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|
SUBROUTINE OSMAP(RSP,WSP,HSP,
& ALFR,
& ALFR_R, ALFR_W, ALFR_H,
& ALFRW_R,ALFRW_W,ALFRW_H ,
& ALFI,
& ALFI_R, ALFI_W, ALFI_H,
& ALFIW_R,ALFIW_W,ALFIW_H , OK)
C---------------------------------------------------------------------
C
C Returns real and imaginary parts of complex wavenumber (Alpha)
C eigenvalue from Orr-Sommerfeld spatial-stability solution
C with mean profiles characterized by shape parameter H.
C Also returns the sensitivities of Alpha with respect to the
C input parameters.
C
C The eigenvalue Alpha(Rtheta,W,H) is stored as a 3-D array at
C discrete points, which is then interpolated to any (Rtheta,W,H)
C via a tricubic spline. The spline coordinates actually used are:
C
C RL = log10(Rtheta)
C WL = log10(W) + 0.5 log10(Rtheta)
C HL = H
C
C
C Input:
C ------
C RSP momentum thickness Reynolds number Rtheta = Theta Ue / v
C WSP normalized disturbance frequency W = w Theta/Ue
C HSP shape parameter of mean profile H = Dstar/Theta
C
C Output:
C -------
C ALFR real part of complex wavenumber * Theta
C ALFR_R d(ALFR)/dRtheta
C ALFR_W d(ALFR)/dW
C ALFR_H d(ALFR)/dH
C ALFRW_R d(dALFR/dW)/dRtheta
C ALFRW_W d(dALFR/dW)/dW
C ALFRW_H d(dALFR/dW)/dH
C
C ALFI imag part of complex wavenumber * Theta
C ALFI_R d(ALFI)/dRtheta
C ALFI_W d(ALFI)/dW
C ALFI_H d(ALFI)/dH
C ALFIW_R d(dALFI/dW)/dRtheta
C ALFIW_W d(dALFI/dW)/dW
C ALFIW_H d(dALFI/dW)/dH
C
C OK T if look up was successful; all values returned are valid
C F if point fell outside (RL,WL) spline domain limits;
C all values (ALFR, ALFR_R, etc.) are returned as zero.
C Exception: If points only falls outside HL spline limits,
C then the HL limit is used and an ALFR value is calculated,
C but OK is still returned as F.
C
C---------------------------------------------------------------------
LOGICAL OK
C
C
REAL B(2,2), BR(2,2), BW(2,2), BH(2,2),
& BRW(2,2),BRH(2,2),BWH(2,2),BRWH(2,2)
REAL C(2) , CR(2) , CW(2) , CH(2) ,
& CRW(2) ,CRH(2) ,CWH(2) ,CRWH(2)
C
REAL AINT(2),
& AINT_R(2), AINT_W(2), AINT_H(2),
& AINTW_R(2),AINTW_W(2),AINTW_H(2)
C
PARAMETER (NRX=31, NWX=41, NHX=21)
COMMON /AICOM_I/ NR, NW, NH,
& IC1, IC2,
& IW1(NHX), IW2(NHX), IR1(NHX),IR2(NHX)
C
C---------------------------------------------------------------
C---- single-precision OS data file
REAL*4 RLSP, WLSP, HLSP,
& RINCR, WINCR, RL, WL, HL,
& A, AR, AW, AH, ARW, ARH, AWH, ARWH
C
C---- native-precision OS data file
c REAL RLSP, WLSP, HLSP,
c & RINCR, WINCR, RL, WL, HL,
c & A, AR, AW, AH, ARW, ARH, AWH, ARWH
C---------------------------------------------------------------
C
COMMON /AICOM_R/ RINCR, WINCR, RL(NRX), WL(NWX), HL(NHX),
& A(NRX,NWX,NHX,2),
& AR(NRX,NWX,NHX,2),
& AW(NRX,NWX,NHX,2),
& AH(NRX,NWX,NHX,2),
& ARW(NRX,NWX,NHX,2),
& ARH(NRX,NWX,NHX,2),
& AWH(NRX,NWX,NHX,2),
& ARWH(NRX,NWX,NHX,2)
C
LOGICAL LOADED, NOFILE
SAVE LOADED, NOFILE
C
C---- set OSFILE to match the absolute OS database filename
CHARACTER*128 OSFILE
INTEGER LOSF
DATA OSFILE / '/var/local/codes/orrs/osmap.dat' /
c DATA OSFILE
c &/'/afs/athena.mit.edu/course/16/16_d0006/Codes/orrs/osmap_lx.dat'/
C
DATA LOADED, NOFILE / .FALSE. , .FALSE. /
C
C---- set ln(10) for derivatives of log10 function
DATA AL10 /2.302585093/
C
C
C---- set default returned variables in case of error, or OS map not available
ALFR = 0.0
ALFR_R = 0.0
ALFR_W = 0.0
ALFR_H = 0.0
ALFRW_R = 0.0
ALFRW_W = 0.0
ALFRW_H = 0.0
C
ALFI = 0.0
ALFI_R = 0.0
ALFI_W = 0.0
ALFI_H = 0.0
ALFIW_R = 0.0
ALFIW_W = 0.0
ALFIW_H = 0.0
C
OK = .FALSE.
