATUS,BOUND)
C GM2 = D_ONE-GM2
C CONSTRUCT THE PDF
C IF(((GM1.EQ.D_ZERO).AND.(GM2.EQ.D_ZERO))
C $ .OR.(GM1.LT.D_ZERO).OR.(GM2.LT.D_ZERO)) THEN
IF((GM1.EQ.D_ZERO).AND.(GM2.EQ.D_ZERO)) THEN
A1 = D_ZERO
A2 = D_ZERO
A1A2FLAG = D_ZERO
ELSE
AG = TRAP(G,ETA_TEMP,NETA-2)
AREA = D_ONE - AG
FRAC = GM1/(GM1+GM2)
A1 = FRAC*AREA
A2 = (D_ONE-FRAC)*AREA
A1A2FLAG = D_ONE
ENDIF
DO IETA = 1,NETA
IF(IETA.EQ.1) THEN
PDF(IETA) = D_TWO*A1/(ETA(2)-ETA(1)) - A1A2FLAG*G(1)
ELSEIF(IETA.EQ.NETA) THEN
PDF(IETA) = D_TWO*A2/(ETA(NETA)-ETA(NETA-1))
$ - A1A2FLAG*G(NETA-2)
ELSE
PDF(IETA) = G(IETA-1)
ENDIF
ENDDO
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE CG_CV(ETA,NETA,MFMEAN,MFVAR,MFMEANGRAD,MFVARGRAD,
$ DT,VEL,CV)
C==========================================================================================
C PURPOSE: COMPUTES THE CONDITIONAL VELOCITY USING THE PDF-GRADIENT
C MODEL BASED CG-PDF
C==========================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C ETA MIXTURE FRACTION GRID DOUBLE PRECISION (ARRAY,SIZE=NETA)
C NETA SIZE OF ETA INTEGER
C MFMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C MFMEANGRAD GRAD. OF MIX. FRAC. MEAN DOUBLE PRECISION (ARRAY, SIZE=3)
C MFVARGRAD GRAD. OF MIX. FRAC. VARIANCE DOUBLE PRECISION (ARRAY, SIZE=3)
C DT TURBULENT DIFFUSIVITY DOUBLE PRECISION
C VEL MEAN VELOCITY VECTOR DOUBLE PRECISION (ARRAY, SIZE=3)
C
C OUTPUT:
C
C CV COND. VELOCITY DOUBLE PRECISION (ARRAY, SIZE=NETA)
C==========================================================================================
IMPLICIT NONE
INCLUDE 'formats.h'
INTEGER I,IETA,NETA
DOUBLE PRECISION MFMEAN,MFVAR,DT
DOUBLE PRECISION MFMEANGRAD(3),MFVARGRAD(3),VEL(3)
DOUBLE PRECISION ETA(NETA),CV(3,NETA),PDF(NETA)
DOUBLE PRECISION M,S,S2,MFMEAN_G,MFVAR_G
DOUBLE PRECISION DPDM(NETA),DPDS2(NETA)
DOUBLE PRECISION DMDMEAN,DMDVAR,ERR_DMDMEAN,ERR_DMDVAR
DOUBLE PRECISION DS2DMEAN,DS2DVAR,ERR_DS2DMEAN,ERR_DS2DVAR
DOUBLE PRECISION S2_V,S2_M,M_V,M_M
EXTERNAL S2_V,S2_M,M_V,M_M
DOUBLE PRECISION H_NEW,ERR,ERR_OLD,H_MEAN,H_VAR
LOGICAL VERBOSE_TEMP
DOUBLE PRECISION LIMINFM,LIMSUPM
DOUBLE PRECISION LIMINFV,LIMSUPV
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
INTEGER I_TWO,I_FOUR
COMMON/INTCONSTANTS/I_TWO,I_FOUR
LOGICAL VERBOSE,PROGRESS
COMMON/LOGICALVARS/VERBOSE,PROGRESS
DOUBLE PRECISION EPSL
COMMON/EPSILON/EPSL
C THESE BLOCKS ARE PASSED TO EXTERNAL FUNCTIONS
DOUBLE PRECISION MFMEANPASS_CG
COMMON/MFMEANBLOK_CG/MFMEANPASS_CG
DOUBLE PRECISION MFVARPASS_CG
COMMON/MFVARBLOK_CG/MFVARPASS_CG
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
INTEGER DIFF_NCHEBCOEFS
COMMON/DIFFERENTIATORVARS1/DIFF_NCHEBCOEFS
DOUBLE PRECISION MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
COMMON/MFMINMAX/MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
DOUBLE PRECISION MFVAR_MAX
CALL CHECKPARMS(MFMEAN,MFVAR)
C FIND THE PDF. TEMPORARILY DISABLE VERBOSITY IF ON.
VERBOSE_TEMP = VERBOSE
VERBOSE = .FALSE.
