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p14.F
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C PROGRAM No. 14: 3D PANEL METHOD, DIRICHLET B.C. (SOURCE + DOUBLET)
C -----------------------------------------------------------------
C 3D-PANEL CODE FOR SIMPLE WING PLANFORMS. NO TIP PATCH!!!
DIMENSION QF(22,14,3),QC(20,13,3),DS(20,13,10),SIGMA(20,13)
DIMENSION DUB(20,13),DL(20,13),DD(20,13),CP(20,13),DDUBJ(13)
DIMENSION CR(21,13,12)
DIMENSION A(260,260),DUB1(260),RHS(260),IP(260)
COMMON/NO1/ DS,CROOT,CTIP,XTIP,ZTIP,B,S,AR,IB,JB,PAY
COMMON/NO2/ QF,QC,CR,SIGMA,DXW,UT,WT
C
C ==========
C INPUT DATA
C ==========
C
ALPHA1=5.0
CROOT=1.0
CTIP=1.0
XTIP=0.0
ZTIP=0.0
B=10.
VT=1.0
JB=3
C CROOT, CTIP - ROOT AND TIP CHORD, XTIP - AFT SWEEP OF TIP
C B - WING SPAN, VT - FREE STREAM SPEED, IB,JP - CHORD, SPANWISE COUNTERS
C SYMMETRY IS ASSUMED (ONLY THE SEMISPAN IS MODELED)
C CONSTANTS
DXW=100.0*B
RO=1.0
PAY=3.141592654
UT=VT*COS(ALPHA1*PAY/180.0)
WT=VT*SIN(ALPHA1*PAY/180.0)
C
C =============
C WING GEOMETRY
C =============
C
CALL GRID
IB1=IB+1
IB2=IB+2
JB1=JB+1
WRITE(6,101)
WRITE(6,102) ALPHA1,B,CROOT,S,AR,VT,IB,JB
WRITE(6,111)
WRITE(6,113)
DO 8 J=1,JB1
DO 8 I=1,IB2
8 WRITE(6,112) I,J,QF(I,J,1),QF(I,J,2),QF(I,J,3)
111 FORMAT(1H ,' I ',' J ','QF(,I,J,1) QF(I,J,2) QF(I,J,3)')
112 FORMAT(1H ,I3,3X,I3,3F12.4)
113 FORMAT(1H ,46('='))
C
C ========================
C AERODYNAMIC CALCULATIONS
C ========================
C
C INFLUENCE COEFFICIENTS CALCULATION
C
C COLLOCATION POINT COUNTER
K=0
DO 14 I=1,IB
DO 14 J=1,JB
K=K+1
L=0
RH=0
C INFLUENCING PANEL COUNTER
DO 10 I1=1,IB
DO 10 J1=1,JB
L=L+1
IF(I1.EQ.1) THEN
C CALCULATE WAKE CONTRIBUTION
C FIRST CONVERT COLLOCATION POINT TO PANEL COORDINATES,
C AND THEN CALCULATE INFLUENCE COEFFICIENTS
CALL CONVERT(QC(IB1,J1,1),QC(IB1,J1,2),QC(IB1,J1,3),
1 QC(I,J,1),QC(I,J,2),QC(I,J,3),
2 DS(IB1,J1,1),DS(IB1,J1,2),DS(IB1,J1,3),
3 DS(IB1,J1,4),DS(IB1,J1,5),DS(IB1,J1,6),
4 DS(IB1,J1,7),DS(IB1,J1,8),DS(IB1,J1,9),
5 XC,YC,ZC )
CALL INFLUENCE(WDUB,DSIG,XC,YC,ZC,
1 CR(IB1,J1,1),CR(IB1,J1,2),CR(IB1,J1,3),
2 CR(IB1,J1,4),CR(IB1,J1,5),CR(IB1,J1,6),
3 CR(IB1,J1,7),CR(IB1,J1,8),CR(IB1,J1,9),
4 CR(IB1,J1,10),CR(IB1,J1,11),CR(IB1,J1,12) )
C ADD WING S IMAGE (SYMMETRY IS ASSUMED)
CALL CONVERT(QC(IB1,J1,1),QC(IB1,J1,2),QC(IB1,J1,3),
