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BETA.f
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executable file
·619 lines (561 loc) · 24.5 KB
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C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE BETA_PDF(ETA,NETA,MFMEAN,MFVAR,PDF)
C==================================================================================
C PURPOSE: COMPUTES THE BETA PROBABILITY DENSITY FUNCTION
C==================================================================================
C VARIABLE DESCRIPTION DATA TYPE
C -------- ----------- ---------
C
C INPUT:
C
C ETA MIXTURE FRACTION GRID DOUBLE PRECISION (ARRAY)
C NETA SIZE OF ETA AND PDF INTEGER
C MFMEAN MIXTURE FRACTION MEAN DOUBLE PRECISION
C MFVAR MIXTURE FRACTION VARIANCE DOUBLE PRECISION
C
C OUTPUT:
C
C PDF PROBABILITY DENSITY FUNCTION DOUBLE PRECISION (ARRAY)
C==================================================================================
IMPLICIT NONE
INCLUDE 'formats.h'
INTEGER IETA,NETA
DOUBLE PRECISION MFMEAN,MFVAR,ETA(NETA),PDF(NETA)
DOUBLE PRECISION G,V,W,B
DOUBLE PRECISION ETA_TEMP1(NETA-1),PDF_TEMP1(NETA-1)
DOUBLE PRECISION ETA_TEMP2(NETA-2),PDF_TEMP2(NETA-2)
DOUBLE PRECISION PDF_AREA,PDF_LA,PDF_RA,PDF_MA,PDF_SCALEFACT
DOUBLE PRECISION BETA,BETAI,TRAP
EXTERNAL BETA,BETAI,TRAP
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
LOGICAL VERBOSE,PROGRESS
COMMON/LOGICALVARS/VERBOSE,PROGRESS
G = (MFMEAN*(D_ONE-MFMEAN)/MFVAR) - D_ONE
V = MFMEAN*G
W = (D_ONE-MFMEAN)*G
B = BETA(V,W)
DO IETA = 1,NETA
PDF(IETA) = (ETA(IETA)**(V-D_ONE))
$ *((D_ONE-ETA(IETA))**(W-D_ONE))/B
ENDDO
C DETERMINE SHAPE TO SET BOUNDARY CONDITIONS
C
IF(((V.GT.D_ONE).AND.(W.GT.D_ONE))) THEN ! UNIMODAL: POSITIVELY SKEWED IF V < W
! NEGATIVELY SKEWED IF V > W
! SYMMETRIC IF V = W
PDF(1) = D_ZERO
PDF(NETA) = D_ZERO
C
ELSEIF(((V.LT.D_ONE).AND.(W.GE.D_ONE)) ! REVERSE J-SHAPED
$ .OR.((V.EQ.D_ONE).AND.(W.GT.D_ONE))) THEN
C USE THE INCOMPLETE BETA FUNCTION TO FIND THE AREA BETWEEN
C THE LEFT BOUNADRY AND THE FIRST INTERIOR GRID POINT
PDF_LA = BETAI(V,W,ETA(2))
PDF(1) = D_TWO*PDF_LA/(ETA(2)-ETA(1)) - PDF(2)
C
ELSEIF(((V.GE.D_ONE).AND.(W.LT.D_ONE)) ! J-SHAPED
$ .OR.((V.GT.D_ONE).AND.(W.EQ.D_ONE))) THEN
C USE THE INCOMPLETE BETA FUNCTION TO FIND THE AREA BETWEEN
C THE LEFT BOUNDARY AND THE LAST INTERIOR GRID POINT.