CALL CG_PDF(ETA,NETA,MFMEAN,MFVAR,PDF)
VERBOSE = VERBOSE_TEMP
CALL FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
M = MFMEAN_G
S = DSQRT(MFVAR_G)
S2 = MFVAR_G
DO IETA = 2,NETA-1
C
C DPDM
DPDM(IETA) = (D_ONE/(S*DSQRT(D_TWO*PI)))*((ETA(IETA)-M)/S2)
$ * DEXP(-((ETA(IETA)-M)/(S*DSQRT(D_TWO)))**D_TWO)
C
C DPDS2
DPDS2(IETA) = -(D_ONE/(D_TWO*DSQRT(D_TWO*PI)))
$ * (D_ONE/(S**D_THREE))*(D_ONE-((ETA(IETA)-M)/S)**D_TWO)
$ * DEXP(-((ETA(IETA)-M)/(S*DSQRT(D_TWO)))**D_TWO)
C
ENDDO
C ESTIMATION OF THE INITIAL STEPSIZE, H, IS ADOPTED FROM REF [2]
CALL FINDDIFFDELTA(MFMEAN,MFVAR,H_MEAN,H_VAR)
MFVAR_MAX = MFMEAN*(D_ONE-MFMEAN)
LIMINFV = DMAX1(MFVAR-H_VAR,MFVAR_MIN)
LIMSUPV = DMIN1(MFVAR+H_VAR,MFVAR_MAX)
LIMINFM = DMAX1(MFMEAN-H_MEAN,MFMEAN_MIN)
LIMSUPM = DMIN1(MFMEAN+H_MEAN,MFMEAN_MAX)
C
C DS2DVAR
MFMEANPASS_CG = MFMEAN
CALL CHEBDERIV(LIMINFV,LIMSUPV,DIFF_NCHEBCOEFS,S2_V,
$ MFVAR,1,DS2DVAR)
C
C DS2DMEAN
MFVARPASS_CG = MFVAR
CALL CHEBDERIV(LIMINFM,LIMSUPM,DIFF_NCHEBCOEFS,S2_M,
$ MFMEAN,1,DS2DMEAN)
C
C DMDVAR
MFMEANPASS_CG = MFMEAN
CALL CHEBDERIV(LIMINFV,LIMSUPV,DIFF_NCHEBCOEFS,M_V,
$ MFVAR,1,DMDVAR)
C
C DMDMEAN
MFVARPASS_CG = MFVAR
CALL CHEBDERIV(LIMINFM,LIMSUPM,DIFF_NCHEBCOEFS,M_M,
$ MFMEAN,1,DMDMEAN)
C
C COMPUTE THE CONDITIONAL VELOCITY
DO IETA = 2,NETA-1
DO I = 1,3
CV(I,IETA) = VEL(I) - (DT/ PDF(IETA))
$ *((DPDS2(IETA)*DS2DMEAN + DPDM(IETA)*DMDMEAN)
$ * MFMEANGRAD(I)
$ + (DPDS2(IETA)*DS2DVAR + DPDM(IETA)*DMDVAR)
$ * MFVARGRAD(I))
ENDDO
ENDDO
IF(VERBOSE) THEN
WRITE(*,50)' '
WRITE(*,50)'============================================='
WRITE(*,50) 'CG: CONDITIONAL VELOCITY:'
WRITE(*,50)'============================================='
WRITE(*,400)'INDEX','ETA','CV_X','CV_Y','CV_Z'
DO IETA = 1,NETA
WRITE(*,500) IETA,ETA(IETA),CV(1,IETA),CV(2,IETA),CV(3,IETA)
ENDDO
WRITE(*,50)'============================================='
WRITE(*,50)' '
ENDIF
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE CG_CSDR_H(ETA,NETA,MFMEAN,MFVAR,CHI,CSDRH)
C==========================================================================================
C PURPOSE: COMPUTES THE [HOMOGENEOUS] VERSION OF THE CONDITIONAL SCALAR
C DISSIPATION RATE MODEL USING THE CG-PDF
C==========================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C ETA MIXTURE FRACTION GRID DOUBLE PRECISION (ARRAY,SIZE=NETA)
C NETA SIZE OF ETA AND CSDRH INTEGER
C MFMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C CHI MEAN SCALAR DISSIPATION RATE DOUBLE PRECISION
C
C OUTPUT:
C
C CSDRH COND. SCALAR DISSIPATION RATE DOUBLE PRECISION (ARRAY, SIZE=NETA)
C==========================================================================================
IMPLICIT NONE
INCLUDE 'formats.h'
INTEGER I,IETA,NETA
DOUBLE PRECISION ETA(NETA),PDF(NETA),CSDRH(NETA)
DOUBLE PRECISION MFMEAN,MFVAR,CHI,DT
DOUBLE PRECISION MFMEANGRAD(3),MFVARGRAD(3)
DOUBLE PRECISION DIIDS2(NETA),DIIDM(NETA),
$ ERR_DMDV,DMDV,ERR_DS2DV,DS2DV,
$ MAXERR_DIIDV
DOUBLE PRECISION H_NEW,ERR,ERR_OLD,H_MEAN,H_VAR
LOGICAL VERBOSE_TEMP
DOUBLE PRECISION S2_V,M_V,ERF
EXTERNAL S2_V,M_V,ERF
DOUBLE PRECISION MFMEANPASS_CG
COMMON/MFMEANBLOK_CG/MFMEANPASS_CG
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
INTEGER DIFF_NCHEBCOEFS
COMMON/DIFFERENTIATORVARS1/DIFF_NCHEBCOEFS
LOGICAL VERBOSE,PROGRESS
COMMON/LOGICALVARS/VERBOSE,PROGRESS
DOUBLE PRECISION MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
COMMON/MFMINMAX/MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
DOUBLE PRECISION MFVAR_MAX
DOUBLE PRECISION LIMINF,LIMSUP
DOUBLE PRECISION MFMEAN_G,MFVAR_G,A1,A2,A3,A4,M,S,S2
CALL CHECKPARMS(MFMEAN,MFVAR)
C FIND THE PDF. TEMPORARILY DISABLE VERBOSITY IF ON.