C
IF(NOFILE) RETURN
C
IF(LOADED) GO TO 9
C--------------------------------------------------------------------
C---- first time OSMAP is called ... load in 3-D spline data
C
CALL GETOSFILE(OSFILE,LOSF)
IF(LOSF.EQ.0) GO TO 800
C
NR = 0
NW = 0
NH = 0
C
LU = 31
OPEN(UNIT=LU,FILE=OSFILE(1:LOSF),STATUS='OLD',
& FORM='UNFORMATTED',ERR=900)
C
READ(LU) NR, NW, NH
C
IF(NR.GT.NRX .OR.
& NW.GT.NWX .OR.
& NH.GT.NHX ) THEN
WRITE(*,*) 'OSMAP: Array limit exceeded.'
IF(NR.GT.NRX) WRITE(*,*) ' Increase NRX to', NR
IF(NW.GT.NWX) WRITE(*,*) ' Increase NWX to', NW
IF(NH.GT.NHX) WRITE(*,*) ' Increase NHX to', NH
STOP
ENDIF
C
READ(LU) (RL(IR), IR=1,NR)
READ(LU) (WL(IW), IW=1,NW)
READ(LU) (HL(IH), IH=1,NH)
READ(LU) (IR1(IH),IR2(IH),IW1(IH),IW2(IH), IH=1,NH)
C
DO IC = 2, 1, -1
DO IH=1, NH
DO IW=IW1(IH), IW2(IH)
READ(LU,END=5)
& ( A(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
READ(LU) ( AR(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
READ(LU) ( AW(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
READ(LU) ( AH(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
READ(LU) ( ARW(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
READ(LU) ( ARH(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
READ(LU) ( AWH(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
READ(LU) (ARWH(IR,IW,IH,IC), IR=IR1(IH),IR2(IH))
ENDDO
ENDDO
ENDDO
C
5 CONTINUE
IF(IH.LT.NH) THEN
C----- only imaginary part is available
IC1 = 2
IC2 = 2
ELSE
C----- both real and imaginary parts available
IC1 = 1
IC2 = 2
ENDIF
CLOSE(LU)
C
C
RINCR = (RL(NR) - RL(1))/FLOAT(NR-1)
WINCR = (WL(NW) - WL(1))/FLOAT(NW-1)
LOADED = .TRUE.
C
C--------------------------------------------------------------------
9 CONTINUE
C
C
IF(NR.EQ.0 .OR. NW.EQ.0 .OR. NH.EQ.0) THEN
C----- map not available for some reason (OPEN or READ error on osmap.dat?)
OK = .FALSE.
RETURN
ENDIF
C
C---- define specified spline coordinates
RLSP = ALOG10(RSP)
WLSP = ALOG10(WSP) + 0.5*RLSP
HLSP = HSP
C
C---- assume map limits will not be exceeded
OK = .TRUE.
C
C---- find H interval
DO IH = 2, NH
IF(HL(IH) .GE. HLSP) GO TO 11
ENDDO
IH = NH
11 CONTINUE
C
IF(HLSP.LT.HL(1) .OR. HLSP.GT.HL(NH)) THEN
CCC OK = .FALSE.