PDF_RA = D_ONE - BETAI(V,W,ETA(NETA-1))
PDF(NETA) = D_TWO*PDF_RA/(ETA(NETA)-ETA(NETA-1))
$ - PDF(NETA-1)
C
ELSEIF((V.LT.D_ONE).AND.(W.LT.D_ONE)) THEN ! U-SHAPED
C USE THE INCOMPLETE BETA FUNCTION TO FIND THE AREA BETWEEN
C THE LEFT BOUNADRY AND THE FIRST INTERIOR GRID POINT
PDF_LA = BETAI(V,W,ETA(2))
PDF(1) = D_TWO*PDF_LA/(ETA(2)-ETA(1)) - PDF(2)
C USE THE INCOMPLETE BETA FUNCTION TO FIND THE AREA BETWEEN
C THE LEFT BOUNDARY AND THE LAST INTERIOR GRID POINT
PDF_RA = D_ONE - BETAI(V,W,ETA(NETA-1))
PDF(NETA) = D_TWO*PDF_RA/(ETA(NETA)-ETA(NETA-1))
$ - PDF(NETA-1)
ENDIF
IF(VERBOSE) THEN
WRITE(*,50)' '
WRITE(*,50)'============================================='
WRITE(*,50) 'BETA: PROBABILITY DENSITY FUNCTION:'
WRITE(*,50)'============================================='
WRITE(*,100) 'V =',V
WRITE(*,100) 'W =',W
WRITE(*,100) 'B =',B
WRITE(*,50)'============================================='
WRITE(*,200)'INDEX','ETA','PDF'
WRITE(*,50)'============================================='
DO IETA = 1,NETA
WRITE(*,300) IETA, ETA(IETA), PDF(IETA)
ENDDO
WRITE(*,50)'============================================='
WRITE(*,50)' '
ENDIF
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE BETA_CV(ETA,NETA,MFMEAN,MFVAR,MFMEANGRAD,MFVARGRAD,
$ DT,VEL,CV)
C==========================================================================================
C PURPOSE: COMPUTES THE CONDITIONAL VELOCITY USING THE BETA-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)
DOUBLE PRECISION G,V,W,B,PDF(NETA)
DOUBLE PRECISION V_VAR,V_MEAN,W_VAR,W_MEAN,PDF_V,PDF_W,C1,C2
DOUBLE PRECISION ETA_TEMP
LOGICAL VERBOSE_TEMP
DOUBLE PRECISION BETA,DPSI
EXTERNAL BETA,DPSI
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
LOGICAL VERBOSE,PROGRESS
COMMON/LOGICALVARS/VERBOSE,PROGRESS
CALL CHECKPARMS(MFMEAN,MFVAR)
G = (MFMEAN*(D_ONE-MFMEAN)/MFVAR) - D_ONE
V = MFMEAN*G
W = (D_ONE-MFMEAN)*G
B = BETA(V,W)
V_MEAN = (D_TWO*MFMEAN - D_THREE*(MFMEAN**D_TWO))/MFVAR - D_ONE
W_MEAN = ((D_ONE-MFMEAN) * (D_ONE - D_THREE*MFMEAN))/MFVAR + D_ONE
V_VAR = -((MFMEAN**D_TWO)*(D_ONE-MFMEAN))/(MFVAR**D_TWO)
W_VAR = -(MFMEAN*((D_ONE-MFMEAN)**D_TWO))/(MFVAR**D_TWO)
C1 = -DPSI(V) + DPSI(V+W)
C2 = -DPSI(W) + DPSI(V+W)
C FIND THE PDF. TEMPORARILY DISABLE VERBOSITY IF ON.
VERBOSE_TEMP = VERBOSE
VERBOSE = .FALSE.
CALL BETA_PDF(ETA,NETA,MFMEAN,MFVAR,PDF)
VERBOSE = VERBOSE_TEMP
DO IETA = 1,NETA
C WRITE(*,*)'BETA CV ETA INDEX',IETA
PDF_V = PDF(IETA)*(DLOG(ETA(IETA)) + C1)
PDF_W = PDF(IETA)*(DLOG(D_ONE-ETA(IETA)) + C2)
DO I = 1,3
CV(I,IETA) = VEL(I) - (DT/ PDF(IETA))
$ *((PDF_V*V_MEAN + PDF_W*W_MEAN)*MFMEANGRAD(I)
$ + (PDF_V*V_VAR + PDF_W*W_VAR)*MFVARGRAD(I))
ENDDO
ENDDO
IF(VERBOSE) THEN
WRITE(*,50)' '
WRITE(*,50)'============================================='
WRITE(*,50) 'BETA: 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 BETA_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 BETA-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 DIIDV(NETA)
DOUBLE PRECISION IM,H_NEW,ERR,ERR_OLD,H_MEAN,H_VAR
LOGICAL VERBOSE_TEMP
DOUBLE PRECISION IIBPDF_V
EXTERNAL IIBPDF_V
DOUBLE PRECISION MFMEANPASS
COMMON/MFMEANBLOK/MFMEANPASS
DOUBLE PRECISION MFVARPASS
COMMON/MFVARBLOK/MFVARPASS
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
DOUBLE PRECISION DIFF_PDFMIN
COMMON/DIFFERENTIATORVARS3/DIFF_PDFMIN
INTEGER DIFF_NCHEBCOEFS_EXTRA
COMMON/DIFFERENTIATORVARS4/DIFF_NCHEBCOEFS_EXTRA
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 D1MACH
EXTERNAL D1MACH
INTEGER DIFF_NCHEBCOEFS_TEMP
CALL CHECKPARMS(MFMEAN,MFVAR)
C FIND THE PDF. TEMPORARILY DISABLE VERBOSITY IF ON.