VERBOSE_TEMP = VERBOSE
VERBOSE = .FALSE.
CALL CG_PDF(ETA,NETA,MFMEAN,MFVAR,PDF)
VERBOSE = VERBOSE_TEMP
C ESTIMATION OF THE INITIAL STEPSIZE, H, IS ADOPTED FROM REF [2]
CALL FINDDIFFDELTA(MFMEAN,MFVAR,H_MEAN,H_VAR)
MFVAR_MAX = MFMEAN*(D_ONE-MFMEAN)
LIMINF = DMAX1(MFVAR-H_VAR,MFVAR_MIN)
LIMSUP = DMIN1(MFVAR+H_VAR,MFVAR_MAX)
C DS2DV AND DMDV
MFMEANPASS_CG = MFMEAN
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS,S2_V,MFVAR,1,
$ DS2DV)
MFMEANPASS_CG = MFMEAN
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS,M_V,MFVAR,1,
$ DMDV)
C
CALL FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
M = MFMEAN_G
S2 = MFVAR_G
S = DSQRT(MFVAR_G)
DO IETA = 2,NETA-1
DIIDS2(IETA) = D_ONE/(D_TWO*DSQRT(D_TWO*PI)*S)
$ * (DEXP(-(((ETA(IETA)-M)/(S*DSQRT(D_TWO)))**D_TWO))
$ - (D_ONE + ETA(IETA)*M/S2)
$ * DEXP(-(M/(S*DSQRT(D_TWO)))**D_TWO))
DIIDM(IETA) = -D_HALF*(ERF((ETA(IETA)-M)/(S*DSQRT(D_TWO)))
$ + ERF(M/(S*DSQRT(D_TWO))))
$ + ETA(IETA)/(DSQRT(D_TWO*PI)*S)
$ * DEXP(-((M/(S*DSQRT(D_TWO)))**D_TWO))
ENDDO
C BOUNDARY VALUES ARE KNOWN
CSDRH(1) = D_ZERO
CSDRH(NETA) = D_ZERO
C COMPUTE CSDR AT INTERNAL GRID POINTS
DO IETA = 2,NETA-1
CSDRH(IETA) = (D_TWO/PDF(IETA))*CHI
$ *(DIIDS2(IETA)*DS2DV + DIIDM(IETA)*DMDV)
ENDDO
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE CG_CSDR_I(ETA,NETA,MFMEAN,MFVAR,MFMEANGRAD,
$ MFVARGRAD,DT,CHI,CSDRI)
C==========================================================================================
C PURPOSE: COMPUTES THE [INHOMOGENEOUS] VERSION OF THE CONDITIONAL SCALAR
C DISSIPATION RATE MODEL USING THE CG-PDF
C==========================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C ETA MIXTURE FRACTION GRID DOUBLE PRECISION (ARRAY,SIZE=NETA)
C NETA SIZE OF ETA AND CSDRI INTEGER
C MFMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C MFMEANGRAD GRAD. OF MIX. FRAC. MEAN DOUBLE PRECISION (ARRAY, SIZE=3)
C MFVARGRAD GRAD. OF MIX. FRAC. VARIANCE DOUBLE PRECISION (ARRAY, SIZE=3)
C DT TURBULENT DIFFUSIVITY DOUBLE PRECISION
C CHI MEAN SCALAR DISSIPATION RATE DOUBLE PRECISION
C
C OUTPUT:
C
C CSDRI COND. SCALAR DISSIPATION RATE DOUBLE PRECISION (ARRAY, SIZE=NETA)
C==========================================================================================
IMPLICIT NONE
INCLUDE 'formats.h'
INTEGER I,IETA,NETA
DOUBLE PRECISION ETA(NETA),PDF(NETA),CSDRI(NETA)
DOUBLE PRECISION MFMEAN,MFVAR,CHI,DT
DOUBLE PRECISION MFMEANGRAD(3),MFVARGRAD(3)
DOUBLE PRECISION PROD1,PROD2,PROD3
DOUBLE PRECISION IM,H,H_NEW,ERR,ERR_OLD,H_MEAN,H_VAR
DOUBLE PRECISION H_MEAN_NEW, H_VAR_NEW
DOUBLE PRECISION DIIDV(NETA)
DOUBLE PRECISION DIIDM(NETA)
DOUBLE PRECISION D2IIDV2(NETA)
DOUBLE PRECISION D2IIDM2(NETA)
DOUBLE PRECISION D2IIDMDV(NETA)
LOGICAL VERBOSE_TEMP
DOUBLE PRECISION IICGPDF_M,IICGPDF_V,IICGPDF_MV
EXTERNAL IICGPDF_M,IICGPDF_V,IICGPDF_MV
DOUBLE PRECISION MFMEANPASS_CG
COMMON/MFMEANBLOK_CG/MFMEANPASS_CG
DOUBLE PRECISION MFVARPASS_CG
COMMON/MFVARBLOK_CG/MFVARPASS_CG
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
INTEGER DIFF_NCHEBCOEFS
COMMON/DIFFERENTIATORVARS1/DIFF_NCHEBCOEFS
LOGICAL VERBOSE,PROGRESS
COMMON/LOGICALVARS/VERBOSE,PROGRESS
DOUBLE PRECISION MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
COMMON/MFMINMAX/MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
DOUBLE PRECISION MFVAR_MAX
DOUBLE PRECISION LIMINF,LIMSUP
CALL CHECKPARMS(MFMEAN,MFVAR)
C FIND THE PDF. TEMPORARILY DISABLE VERBOSITY IF ON.