CCC WRITE(*,*) 'Over H limits. R w H:', RSP,WSP,HSP
CCC RETURN
HLSP = MAX( HL(1) , MIN( HL(NH) , HLSP ) )
ENDIF
C
C---- find R interval
IR = INT((RLSP-RL(1))/RINCR + 2.001)
IR1X = MAX( IR1(IH) , IR1(IH-1) )
IR2X = MIN( IR2(IH) , IR2(IH-1) )
IF(IR-1.LT.IR1X .OR. IR.GT.IR2X) THEN
OK = .FALSE.
CCC WRITE(*,*) 'Over R limits. R w H:', RSP,WSP,HSP
CCC RETURN
IR = MAX( IR1X+1 , MIN( IR2X , IR ) )
RLSP = MAX( RL(1) , MIN( RL(NR) , RLSP ) )
ENDIF
C
C---- find W interval
IW = INT((WLSP-WL(1))/WINCR + 2.001)
IW1X = MAX( IW1(IH) , IW1(IH-1) )
IW2X = MIN( IW2(IH) , IW2(IH-1) )
IF(IW-1.LT.IW1X .OR. IW.GT.IW2X) THEN
OK = .FALSE.
CCC WRITE(*,*) 'Over w limits. R w H:', RSP,WSP,HSP
CCC RETURN
IW = MAX( IW1X+1 , MIN( IW2X , IW ) )
WLSP = MAX( WL(1) , MIN( WL(NW) , WLSP ) )
ENDIF
C
DRL = RL(IR) - RL(IR-1)
DWL = WL(IW) - WL(IW-1)
DHL = HL(IH) - HL(IH-1)
TR = (RLSP - RL(IR-1)) / DRL
TW = (WLSP - WL(IW-1)) / DWL
TH = (HLSP - HL(IH-1)) / DHL
C
TR = MAX( 0.0 , MIN( 1.0 , TR ) )
TW = MAX( 0.0 , MIN( 1.0 , TW ) )
TH = MAX( 0.0 , MIN( 1.0 , TH ) )
C
C---- compute real and imaginary parts
DO 1000 IC = IC1, IC2
C
C---- evaluate spline in Rtheta at the corners of HL,WL cell
DO 20 KH=1, 2
JH = IH + KH-2
DO 205 KW=1, 2
JW = IW + KW-2
A1 = A (IR-1,JW,JH,IC)
AR1 = AR (IR-1,JW,JH,IC)
AW1 = AW (IR-1,JW,JH,IC)
AH1 = AH (IR-1,JW,JH,IC)
ARW1 = ARW (IR-1,JW,JH,IC)
ARH1 = ARH (IR-1,JW,JH,IC)
AWH1 = AWH (IR-1,JW,JH,IC)
ARWH1 = ARWH(IR-1,JW,JH,IC)
C
A2 = A (IR ,JW,JH,IC)
AR2 = AR (IR ,JW,JH,IC)
AW2 = AW (IR ,JW,JH,IC)
AH2 = AH (IR ,JW,JH,IC)
ARW2 = ARW (IR ,JW,JH,IC)
ARH2 = ARH (IR ,JW,JH,IC)
AWH2 = AWH (IR ,JW,JH,IC)
ARWH2 = ARWH(IR ,JW,JH,IC)
C
DA1 = DRL*AR1 - A2 + A1
DA2 = DRL*AR2 - A2 + A1
DAW1 = DRL*ARW1 - AW2 + AW1
DAW2 = DRL*ARW2 - AW2 + AW1
DAH1 = DRL*ARH1 - AH2 + AH1
DAH2 = DRL*ARH2 - AH2 + AH1
DAWH1 = DRL*ARWH1 - AWH2 + AWH1
DAWH2 = DRL*ARWH2 - AWH2 + AWH1
C
C-------- set ALFI, dALFI/dWL, dALFI/dHL, d2ALFI/dHLdWL
B(KW,KH) = (1.0-TR)* A1 + TR* A2
& + ((1.0-TR)*DA1 - TR*DA2 )*(TR-TR*TR)
BW(KW,KH) = (1.0-TR)* AW1 + TR* AW2
& + ((1.0-TR)*DAW1 - TR*DAW2 )*(TR-TR*TR)
BH(KW,KH) = (1.0-TR)* AH1 + TR* AH2
& + ((1.0-TR)*DAH1 - TR*DAH2 )*(TR-TR*TR)
BWH(KW,KH) = (1.0-TR)* AWH1 + TR* AWH2
& + ((1.0-TR)*DAWH1 - TR*DAWH2)*(TR-TR*TR)
C