1 QC(I,J,1),-QC(I,J,2),QC(I,J,3),
2 DS(IB1,J1,1),DS(IB1,J1,2),DS(IB1,J1,3),
3 DS(IB1,J1,4),DS(IB1,J1,5),DS(IB1,J1,6),
4 DS(IB1,J1,7),DS(IB1,J1,8),DS(IB1,J1,9),
5 XC,YC,ZC )
CALL INFLUENCE(WDUB1,DSIG,XC,YC,ZC,
1 CR(IB1,J1,1),CR(IB1,J1,2),CR(IB1,J1,3),
2 CR(IB1,J1,4),CR(IB1,J1,5),CR(IB1,J1,6),
3 CR(IB1,J1,7),CR(IB1,J1,8),CR(IB1,J1,9),
4 CR(IB1,J1,10),CR(IB1,J1,11),CR(IB1,J1,12) )
DDUBJ(J1)=WDUB+WDUB1
DMU2=DDUBJ(J1)
ELSE
DMU2=0.0
ENDIF
IF(I1.EQ.IB) DMU2=-DDUBJ(J1)
C END OF WAKE INFLUENCE CALCULATION
C CONVERT COLLOCATION POINT TO PANEL COORDINATES
CALL CONVERT(QC(I1,J1,1),QC(I1,J1,2),QC(I1,J1,3),
1 QC(I,J,1),QC(I,J,2),QC(I,J,3),
2 DS(I1,J1,1),DS(I1,J1,2),DS(I1,J1,3),
3 DS(I1,J1,4),DS(I1,J1,5),DS(I1,J1,6),
4 DS(I1,J1,7),DS(I1,J1,8),DS(I1,J1,9),
5 XC,YC,ZC )
CALL INFLUENCE(DMU,DSIG,XC,YC,ZC,
1 CR(I1,J1,1),CR(I1,J1,2),CR(I1,J1,3),
2 CR(I1,J1,4),CR(I1,J1,5),CR(I1,J1,6),
3 CR(I1,J1,7),CR(I1,J1,8),CR(I1,J1,9),
4 CR(I1,J1,10),CR(I1,J1,11),CR(I1,J1,12) )
IF((I1.EQ.I).AND.(J1.EQ.J)) DMU=-0.5
C A PANEL INFLUENCE ON ITSELF IS DMU=1/2
C
C ADD INFLUENCE OF WING S IMAGE (OTHER HALF)
CALL CONVERT(QC(I1,J1,1),QC(I1,J1,2),QC(I1,J1,3),
1 QC(I,J,1),-QC(I,J,2),QC(I,J,3),
2 DS(I1,J1,1),DS(I1,J1,2),DS(I1,J1,3),
3 DS(I1,J1,4),DS(I1,J1,5),DS(I1,J1,6),
4 DS(I1,J1,7),DS(I1,J1,8),DS(I1,J1,9),
5 XC,YC,ZC )
CALL INFLUENCE(DMU1,DSIG1,XC,YC,ZC,
1 CR(I1,J1,1),CR(I1,J1,2),CR(I1,J1,3),
2 CR(I1,J1,4),CR(I1,J1,5),CR(I1,J1,6),
3 CR(I1,J1,7),CR(I1,J1,8),CR(I1,J1,9),
4 CR(I1,J1,10),CR(I1,J1,11),CR(I1,J1,12) )
C A(K,L) - IS THE INFLUENCE MATRIX COEFFICIENT
C
A(K,L)=DMU+DMU1-DMU2
RH=RH+(DSIG+DSIG1)*SIGMA(I1,J1)
10 CONTINUE
C
C CALCULATE RHS
C
RHS(K)=RH
14 CONTINUE
C
C SOLUTION OF THE PROBLEM: A(K,L)*DUB(K)=RHS(K)
C
PRINT*
PRINT*, ' AIC'
PRINT*, '============'
PRINT*, A(1:IB*JB, 1:IB*JB)
K1=IB*JB
DO 15 K=1,K1
15 DUB1(K)=RHS(K)
PRINT*
PRINT*, ' RHS'
PRINT*, '============='
PRINT*, RHS(1:IB*JB)
CALL DECOMP(K1,260,A,IP)
16 CONTINUE
CALL SOLVER(K1,260,A,DUB1,IP)
C HERE * THE SAME ARRAY SIZE IS REQUIRED,
C AS SPECIFIED IN THE BEGINNING OF THE CODE
C
C WING DOUBLET LATTICE LISTING
C
K=0
DO 17 I=1,IB
DO 17 J=1,JB
K=K+1
17 DUB(I,J)=DUB1(K)
DO 18 J=1,JB
18 DUB(IB1,J)=DUB(1,J)-DUB(IB,J)
C
C ==================
C FORCES CALCULATION
C ==================
C
FL=0.