VERBOSE_TEMP = VERBOSE
VERBOSE = .FALSE.
CALL CG_PDF(ETA,NETA,MFMEAN,MFVAR,PDF)
VERBOSE = VERBOSE_TEMP
C ESTIMATION OF THE INITIAL STEPSIZE, H, IS ADOPTED FROM REF [2]
CALL FINDDIFFDELTA(MFMEAN,MFVAR,H_MEAN,H_VAR)
MFVAR_MAX = MFMEAN*(D_ONE-MFMEAN)
C
C DIIDV AND D2IIDV2
LIMINF = DMAX1(MFVAR-H_VAR,MFVAR_MIN)
LIMSUP = DMIN1(MFVAR+H_VAR,MFVAR_MAX)
MFMEANPASS_CG = MFMEAN
DO IETA = 2,NETA-1
ETAPASS = ETA(IETA)
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS,IICGPDF_V,
$ MFVAR,1,DIIDV(IETA))
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS,IICGPDF_V,
$ MFVAR,2,D2IIDV2(IETA))
ENDDO
C
C D2IIDM2
LIMINF = DMAX1(MFMEAN-H_MEAN,MFMEAN_MIN)
LIMSUP = DMIN1(MFMEAN+H_MEAN,MFMEAN_MAX)
MFVARPASS_CG = MFVAR
DO IETA = 2,NETA-1
ETAPASS = ETA(IETA)
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS,IICGPDF_M,
$ MFMEAN,2,D2IIDM2(IETA))
ENDDO
WRITE(*,*)'MORE WORK NEEDED FOR IN CG_CSDR_I'
WRITE(*,*)'A STOP WAS INSERTED HERE'
STOP
C COMPUTE THE SCALAR PRODUCTS
PROD1 = D_ZERO ! SCALAR PRODUCT OF THE GRADS OF MIX FRAC. MEAN
PROD2 = D_ZERO ! SCALAR PRODUCT OF THE GRADS OF MIX FRAC. VARIANCE
PROD3 = D_ZERO ! SCALAR PRODUCT OF MIX FRAC. MEAN AND MIX FRAC VARIANCE GRADS
DO I = 1,3
PROD1 = PROD1 + MFMEANGRAD(I)**D_TWO
PROD2 = PROD2 + MFVARGRAD(I)**D_TWO
PROD3 = PROD3 + MFMEANGRAD(I)*MFVARGRAD(I)
ENDDO
C BOUNDARY VALUES ARE KNOWN
CSDRI(1) = D_ZERO
CSDRI(NETA) = D_ZERO
C COMPUTE CSDR AT INTERNAL GRID POINTS
DO IETA = 2,NETA-1
CSDRI(IETA) = (D_TWO/PDF(IETA))
$ *(-DIIDV(IETA)* (-CHI + D_TWO*DT*PROD1)
$ + DT*(PROD2* D2IIDV2(IETA) + PROD1*D2IIDM2(IETA)
$ + D_TWO*PROD3*D2IIDMDV(IETA)))
ENDDO
IF(VERBOSE) THEN
WRITE(*,50)' '
WRITE(*,50)'============================================='
WRITE(*,200)'INDEX','ETA','CSDRH'
DO IETA = 1,NETA
WRITE(*,300) IETA, ETA(IETA), CSDRI(IETA)
ENDDO
WRITE(*,50)'============================================='
WRITE(*,50)' '
ENDIF
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
C==================================================================================
C PURPOSE: COMPUTES THE MEAN AND VARIANCE OF THE CGPDF GIVEN THE MIXTURE
C FRACTION MEAN AND VARIANCE
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C MMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C
C OUTPUT:
C
C MMEAN_G MEAN OF THE CGPDF DOUBLE PRECISION
C MFVAR_G VARIANCE OF THE CGPDF DOUBLE PRECISION
C==================================================================================
IMPLICIT NONE
DOUBLE PRECISION MFMEAN,MFVAR,MFMEAN_G,MFVAR_G
DOUBLE PRECISION MFMEANPASS
COMMON/MFMEANBLOK/MFMEANPASS
DOUBLE PRECISION MFVARPASS
COMMON/MFVARBLOK/MFVARPASS
C NON-LINEAR SOLVER VARIABLES
LOGICAL CHECK
INTEGER NNLEQ,LDFJAC,INFO,LWA,IFLAG
PARAMETER(NNLEQ = 2,LWA = (NNLEQ*(NNLEQ+13))/2+1,
$ LDFJAC = NNLEQ)
DOUBLE PRECISION FNORM
DOUBLE PRECISION X(NNLEQ),FVEC(NNLEQ),FJAC(NNLEQ,NNLEQ),WA(LWA)
DOUBLE PRECISION ENORM,DPMPAR
EXTERNAL FCGPDF
DOUBLE PRECISION NLS_TOL
COMMON/NONLINEARSOLVERVARS/NLS_TOL
MFMEANPASS = MFMEAN