C-------- also, the RL derivatives of the quantities above
BR(KW,KH) = (A2 - A1
& + (1.0-4.0*TR+3.0*TR*TR)*DA1 + (3.0*TR-2.0)*TR*DA2 )/DRL
BRW(KW,KH) = (AW2 - AW1
& + (1.0-4.0*TR+3.0*TR*TR)*DAW1 + (3.0*TR-2.0)*TR*DAW2 )/DRL
BRH(KW,KH) = (AH2 - AH1
& + (1.0-4.0*TR+3.0*TR*TR)*DAH1 + (3.0*TR-2.0)*TR*DAH2 )/DRL
BRWH(KW,KH) = (AWH2 - AWH1
& + (1.0-4.0*TR+3.0*TR*TR)*DAWH1 + (3.0*TR-2.0)*TR*DAWH2)/DRL
C
205 CONTINUE
20 CONTINUE
C
C---- evaluate spline in HL at the two WL-interval endpoints
DO 30 KW=1, 2
B1 = B (KW,1)
BR1 = BR (KW,1)
BW1 = BW (KW,1)
BH1 = BH (KW,1)
BRW1 = BRW (KW,1)
BRH1 = BRH (KW,1)
BWH1 = BWH (KW,1)
BRWH1 = BRWH(KW,1)
C
B2 = B (KW,2)
BR2 = BR (KW,2)
BW2 = BW (KW,2)
BH2 = BH (KW,2)
BRW2 = BRW (KW,2)
BRH2 = BRH (KW,2)
BWH2 = BWH (KW,2)
BRWH2 = BRWH(KW,2)
C
DB1 = DHL*BH1 - B2 + B1
DB2 = DHL*BH2 - B2 + B1
DBR1 = DHL*BRH1 - BR2 + BR1
DBR2 = DHL*BRH2 - BR2 + BR1
DBW1 = DHL*BWH1 - BW2 + BW1
DBW2 = DHL*BWH2 - BW2 + BW1
DBRW1 = DHL*BRWH1 - BRW2 + BRW1
DBRW2 = DHL*BRWH2 - BRW2 + BRW1
C
C------ set ALFI, dALFI/dRL, dALFI/dWL
C(KW) = (1.0-TH)* B1 + TH* B2
& + ((1.0-TH)*DB1 - TH*DB2 )*(TH-TH*TH)
CR(KW) = (1.0-TH)* BR1 + TH* BR2
& + ((1.0-TH)*DBR1 - TH*DBR2 )*(TH-TH*TH)
CW(KW) = (1.0-TH)* BW1 + TH* BW2
& + ((1.0-TH)*DBW1 - TH*DBW2 )*(TH-TH*TH)
CRW(KW) = (1.0-TH)* BRW1 + TH* BRW2
& + ((1.0-TH)*DBRW1 - TH*DBRW2)*(TH-TH*TH)
C
C------ also, the HL derivatives of the quantities above
CH(KW) = (B2 - B1
& + (1.0-4.0*TH+3.0*TH*TH)*DB1 + (3.0*TH-2.0)*TH*DB2 )/DHL
CRH(KW) = (BR2 - BR1
& + (1.0-4.0*TH+3.0*TH*TH)*DBR1 + (3.0*TH-2.0)*TH*DBR2 )/DHL
CWH(KW) = (BW2 - BW1
& + (1.0-4.0*TH+3.0*TH*TH)*DBW1 + (3.0*TH-2.0)*TH*DBW2 )/DHL
CRWH(KW) = (BRW2 - BRW1
& + (1.0-4.0*TH+3.0*TH*TH)*DBRW1 + (3.0*TH-2.0)*TH*DBRW2)/DHL
C
30 CONTINUE
C
C---- evaluate cubic in WL
C1 = C (1)
CR1 = CR (1)
CW1 = CW (1)
CH1 = CH (1)
CRW1 = CRW (1)
CRH1 = CRH (1)
CWH1 = CWH (1)
CRWH1 = CRWH(1)
C
C2 = C (2)
CR2 = CR (2)
CW2 = CW (2)
CH2 = CH (2)
CRW2 = CRW (2)
CRH2 = CRH (2)
CWH2 = CWH (2)
CRWH2 = CRWH(2)
C
DC1 = DWL*CW1 - C2 + C1
DC2 = DWL*CW2 - C2 + C1
DCH1 = DWL*CWH1 - CH2 + CH1
DCH2 = DWL*CWH2 - CH2 + CH1
DCR1 = DWL*CRW1 - CR2 + CR1
DCR2 = DWL*CRW2 - CR2 + CR1
CC DCRH1 = DWL*CRWH1 - CRH2 + CRH1
CC DCRH2 = DWL*CRWH2 - CRH2 + CRH1
C
C---- set AINT, dAINT/dRL, dAINT/dHL