FD=0.
FM=0.
QUE=0.5*RO*VT*VT
DO 20 J=1,JB
DO 20 I=1,IB
C
I1=I-1
I2=I+1
J1=J-1
J2=J+1
IF(I.EQ.1) I1=1
IF(I.EQ.IB) I2=IB
IF(J.EQ.1) J1=1
IF(J.EQ.JB) J2=JB
C CHORDWISE VELOCITY
XF=0.5*(QF(I+1,J,1)+QF(I+1,J+1,1))
YF=0.5*(QF(I+1,J,2)+QF(I+1,J+1,2))
ZF=0.5*(QF(I+1,J,3)+QF(I+1,J+1,3))
XR=0.5*(QF(I,J,1)+QF(I,J+1,1))
YR=0.5*(QF(I,J,2)+QF(I,J+1,2))
ZR=0.5*(QF(I,J,3)+QF(I,J+1,3))
DX2=QC(I2,J,1)-XF
DY2=QC(I2,J,2)-YF
DZ2=QC(I2,J,3)-ZF
DX3=QC(I1,J,1)-XR
DY3=QC(I1,J,2)-YR
DZ3=QC(I1,J,3)-ZR
DL1=SQRT((XF-XR)**2+(YF-YR)**2+(ZF-ZR)**2)
DL2=SQRT(DX2**2+DY2**2+DZ2**2)
DL3=SQRT(DX3**2+DY3**2+DZ3**2)
DLL=DL1+DL2+DL3
IF(I.EQ.1) DLL=DL1/2.0+DL2
IF(I.EQ.IB) DLL=DL1/2.0+DL3
QL=-(DUB(I2,J)-DUB(I1,J))/DLL
C SPANWISE VELOCITY
DX=QC(I,J2,1)-QC(I,J1,1)
DY=QC(I,J2,2)-QC(I,J1,2)
DZ=QC(I,J2,3)-QC(I,J1,3)
DR=SQRT(DX**2+DY**2+DZ**2)
QM=-(DUB(I,J2)-DUB(I,J1))/DR
C FIRST ORDER CORRECTION FOR PANEL SWEEP
QL=QL+QM*(DX**2+DZ**2)/DR
QM=QM*(DY**2+DZ**2)/DR
QINF=UT*DS(I,J,9)-WT*DS(I,J,7)
CP(I,J)=1.0-((QINF+QL)**2+QM**2)/(VT**2)
DL(I,J)=-CP(I,J)*DS(I,J,10)*DS(I,J,9)
DD(I,J)=CP(I,J)*DS(I,J,10)*DS(I,J,7)
FL=FL+DL(I,J)
FD=FD+DD(I,J)
FM=FM+DL(I,J)*QC(I,J,1)
20 CONTINUE
CL=FL/(QUE*S)
CD=FD/(QUE*S)
CM=FM/(QUE*S*CROOT)
C
C OUTPUT
C
WRITE(6,110)
DO 21 J=1,JB
DO 21 I=1,IB1
21 WRITE(6,105)I,J,QC(I,J,1),CP(I,J),DL(I,J),DD(I,J),DUB(I,J),
1 SIGMA(I,J)
WRITE(6,104) CL,FL,CM,CD
C
C END OF PROGRAM
100 CONTINUE
C
C FORMATS
C
101 FORMAT(1H ,/,20X,'INTERNAL POTENTIAL BASED PANEL CODE',
1 /,20X,36('-'))
102 FORMAT(1H ,/,10X,'ALFA:',F10.2,8X,'B :',
1F10.2,8X,'C :',F13.2,/,10X,
2'S :',F10.2,8X,'AR :',F10.2,8X,'V(INF) :',F10.2,/,10X,
3'IB :',I10,8X,'JB :',I10,8X,/)
103 FORMAT(1H ,I3,' I ',F9.3,' II ',4(F9.3,' I '),' I ',4(F9.3,' I '))
104 FORMAT(/,1H ,'CL=',F10.4,2X,'L=',F10.4,4X,'CM=',F10.4,3X,
1'CD=',F10.4)
105 FORMAT(2I4,6F10.4)
110 FORMAT(/,1H ,2X,'I J',7X,'X',8X,'CP',8X,'DL',8X,'DD',7X,
1'DUB',6X,'SIGMA',/,68('='))
C
STOP
END
C
SUBROUTINE GRID