MFVARPASS = MFVAR
C INITIAL GUESS
C X(1) = MFMEAN
C X(2) = DSQRT(MFVAR)
X(1) = MFMEAN
X(2) = DSQRT(MFVAR)
C COMPUTE MFMEAN_G AND MFVAR_G
C IFLAG = 1
C CALL FCGPDF(NNLEQ,X,FVEC,FJAC,LDFJAC,IFLAG)
CALL HYBRJ1(FCGPDF,NNLEQ,X,FVEC,FJAC,LDFJAC,NLS_TOL,
$ INFO,WA,LWA)
MFMEAN_G = X(1)
MFVAR_G = X(2)*X(2)
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE FCGPDF(N,X,FVEC,FJAC,LDFJAC,IFLAG)
C==================================================================================
C PURPOSE: COMPUTES THE THE FUNCTIONS AND THE JACOBIAN MATRIX REQUIRED BY THE
C THE NON-LINERA EQUATION SOLVER HYBRJ1 FOR THE CALCULATION OF THE
C MEAN AND VARIANCE OF THE CGPDF
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C N NUMBER OF VARIABLES INTEGER
C X X(1) = MEAN OF THE CGPDF DOUBLE PRECISION (ARRAY,SIZE=2)
C X(2) = STANDARD DEVIATION
C OF THE CGPDF
C FVEC VECTOR CONTAINING THE DOUBLE PRECISION (ARRAY,SIZE=2)
C SYSTEM OF NON-LINEAR
C EQUATIONS
C FJAC JACOBIAN MATRIX OF THE DOUBLE PRECISION (ARRAY,SIZE=2:2)
C SYSTEM OF NON-LINEAR
C EQUATIONS
C LDFJAC LEADING DIMENSION OF FJAC INTEGER (LDFJAC.GT.N)
C IFLAG CONTROL FLAG INTEGER
C IFLAG = 1: CALCULATE THE
C FUNCTIONS AT X AND RETURN
C THE VECTOR IN FVEC.
C IFLAG = 2: CALCULATE THE
C JACOBIAN AT X AND RETURN
C THE MATRIX IN FJAC.
C==================================================================================
INTEGER N,LDFJAC,IFLAG
DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)
IF (IFLAG.EQ.1) CALL CGPDFVEC(X,FVEC)
IF (IFLAG.EQ.2) CALL CGPDFJAC(X,FJAC)
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE CGPDFVEC(X,FVEC)
C==================================================================================
C PURPOSE: SETS THE SYSTEM OF NON-LINEAR EQUATION REQUIRED FOR THE COMPUTATION
C OF THE MEAN AND THE VARIANCE OF THE CGPDF
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C X X(1) = MEAN OF THE CGPDF DOUBLE PRECISION (ARRAY,SIZE=2)
C X(2) = STANDARD DEVIATION
C OF THE CGPDF
C
C OUTPUT:
C
C FVEC VECTOR CONTAINING THE DOUBLE PRECISION (ARRAY,SIZE=2)
C SYSTEM OF NON-LINEAR
C EQUATIONS
C==================================================================================
IMPLICIT NONE
INTEGER N
PARAMETER(N = 2)
DOUBLE PRECISION X(N),FVEC(N)
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
INTEGER I_TWO,I_FOUR
COMMON/INTCONSTANTS/I_TWO,I_FOUR
DOUBLE PRECISION M,S,Z0,Z1,PZ0,PZ1
DOUBLE PRECISION MFMEANPASS
COMMON/MFMEANBLOK/MFMEANPASS
DOUBLE PRECISION MFVARPASS
COMMON/MFVARBLOK/MFVARPASS
DOUBLE PRECISION ERF
EXTERNAL ERF
M = X(1)
S = X(2)
Z0 = -M/S
Z1 = (D_ONE-M)/S
PZ0 = D_HALF * (D_ONE + ERF(Z0/DSQRT(D_TWO)))
PZ1 = D_HALF * (D_ONE + ERF(Z1/DSQRT(D_TWO)))
FVEC(1) = D_ONE + (M-D_ONE)*PZ1 - M*PZ0 + (S/(2.0D0*PI))
$ * (DEXP(-(Z0**D_TWO)/2.0D0) - DEXP(-(Z1**D_TWO)/D_TWO))
$ - MFMEANPASS
FVEC(2) = D_ONE + ((S**D_TWO)+(M**D_TWO)-D_ONE)*PZ1
$ - ((S**D_TWO)+(M**D_TWO))*PZ0
$ + ((S**D_TWO)/DSQRT(D_TWO*PI))
$ * (Z0*DEXP(-(Z0**D_TWO)/D_TWO)
$ - Z1*DEXP(-(Z1**D_TWO)/D_TWO))