VERBOSE_TEMP = VERBOSE
VERBOSE = .FALSE.
CALL BETA_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 DIIDV
LIMINF = DMAX1(MFVAR-H_VAR,MFVAR_MIN)
LIMSUP = DMIN1(MFVAR+H_VAR,MFVAR_MAX)
MFMEANPASS = MFMEAN
DO IETA = 2,NETA-1
C
C ADJUST NUMBER OF COEFS IF NECESSARY
IF(PDF(IETA).LE.DIFF_PDFMIN) THEN
DIFF_NCHEBCOEFS_TEMP = DIFF_NCHEBCOEFS+DIFF_NCHEBCOEFS_EXTRA
ELSE
DIFF_NCHEBCOEFS_TEMP = DIFF_NCHEBCOEFS
ENDIF
C WRITE(*,*)'BETA CSDR-H',IETA,PDF(IETA),DIFF_NCHEBCOEFS
C
ETAPASS = ETA(IETA)
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS_TEMP,IIBPDF_V,
$ MFVAR,1,DIIDV(IETA))
C
ENDDO
C
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*DIIDV(IETA)
ENDDO
IF(VERBOSE) THEN
WRITE(*,50)' '
WRITE(*,50)'============================================='
WRITE(*,200)'INDEX','ETA','CSDRH'
DO IETA = 1,NETA
WRITE(*,300) IETA, ETA(IETA), CSDRH(IETA)
ENDDO
WRITE(*,50)'============================================='
WRITE(*,50)' '
ENDIF
RETURN
END
C==========================================================================================
C==========================================================================================
C==========================================================================================
C==========================================================================================
SUBROUTINE BETA_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 BETA-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 IIBPDF_M,IIBPDF_V,IIBPDF_MV
EXTERNAL IIBPDF_M,IIBPDF_V,IIBPDF_MV
DOUBLE PRECISION MFMEANPASS
COMMON/MFMEANBLOK/MFMEANPASS
DOUBLE PRECISION MFVARPASS
COMMON/MFVARBLOK/MFVARPASS
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION BPDFPASS
COMMON/PPASS/BPDFPASS
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
DOUBLE PRECISION DIFF_PDFMIN
COMMON/DIFFERENTIATORVARS3/DIFF_PDFMIN
INTEGER DIFF_NCHEBCOEFS_EXTRA
COMMON/DIFFERENTIATORVARS4/DIFF_NCHEBCOEFS_EXTRA
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 D1MACH
EXTERNAL D1MACH
INTEGER DIFF_NCHEBCOEFS_TEMP
INTEGER FLAGOS,FLAGUS,IETAINTOS,IETAINTUS
CALL CHECKPARMS(MFMEAN,MFVAR)
C FIND THE PDF. TEMPORARILY DISABLE VERBOSITY IF ON.
VERBOSE_TEMP = VERBOSE
VERBOSE = .FALSE.
CALL BETA_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)
DO IETA = 2,NETA-1
C
C ADJUST NUMBER OF COEFS IF NECESSARY
IF(PDF(IETA).LE.DIFF_PDFMIN) THEN
DIFF_NCHEBCOEFS_TEMP = DIFF_NCHEBCOEFS+DIFF_NCHEBCOEFS_EXTRA
ELSE
DIFF_NCHEBCOEFS_TEMP = DIFF_NCHEBCOEFS
ENDIF
C WRITE(*,*)'BETA CSDR-I',IETA,PDF(IETA),DIFF_NCHEBCOEFS
C
C DIIDV AND D2IIDV2
LIMINF = DMAX1(MFVAR-H_VAR,MFVAR_MIN)
LIMSUP = DMIN1(MFVAR+H_VAR,MFVAR_MAX)
MFMEANPASS = MFMEAN
ETAPASS = ETA(IETA)
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS_TEMP,IIBPDF_V,
$ MFVAR,1,DIIDV(IETA))
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS_TEMP,IIBPDF_V,
$ MFVAR,2,D2IIDV2(IETA))
C
C D2IIDM2
LIMINF = DMAX1(MFMEAN-H_MEAN,MFMEAN_MIN)
LIMSUP = DMIN1(MFMEAN+H_MEAN,MFMEAN_MAX)
MFVARPASS = MFVAR
ETAPASS = ETA(IETA)
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS_TEMP,IIBPDF_M,
$ MFMEAN,2,D2IIDM2(IETA))
C
C D2IIDMDV
LIMINF = DMAX1(MFMEAN-H_MEAN,MFMEAN_MIN)