DIMENSION QF(22,14,3),QC(20,13,3),DS(20,13,10),SIGMA(20,13)
DIMENSION CR(21,13,12)
COMMON/NO1/ DS,CROOT,CTIP,XTIP,ZTIP,B,S,AR,IB,JB,PAY
COMMON/NO2/ QF,QC,CR,SIGMA,DXW,UT,WT
C
WRITE(6,9)
C 9 FORMAT( 1X,'AIRFOIL COORDINATES',/,1X,19('='),/,8X,'X Z')
9 FORMAT( 1X,'READING AIRFOIL COORDINATES FROM FILE surface.dat')
OPEN(UNIT=121, FILE='surface.dat')
READ(121,11) IB1
DO 10 I=1, IB1
READ(121,*) QF(I,1,1),QF(I,1,3)
10 WRITE(6,12) QF(I,1,1),QF(I,1,3)
PRINT*,'surface.dat FILE READ SUCCESSFUL'
CLOSE(121)
11 FORMAT(I3)
12 FORMAT(2F10.4)
C IB: NO. OF CHORDWISE PANELS, JB: NO. OF SPANWISE PANELS
IB=IB1-1
IB2=IB1+1
JB1=JB+1
C
C CALCULATE PANEL CORNERPOINTS; QF(I,J,(X,Y,Z))
C
DO 3 J=1,JB1
Y=B/2.0/JB*(J-1)
DXLE=XTIP*2.0*Y/B
DZLE=ZTIP*2.0*Y/B
CHORD=CROOT-(CROOT-CTIP)*2.0*Y/B
C B - FULL SPAN, DXLE - LOCAL SWEEP
DO 1 I=1,IB1
QF(I,J,1)=QF(I,1,1)*CHORD+DXLE
QF(I,J,2)=Y
QF(I,J,3)=QF(I,1,3)*CHORD+DZLE
1 CONTINUE
C WAKE FAR FIELD POINTS (QF - IS IN BODY FRAME OF REFERENCE)
QF(IB2,J,1)=QF(IB1,J,1)+DXW
QF(IB2,J,2)=QF(IB1,J,2)
QF(IB2,J,3)=QF(IB1,J,3)
3 CONTINUE
C
C WING COLLOCATION POINTS
C
DO 4 J=1,JB
DO 4 I=1,IB1
QC(I,J,1)=(QF(I,J,1)+QF(I,J+1,1)+QF(I+1,J+1,1)+QF(I+1,J,1))/4
QC(I,J,2)=(QF(I,J,2)+QF(I,J+1,2)+QF(I+1,J+1,2)+QF(I+1,J,2))/4
QC(I,J,3)=(QF(I,J,3)+QF(I,J+1,3)+QF(I+1,J+1,3)+QF(I+1,J,3))/4
C
C COMPUTATION OF CHORDWISE VECTORS DS(IJ,1,2,3),
C TANGENTIAL AND NORMAL VECTORS DS(IJ,4 TO 9), PANEL AREA DS(IJ,1-10)
C AND SOURCE STRENGTH (SIGMA)
C
CALL PANEL(QF(I,J,1),QF(I,J,2),QF(I,J,3),QF(I+1,J,1),QF(I+1,J,2),
1QF(I+1,J,3),QF(I,J+1,1),QF(I,J+1,2),QF(I,J+1,3),QF(I+1,J+1,1),
2QF(I+1,J+1,2),QF(I+1,J+1,3),DS(I,J,1),DS(I,J,2),DS(I,J,3),
3DS(I,J,4),DS(I,J,5),DS(I,J,6),DS(I,J,7),DS(I,J,8),DS(I,J,9),
4DS(I,J,10))
C
SIGMA(I,J)=DS(I,J,7)*UT+DS(I,J,9)*WT
4 CONTINUE
C
C B -IS FULL SPAN, C -ROOT CHORD, S - AREA
S=0.5*B*(CROOT+CTIP)
C=S/B
AR=B*B/S
C
C TRANSFORM THE 4 PANEL CORNER POINTS INTO PANEL FRAME OF REF.