$ + ((D_TWO*S*M)/DSQRT(D_TWO*PI))
$ * (DEXP(-(Z0**D_TWO)/D_TWO)
$ - DEXP(-(Z1**D_TWO)/D_TWO))
$ - (MFMEANPASS**D_TWO) - MFVARPASS
RETURN
END
C==========================================================================================
C=========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE CGPDFJAC(X,FJAC)
C==================================================================================
C PURPOSE: COMPUTES THE (ANALYTICAL) JACOBIAN MATRIX OF THE SYSTEM OF NON-
C LINEAR EQUATION REQUIRED FOR THE COMPUTATION OF THE MEAN AND THE
C VARIANCE OF THE CGPDF
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C X X(1) = MEAN OF THE CGPDF DOUBLE PRECISION (ARRAY,SIZE=2)
C X(2) = STANDARD DEVIATION
C OF THE CGPDF
C
C OUTPUT:
C
C FJAC JACOBIAN MATRIX OF THE DOUBLE PRECISION (ARRAY,SIZE=2:2)
C SYSTEM OF NON-LINEAR
C EQUATIONS
C==================================================================================
IMPLICIT NONE
INTEGER N
PARAMETER(N = 2)
DOUBLE PRECISION X(N),FVEC(N),FJAC(N,N)
DOUBLE PRECISION M,S,Z0,Z1,PZ0,PZ1
DOUBLE PRECISION PZ0_M,PZ1_M,PZ0_S,PZ1_S
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
INTEGER I_TWO,I_FOUR
COMMON/INTCONSTANTS/I_TWO,I_FOUR
DOUBLE PRECISION ERF
EXTERNAL ERF
M = X(1)
S = X(2)
Z0 = -M/S
Z1 = (D_ONE-M)/S
C PZ = D_HALF * (D_ONE + ERF(Z/DSQRT(D_TWO)))
PZ0 = D_HALF * (D_ONE + ERF(Z0/DSQRT(D_TWO)))
PZ1 = D_HALF * (D_ONE + ERF(Z1/DSQRT(D_TWO)))
PZ0_M = -(D_ONE/(S*DSQRT(D_TWO*PI)))*DEXP(-(Z0**D_TWO)/D_TWO)
PZ1_M = -(D_ONE/(S*DSQRT(D_TWO*PI)))*DEXP(-(Z1**D_TWO)/D_TWO)
PZ0_S = (M/((S**D_TWO)*DSQRT(D_TWO*PI)))
$ *DEXP(-(Z0**D_TWO)/D_TWO)
PZ1_S = -((D_ONE-M)/((S**D_TWO)*DSQRT(D_TWO*PI)))
$ *DEXP(-(Z1**D_TWO)/D_TWO)
FJAC(1,1) = (M-D_ONE)*PZ1_M + PZ1 - M*PZ0_M -PZ0
$ - (D_ONE/(S*DSQRT(D_TWO*PI)))*
$ (M*DEXP(-(Z0**D_TWO)/2.0D0)
$ + (D_ONE-M)*DEXP(-(Z1**D_TWO)/2.0D0))
FJAC(1,2) = (M-D_ONE)*PZ1_S - M*PZ0_S
$ + (D_ONE/((S**D_TWO)*DSQRT(D_TWO*PI)))
$ *((M**D_TWO)*DEXP(-(Z0**D_TWO)/D_TWO)
$ + (D_ONE-M)*DEXP(-(Z1**D_TWO)/D_TWO))
$ + (D_ONE/DSQRT(D_TWO*PI))
$ *(DEXP(-(Z0**D_TWO)/D_TWO)
$ + DEXP(-(Z1**D_TWO)/D_TWO))
FJAC(2,1) = ((S**D_TWO)+(M**D_TWO)-D_ONE)*PZ1_M + D_TWO*M*PZ1
$ - ((S**D_TWO)+(M**D_TWO))*PZ0_M - D_TWO*M*PZ0
$ + (S/DSQRT(D_TWO*PI))
$ *(-DEXP(-(Z0**D_TWO)/D_TWO)*(D_ONE+(Z0**2.0D0))
$ + DEXP(-(Z1**D_TWO)/D_TWO)*(D_ONE-(Z1**2.0D0)))
$ + (D_TWO*M/(S*DSQRT(D_TWO*PI)))
$ * (M*DEXP(-(Z0**D_TWO)/D_TWO)
$ + (D_ONE-M)*DEXP(-(Z1**D_TWO)/D_TWO))
$ + (D_TWO*S/(DSQRT(D_TWO*PI)))
$ * (DEXP(-(Z0**D_TWO)/D_TWO)
$ + DEXP(-(Z1**D_TWO)/D_TWO))
FJAC(2,2) = ((S**D_TWO)+(M**D_TWO)-D_ONE)*PZ1_S + D_TWO*S*PZ1
$ - ((S**D_TWO)+(M**D_TWO))*PZ0_S - D_TWO*S*PZ0
$ + (D_ONE/DSQRT(D_TWO*PI))
$ * (M*(D_ONE-(Z0**D_TWO))*DEXP(-(Z0**D_TWO)/D_TWO)
$ + (D_ONE-M)*(D_ONE-(Z1**D_TWO))*DEXP(-(Z1**D_TWO)/D_TWO))
$ + (D_TWO*S/DSQRT(D_TWO*PI))
$ * (Z0*DEXP(-(Z0**D_TWO)/D_TWO)
$ + Z1*DEXP(-(Z1**D_TWO)/D_TWO))
$ + (D_TWO*M/(DSQRT(D_TWO*PI)))
$ * (DEXP(-(Z0**D_TWO)/D_TWO)
$ + DEXP(-(Z1**D_TWO)/D_TWO))