AINT(IC) = (1.0-TW)* C1 + TW* C2
& + ((1.0-TW)*DC1 - TW*DC2 )*(TW-TW*TW)
AINT_RL = (1.0-TW)* CR1 + TW* CR2
& + ((1.0-TW)*DCR1 - TW*DCR2 )*(TW-TW*TW)
AINT_HL = (1.0-TW)* CH1 + TW* CH2
& + ((1.0-TW)*DCH1 - TW*DCH2 )*(TW-TW*TW)
C
C---- also, the WL derivatives of the quantities above
AINT_WL = (C2 - C1
& + (1.0-4.0*TW+3.0*TW*TW)*DC1 + (3.0*TW-2.0)*TW*DC2 )/DWL
AINTW_RL = (CR2 - CR1
& + (1.0-4.0*TW+3.0*TW*TW)*DCR1 + (3.0*TW-2.0)*TW*DCR2 )/DWL
AINTW_HL = (CH2 - CH1
& + (1.0-4.0*TW+3.0*TW*TW)*DCH1 + (3.0*TW-2.0)*TW*DCH2 )/DWL
C
AINTW_WL = ((6.0*TW-4.0)*DC1 + (6.0*TW-2.0)*DC2 )/DWL**2
C
C
C---- convert derivatives wrt to spline coordinates (RL,WL,HL) into
C- derivatives wrt input variables (Rtheta,f,H)
AINT_R(IC) = (AINT_RL + 0.5*AINT_WL) / (AL10 * RSP)
AINT_W(IC) = (AINT_WL ) / (AL10 * WSP)
AINT_H(IC) = AINT_HL
C
AINTW_R(IC) = (AINTW_RL + 0.5*AINTW_WL) / (AL10**2 * WSP*RSP)
AINTW_W(IC) = (AINTW_WL - AL10*AINT_WL) / (AL10**2 * WSP*WSP)
AINTW_H(IC) = AINTW_HL / (AL10 * WSP )
C
1000 CONTINUE
C
ALFR = AINT(1)
ALFR_R = AINT_R(1)
ALFR_W = AINT_W(1)
ALFR_H = AINT_H(1)
ALFRW_R = AINTW_R(1)
ALFRW_W = AINTW_W(1)
ALFRW_H = AINTW_H(1)
C
ALFI = AINT(2)
ALFI_R = AINT_R(2)
ALFI_W = AINT_W(2)
ALFI_H = AINT_H(2)
ALFIW_R = AINTW_R(2)
ALFIW_W = AINTW_W(2)
ALFIW_H = AINTW_H(2)
C
C---- if we're within the spline data space, the derivatives are valid
IF(OK) RETURN
C
C---- if not, the ai value is clamped, and its derivatives are zero
ALFR_R = 0.0
ALFR_W = 0.0
ALFR_H = 0.0
ALFRW_R = 0.0
ALFRW_W = 0.0
ALFRW_H = 0.0
C
ALFI_R = 0.0
ALFI_W = 0.0
ALFI_H = 0.0
ALFIW_R = 0.0
ALFIW_W = 0.0
ALFIW_H = 0.0
C
RETURN
C
C--------------------------------------------------------
C---- pick up here if OS file not given
800 CONTINUE
WRITE(*,*)'OSMAP: Environment variable OSMAP not defined'
WRITE(*,*)' Must be set to Orr-Sommerfeld database filename'
C---- don't try again
NOFILE = .TRUE.
RETURN
C
C--------------------------------------------------------
C---- pick up here for file open error
900 CONTINUE
WRITE(*,*)
WRITE(*,*)'OSMAP: Orr-Sommerfeld database file not found: ',
& OSFILE(1:LOSF)
WRITE(*,*)' Will return zero amplification rates'
C---- don't try again
NOFILE = .TRUE.
OK = .FALSE.
C
RETURN
END ! OSMAP
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