C THIS IS NEEDED LATER TO CALCULATE THE INFLUENCE COEFFICIENTS
DO 5 J=1,JB
DO 5 I=1,IB1
CALL CONVERT(QC(I,J,1),QC(I,J,2),QC(I,J,3),
1 QF(I,J,1),QF(I,J,2),QF(I,J,3),
2 DS(I,J,1),DS(I,J,2),DS(I,J,3),
3 DS(I,J,4),DS(I,J,5),DS(I,J,6),
4 DS(I,J,7),DS(I,J,8),DS(I,J,9),
5 CR(I,J,1),CR(I,J,2),CR(I,J,3) )
CALL CONVERT(QC(I,J,1),QC(I,J,2),QC(I,J,3),
1 QF(I+1,J,1),QF(I+1,J,2),QF(I+1,J,3),
2 DS(I,J,1),DS(I,J,2),DS(I,J,3),
3 DS(I,J,4),DS(I,J,5),DS(I,J,6),
4 DS(I,J,7),DS(I,J,8),DS(I,J,9),
5 CR(I,J,4),CR(I,J,5),CR(I,J,6) )
CALL CONVERT(QC(I,J,1),QC(I,J,2),QC(I,J,3),
1 QF(I+1,J+1,1),QF(I+1,J+1,2),QF(I+1,J+1,3),
2 DS(I,J,1),DS(I,J,2),DS(I,J,3),
3 DS(I,J,4),DS(I,J,5),DS(I,J,6),
4 DS(I,J,7),DS(I,J,8),DS(I,J,9),
5 CR(I,J,7),CR(I,J,8),CR(I,J,9) )
CALL CONVERT(QC(I,J,1),QC(I,J,2),QC(I,J,3),
1 QF(I,J+1,1),QF(I,J+1,2),QF(I,J+1,3),
2 DS(I,J,1),DS(I,J,2),DS(I,J,3),
3 DS(I,J,4),DS(I,J,5),DS(I,J,6),
4 DS(I,J,7),DS(I,J,8),DS(I,J,9),
5 CR(I,J,10),CR(I,J,11),CR(I,J,12) )
5 CONTINUE
RETURN
END
C
SUBROUTINE PANEL(X1,Y1,Z1,X2,Y2,Z2,X3,Y3,Z3,X4,Y4,Z4,C1,C2,C3,
1 T1,T2,T3,V1,V2,V3,S)
C X,Y,Z-PANEL CORNERPOINTS, C,T,V-CHORDWISE, TANGENTIAL, NORMAL VECTORS
C FIRST CALCULATE CHORWISE VECTOR
A1=((X2+X4)-(X1+X3))/2.0
A2=((Y2+Y4)-(Y1+Y3))/2.0
A3=((Z2+Z4)-(Z1+Z3))/2.0
AA=SQRT(A1**2+A2**2+A3**2)
C1=A1/AA
C2=A2/AA
C3=A3/AA
C NEXT, ANOTHER VECTOR IN THIS PLANE
B1=X4-X1
B2=Y4-Y1
B3=Z4-Z1
C NORMAL VECTOR
V1=C2*B3-C3*B2
V2=B1*C3-C1*B3
V3=C1*B2-C2*B1
VV=SQRT(V1**2+V2**2+V3**2)
V1=V1/VV
V2=V2/VV
V3=V3/VV
C TANGENTIAL VECTOR
T1=V2*C3-V3*C2
T2=C1*V3-V1*C3
T3=V1*C2-V2*C1
C CALCULATION OF PANEL AREA
E1=X3-X1
E2=Y3-Y1
E3=Z3-Z1
F1=X2-X1
F2=Y2-Y1
F3=Z2-Z1
C NORMAL AREAS (F*B+B*E)
S11=F2*B3-F3*B2
S12=B1*F3-F1*B3
S13=F1*B2-F2*B1
S21=B2*E3-B3*E2
S22=E1*B3-B1*E3
S23=B1*E2-B2*E1
S=0.5*(SQRT(S11**2+S12**2+S13**2)+SQRT(S21**2+S22**2+S23**2))
RETURN
END
C
SUBROUTINE CONVERT(XO,YO,ZO,XB,YB,ZB,C1,C2,C3,T1,
*T2,T3,V1,V2,V3,XP,YP,ZP)
C TRANSFORMATION OF A FIELD POINT XB,YB,ZB INTO PANEL COORDINATES
C XO,YO,ZO - PANEL COLLOCATION POINT, C,T,V - ARE CHORDWISE,
C TANGENTIAL, AND NORMAL VECTORS
XP=(XB-XO)*C1+(YB-YO)*C2+(ZB-ZO)*C3
YP=(XB-XO)*T1+(YB-YO)*T2+(ZB-ZO)*T3
ZP=(XB-XO)*V1+(YB-YO)*V2+(ZB-ZO)*V3
RETURN
END
C
SUBROUTINE INFLUENCE(A,B,XC,YC,ZC,X1,Y1,Z1,X2,Y2,Z2,X3,Y3,Z3,
1 X4,Y4,Z4)
C DOUBLET (A) AND SOURCE (B) INFLUENCE AT POINT (XC,YC,ZC) DUE TO PANEL
C (X1,Y1,Z1,...X4,Y4,Z4), SEE KATZ & PLOTKIN PP 283-6. BY M. VEST, 1993.