$ + (D_TWO*M/DSQRT(D_TWO*PI))
$ * ((Z0**D_TWO)*DEXP(-(Z0**D_TWO)/D_TWO)
$ - (Z1**D_TWO)*DEXP(-(Z1**D_TWO)/D_TWO))
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
DOUBLE PRECISION FUNCTION IICGPDF_M(MFMEAN)
C==================================================================================
C PURPOSE: FUNCTION NECESSARY FOR THE COMPUTATION OF THE SECOND-ORDER
C PARTIAL DERIVATIVE OF II(ETA) WITH RESPECT TO THE
C [MIXTURE FRACTION MEAN]
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C MFMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C==================================================================================
IMPLICIT NONE
DOUBLE PRECISION MFMEAN,MFVAR,MFMEAN_G,MFVAR_G
C THESE BLOCKS ARE PASSED FROM SUBROUTINE CG_CSDR
DOUBLE PRECISION MFVARPASS_CG
COMMON/MFVARBLOK_CG/MFVARPASS_CG
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION ERF
EXTERNAL ERF
DOUBLE PRECISION Q1,Q2
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
C MFMEAN IS PROVIDED IN THE ARGUMENT OF FUNCTION IICGPDF_M
C MFVAR IS PASSED FROM SUBROUTINE CG_CSDR (FIXED)
MFVAR = MFVARPASS_CG
CALL FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
Q1 = (ETAPASS-MFMEAN_G)/DSQRT(D_TWO*MFVAR_G)
Q2 = MFMEAN_G/DSQRT(D_TWO*MFVAR_G)
IICGPDF_M = D_HALF*(ETAPASS-MFMEAN_G)*(ERF(Q1)+ERF(Q2))
$ + DSQRT(MFVAR_G/(D_TWO*PI))
$ *(DEXP(-(Q1**D_TWO))-DEXP(-(Q2**D_TWO)))
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
DOUBLE PRECISION FUNCTION IICGPDF_V(MFVAR)
C==================================================================================
C PURPOSE: FUNCTION NECESSARY FOR THE COMPUTATION OF THE FIRST- AND
C SECOND-ORDER PARTIAL DERIVATIVES OF II(ETA) WITH RESPECT TO THE
C [MIXTURE FRACTION VARIANCE]
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C==================================================================================
IMPLICIT NONE
DOUBLE PRECISION MFMEAN,MFVAR,MFMEAN_G,MFVAR_G
C THESE BLOCKS ARE PASSED FROM SUBROUTINE CG_CSDR
DOUBLE PRECISION MFMEANPASS_CG
COMMON/MFMEANBLOK_CG/MFMEANPASS_CG
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION ERF
EXTERNAL ERF
DOUBLE PRECISION Q1,Q2
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
C MFVAR IS PROVIDED IN THE ARGUMENT OF FUNCTION IICGPDF_V
C MFMEAN IS PASSED FROM SUBROUTINE CG_CSDR (FIXED)
MFMEAN = MFMEANPASS_CG
CALL FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
Q1 = (ETAPASS-MFMEAN_G)/DSQRT(D_TWO*MFVAR_G)
Q2 = MFMEAN_G/DSQRT(D_TWO*MFVAR_G)
IICGPDF_V = D_HALF*(ETAPASS-MFMEAN_G)*(ERF(Q1)+ERF(Q2))
$ + DSQRT(MFVAR_G/(D_TWO*PI))
$ *(DEXP(-(Q1**D_TWO))-DEXP(-(Q2**D_TWO)))
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
DOUBLE PRECISION FUNCTION IICGPDF_MV(MFMEAN,MFVAR)
C==================================================================================
C PURPOSE: FUNCTION NECESSARY FOR THE COMPUTATION OF THE MIXED
C DERIVATIVE OF II(ETA) WITH RESPECT TO THE [MIXTURE FRACTION
C MEAN AND THE MIXTURE FRACTION VARIANCE].