LIMSUP = DMIN1(MFMEAN+H_MEAN,MFMEAN_MAX)
MFVARPASS = MFVAR
BPDFPASS = PDF(IETA)
ETAPASS = ETA(IETA)
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS_TEMP,IIBPDF_MV,
$ MFMEAN,1,D2IIDMDV(IETA))
C
ENDDO
C
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*(PROD1*D2IIDM2(IETA) + PROD2*D2IIDV2(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===========================================================================
DOUBLE PRECISION FUNCTION IIBPDF_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 MFVAR
DOUBLE PRECISION MFMEANPASS
COMMON/MFMEANBLOK/MFMEANPASS
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION BETAI,BETA
EXTERNAL BETAI,BETA
DOUBLE PRECISION B1,B2,G,P
G = (MFMEANPASS*(1.0D0-MFMEANPASS)/MFVAR) - 1.0D0
B1 = MFMEANPASS*G
B2 = (1.0D0-MFMEANPASS)*G
P = (ETAPASS**B1)*((1.0D0-ETAPASS)**B2)/BETA(B1+1.0D0,B2+1.0D0)
IIBPDF_V = (ETAPASS-MFMEANPASS)*BETAI(B1,B2,ETAPASS)+ MFVAR*P
RETURN
END
C===========================================================================
C===========================================================================
C===========================================================================
DOUBLE PRECISION FUNCTION IIBPDF_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
DOUBLE PRECISION MFVARPASS
COMMON/MFVARBLOK/MFVARPASS
DOUBLE PRECISION ETAPASS
COMMON/EPASS/ETAPASS
DOUBLE PRECISION BETAI,BETA
EXTERNAL BETAI,BETA
DOUBLE PRECISION B1,B2,G,P
G = (MFMEAN*(1.0D0-MFMEAN)/MFVARPASS) - 1.0D0
B1 = MFMEAN*G
B2 = (1.0D0-MFMEAN)*G
P = (ETAPASS**B1)*((1.0D0-ETAPASS)**B2)/BETA(B1+1.0D0,B2+1.0D0)
IIBPDF_M = (ETAPASS-MFMEAN)*BETAI(B1,B2,ETAPASS)+ MFVARPASS*P
RETURN
END
C===========================================================================
C===========================================================================
C===========================================================================
DOUBLE PRECISION FUNCTION IIBPDF_MV(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
DOUBLE PRECISION MFVAR
DOUBLE PRECISION MFMEANPASS
COMMON/MFMEANBLOK/MFMEANPASS
DOUBLE PRECISION MFVARPASS
COMMON/MFVARBLOK/MFVARPASS
DOUBLE PRECISION BPDFPASS
COMMON/PPASS/BPDFPASS
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
DOUBLE PRECISION IIBPDF_V
EXTERNAL IIBPDF_V
DOUBLE PRECISION H_MEAN,H_VAR
INTEGER DIFF_NCHEBCOEFS
COMMON/DIFFERENTIATORVARS1/DIFF_NCHEBCOEFS
DOUBLE PRECISION DIFF_PDFMIN
COMMON/DIFFERENTIATORVARS3/DIFF_PDFMIN
INTEGER DIFF_NCHEBCOEFS_EXTRA
COMMON/DIFFERENTIATORVARS4/DIFF_NCHEBCOEFS_EXTRA
DOUBLE PRECISION LIMINF,LIMSUP
DOUBLE PRECISION H_NEW
DOUBLE PRECISION ERR,ERR_OLD
DOUBLE PRECISION MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
COMMON/MFMINMAX/MFMEAN_MAX,MFMEAN_MIN,MFVAR_MIN
DOUBLE PRECISION MFVAR_MAX
INTEGER DIFF_NCHEBCOEFS_TEMP
MFVAR = MFVARPASS
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 = MFMEAN
C ADJUST NUMBER OF COEFS IF NECESSARY
IF(BPDFPASS.LE.DIFF_PDFMIN) THEN
DIFF_NCHEBCOEFS_TEMP = DIFF_NCHEBCOEFS+DIFF_NCHEBCOEFS_EXTRA
ELSE
DIFF_NCHEBCOEFS_TEMP = DIFF_NCHEBCOEFS
ENDIF
CALL CHEBDERIV(LIMINF,LIMSUP,DIFF_NCHEBCOEFS_TEMP,IIBPDF_V,
$ MFVAR,1,IIBPDF_MV)
RETURN
END