PI=3.141592653580732
EP=0.000001
C EP, PANEL SIDE CUTOFF DISTANCE
C PANEL SIDE (D) DISTANCE (R), E, AND H (EQS. 10.90 & 10.92-10.94)
R1=SQRT((XC-X1)**2+(YC-Y1)**2+ZC**2)
R2=SQRT((XC-X2)**2+(YC-Y2)**2+ZC**2)
R3=SQRT((XC-X3)**2+(YC-Y3)**2+ZC**2)
R4=SQRT((XC-X4)**2+(YC-Y4)**2+ZC**2)
C
D1=SQRT((X2-X1)**2+(Y2-Y1)**2)
D2=SQRT((X3-X2)**2+(Y3-Y2)**2)
D3=SQRT((X4-X3)**2+(Y4-Y3)**2)
D4=SQRT((X1-X4)**2+(Y1-Y4)**2)
C
E1=(XC-X1)**2+ZC**2
E2=(XC-X2)**2+ZC**2
E3=(XC-X3)**2+ZC**2
E4=(XC-X4)**2+ZC**2
C
H1=(XC-X1)*(YC-Y1)
H2=(XC-X2)*(YC-Y2)
H3=(XC-X3)*(YC-Y3)
H4=(XC-X4)*(YC-Y4)
C
C SOURCE (S, B) AND DOUBLET (Q, A) INFLUENCE IN PANEL COORDINATES
C FOR TRIANGULAR PANEL THE 4TH SIDE CONTRIBUTION IS ZERO
C
IF (D1.LT.EP) THEN
S1=0.
Q1=0.
ELSE
F=(Y2-Y1)*E1-(X2-X1)*H1
G=(Y2-Y1)*E2-(X2-X1)*H2
Q1=ATAN2(ZC*(X2-X1)*(F*R2-G*R1),ZC**2*(X2-X1)**2*R1*R2+F*G)
S1=((XC-X1)*(Y2-Y1)-(YC-Y1)*(X2-X1))/D1*LOG((R1+R2+D1)/
* (R1+R2-D1))
ENDIF
C
IF (D2.LT.EP) THEN
S2=0.
Q2=0.
ELSE
F=(Y3-Y2)*E2-(X3-X2)*H2
G=(Y3-Y2)*E3-(X3-X2)*H3
Q2=ATAN2(ZC*(X3-X2)*(F*R3-G*R2),ZC**2*(X3-X2)**2*R2*R3+F*G)
S2=((XC-X2)*(Y3-Y2)-(YC-Y2)*(X3-X2))/D2*LOG((R2+R3+D2)/
* (R2+R3-D2))
ENDIF
C
IF (D3.LT.EP) THEN
S3=0.
Q3=0.
ELSE
F=(Y4-Y3)*E3-(X4-X3)*H3
G=(Y4-Y3)*E4-(X4-X3)*H4
Q3=ATAN2(ZC*(X4-X3)*(F*R4-G*R3),ZC**2*(X4-X3)**2*R3*R4+F*G)
S3=((XC-X3)*(Y4-Y3)-(YC-Y3)*(X4-X3))/D3*LOG((R3+R4+D3)/
* (R3+R4-D3))
ENDIF
C
IF (D4.LT.EP) THEN
S4=0.