C THIS FUNCTION IS INVOKED WHEN DIFFERENTIATION IS PERFORMED
C USING RIDDERS' METHOD
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C==================================================================================
IMPLICIT NONE
DOUBLE PRECISION MFMEAN,MFVAR,MFMEAN_G,MFVAR_G
C THESE BLOCKS ARE PASSED FROM SUBROUTINE CG_CSDR
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION ERF
EXTERNAL ERF
DOUBLE PRECISION Q1,Q2
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
C NOTHING TO BE TRANSFERRED HERE:
C MFMEAN AND MFVAR ARE PROVIDED IN THE ARGUMENT OF IICGPDF_MV
CALL FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
Q1 = (ETAPASS-MFMEAN_G)/DSQRT(D_TWO*MFVAR_G)
Q2 = MFMEAN_G/DSQRT(D_TWO*MFVAR_G)
IICGPDF_MV= D_HALF*(ETAPASS-MFMEAN_G)*(ERF(Q1)+ERF(Q2))
$ + DSQRT(MFVAR_G/(D_TWO*PI))
$ *(DEXP(-(Q1**D_TWO))-DEXP(-(Q2**D_TWO)))
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
DOUBLE PRECISION FUNCTION IICGPDF_MV2(MFMEAN)
C==================================================================================
C PURPOSE: FUNCTION NECESSARY FOR THE COMPUTATION OF THE MIXED
C DERIVATIVE OF II(ETA) WITH RESPECT TO THE [MIXTURE FRACTION
C MEAN AND THE MIXTURE FRACTION VARIANCE].
C THIS FUNCTION IS INVOKED WHEN DIFFERENTIATION IS PERFORMED
C USING CHEBYSHEV'S APPROXIMATION
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C MFMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C==================================================================================
IMPLICIT NONE
DOUBLE PRECISION MFMEAN,MFVAR,MFMEAN_G,MFVAR_G
C THESE BLOCKS ARE PASSED FROM SUBROUTINE CG_CSDR
DOUBLE PRECISION MFVARPASS_CG
COMMON/MFVARBLOK_CG/MFVARPASS_CG
DOUBLE PRECISION MFMEANPASS_CG
COMMON/MFMEANBLOK_CG/MFMEANPASS_CG
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION ERF,IICGPDF_V
EXTERNAL ERF,IICGPDF_V
DOUBLE PRECISION Q1,Q2
DOUBLE PRECISION MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
COMMON/MFMINMAX/MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
DOUBLE PRECISION MFVAR_MAX
DOUBLE PRECISION H_MEAN,H_VAR,LIMINF,LIMSUP
INTEGER DIFF_NCHEBCOEFS
COMMON/DIFFERENTIATORVARS1/DIFF_NCHEBCOEFS
DOUBLE PRECISION PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
COMMON/DBLECONSTANTS/PI,D_ZERO,D_ONE,D_HALF,D_TWO,D_THREE
C MFMEAN IS PROVIDED IN THE ARGUMENT OF FUNCTION IICGPDF_M
C MFVAR IS PASSED FROM SUBROUTINE CG_CSDR (FIXED)
MFVAR = MFVARPASS_CG
CALL FINDDIFFDELTA(MFMEAN,MFVAR,H_MEAN,H_VAR)
MFVAR_MAX = MFMEAN*(D_ONE-MFMEAN)
LIMINF = DMAX1(MFVAR-H_VAR,MFVAR_MIN)
LIMSUP = DMIN1(MFVAR+H_VAR,MFVAR_MAX)
MFMEANPASS_CG = MFMEAN
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS,IICGPDF_V,
$ MFVAR,1,IICGPDF_MV2)
RETURN
END
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DOUBLE PRECISION FUNCTION S2_V(MFVAR)
C==================================================================================
C PURPOSE: FUNCTION NECESSARY FOR THE COMPUTATION OF THE FIRST-ORDER
C PARTIAL DERIVATIVE OF THE VARIANCE OF THE CG-PDF WITH RESPECT TO THE
C [MIXTURE FRACTION VARIANCE]
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C==================================================================================
IMPLICIT NONE
DOUBLE PRECISION MFMEAN,MFVAR,MFMEAN_G,MFVAR_G
C THESE BLOCKS ARE PASSED FROM SUBROUTINE CG_CSDR_X
DOUBLE PRECISION MFMEANPASS_CG
COMMON/MFMEANBLOK_CG/MFMEANPASS_CG
C MFVAR IS PROVIDED IN THE ARGUMENT OF FUNCTION S2_V
C MFMEAN IS PASSED FROM SUBROUTINE (FIXED)
MFMEAN = MFMEANPASS_CG
CALL FIND_CGPDF_PARMS(MFMEAN,MFVAR,MFMEAN_G,MFVAR_G)
S2_V = MFVAR_G
RETURN
END
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DOUBLE PRECISION FUNCTION S2_M(MFMEAN)
C==================================================================================
C PURPOSE: FUNCTION NECESSARY FOR THE COMPUTATION OF THE FIRST-ORDER
C PARTIAL DERIVATIVE OF THE VARIANCE OF THE CG-PDF WITH RESPECT TO THE
C [MIXTURE FRACTION MEAN]
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C MFMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C==================================================================================