Q4=0.
ELSE
F=(Y1-Y4)*E4-(X1-X4)*H4
G=(Y1-Y4)*E1-(X1-X4)*H1
Q4=ATAN2(ZC*(X1-X4)*(F*R1-G*R4),ZC**2*(X1-X4)**2*R4*R1+F*G)
S4=((XC-X4)*(Y1-Y4)-(YC-Y4)*(X1-X4))/D4*LOG((R4+R1+D4)/
* (R4+R1-D4))
ENDIF
C
C ADD CONTRIBUTIONS FROM THE 4 SIDES
C
A=-(Q1+Q2+Q3+Q4)/4./PI ! times doublet strength
IF(ABS(ZC).LT.EP) A=0.
B=-(S1+S2+S3+S4)/4./PI-ZC*A ! times source strength
RETURN
END
C
C
SUBROUTINE DECOMP(N,NDIM,A,IP)
REAL A(NDIM,NDIM),T
INTEGER IP(NDIM)
C MATRIX TRIANGULARIZATION BY GAUSSIAN ELIMINATION.
C N = ORDER OF MATRIX. NDIM = DECLARED DIMENSION OF ARRAY A.
C A = MATRIX TO BE TRIANGULARIZED.
C IP(K) , K .LT. N = INDEX OF K-TH PIVOT ROW.
C
IP(N) = 1
DO 6 K = 1, N
IF(K.EQ.N) GOTO 5
KP1 = K + 1
M = K
DO 1 I = KP1, N
IF( ABS(A(I,K)).GT.ABS(A(M,K))) M=I
1 CONTINUE
IP(K) = M
IF(M.NE.K) IP(N) = -IP(N)
T = A(M,K)
A(M,K) = A(K,K)
A(K,K) = T
IF(T.EQ.0.E0) GO TO 5
DO 2 I = KP1, N
2 A(I,K) = -A(I,K)/T
DO 4 J = KP1, N
T = A(M,J)
A(M,J) = A(K,J)
A(K,J) = T
IF(T .EQ. 0.E0) GO TO 4
DO 3 I = KP1, N
3 A(I,J) = A(I,J) + A(I,K)*T
4 CONTINUE
5 IF(A(K,K) .EQ. 0.E0) IP(N) = 0
6 CONTINUE
RETURN
END
C
SUBROUTINE SOLVER(N,NDIM,A,B,IP)
REAL A(NDIM,NDIM), B(NDIM), T
INTEGER IP(NDIM)
C SOLUTION OF LINEAR SYSTEM, A*X = B.
C N = ORDER OF MATRIX.
C NDIM = DECLARED DIMENSION OF THE ARRAY A.
C B = RIGHT HAND SIDE VECTOR.
C IP = PIVOT VECTOR OBTAINED FROM SUBROUTINE DECOMP.
C B = SOLUTION VECTOR, X.
C
IF(N.EQ.1) GOTO 9
NM1 = N - 1
DO 7 K = 1, NM1
KP1 = K + 1
M = IP(K)
T = B(M)
B(M) = B(K)
B(K) = T
DO 7 I = KP1, N
7 B(I) = B(I) + A(I,K)*T
DO 8 KB = 1, NM1
KM1 = N - KB
K = KM1 + 1
B(K) = B(K)/A(K,K)
T = -B(K)
DO 8 I = 1, KM1
8 B(I) = B(I) + A(I,K)*T
9 B(1) = B(1)/A(1,1)
RETURN
END
C TYPICAL INPUT FOR SUBROUTINE GRID
C 19 NACA 0012 AIRFOIL
C 1.000 0.000
C 0.905 -0.012
C 0.794 -0.026
C 0.655 -0.046
C 0.500 -0.058
C 0.345 -0.060
C 0.206 -0.050
C 0.095 -0.038
C 0.024 -0.021
C 0.000 0.000
C 0.024 0.021
C 0.095 0.038
C 0.206 0.050
C 0.345 0.060
C 0.500 0.058
C 0.655 0.046
C 0.794 0.026
C 0.905 0.012
C 1.000 0.000