Linear vorticity Panel Method for Aerofoils.
Influence Coefficents Ai,j and Bi
DO I=1,NUMPAN
XC=(X(I)+X(I+1))*0.5 control point X -coord
YC=(Y(I)+Y(I+1))*0.5 control point Y -coord
DX=X(I+1)-X(I) X length of panel I
DY=Y(I+1)-Y(I) Y Length of panel I
THETI=ARCTAN2(DY,DX) angle of Panel I
SNI=SIN(THETI)
CSI=COS(THETI)
DO J=1,NUMPAN
XT=XC-X(J) X length - control point to J end of panel J
YT=YC-Y(J) Y length - control point to J end of panel J
DX=X(J+1)-X(J) X length of panel J
DY=Y(J+1)-Y(J) Y length of panel J
THETA=ARCTAN2(DY,DX) angle of panel J
CS=COS(THETA)
SN=SIN(THETA)
CSM=COS(-THETA)
SNM=SIN(-THETA)
X1=XT*CS+YT*SN
Y1=-XT*SN+YT*CS
X2=DX*CS+DY*SN
R1=SQRT(ABS(X1*X1+Y1*Y1))
R2=SQRT(ABS((X1-X2)*(X1-X2)+Y1*Y1))
TH1=ARCTAN2(Y1,X1)
TH2=ARCTAN2(Y1,(X1-X2))
IF (I.EQ.J) THEN effect of panel on itself
U1L=-0.5*(X1-X2)/X2
U2L=0.5*X1/X2
W1L=-0.15916
W2L=0.15916
ELSE
U1L=-(Y1*LOG(R2/R1)+X1*(TH2-TH1)-X2*(TH2-TH1))/(TWOPI*X2)
U2L=(Y1*LOG(R2/R1)+X1*(TH2-TH1))/(TWOPI*X2)
W1L=-((X2-Y1*(TH2-TH1))-X1*LOG(R1/R2)+X2*LOG(R1/R2))/(TWOPI*X2)
W2L=((X2-Y1*(TH2-TH1))-X1*LOG(R1/R2))/(TWOPI*X2)
ENDIF
U1=U1L*CSM+W1L*SNM
U2=U2L*CSM+W2L*SNM
W1=-U1L*SNM+W1L*CSM
W2=-U2L*SNM+W2L*CSM
IF (J.EQ.1) THEN
AMAT(I,1)=-U1*SNI+W1*CSI A(I,1)
HOLDA=-U2*SNI+W2*CSI
ELSEIF (J.EQ.NUMPAN) THEN
AMAT(I,NUMPAN)=-U1*SNI+W1*CSI+HOLDA A(I,N-1)
AMAT(I,NUMPNT)=-U2*SNI+W2*CSI A(I,N)
ELSE
AMAT(I,J)=-U1*SNI+W1*CSI+HOLDA A(I,J)
HOLDA=-U2*SNI+W2*CSI
ENDIF
ENDDO
RHS(I)=COS(ALF)*SNI-SIN(ALF)*CSI B(I)
ENDDO
SET Kutta condition
DO J=1,NUMPNT
AMAT(NUMPNT,J)=0.0 A(N,.. .) = 0
ENDDO
RHS(NUMPNT) = 0.0 B(N)
AMAT(NUMPNT,1)=1.0
A(N,1)=AMAT(NUMPNT,NUMPNT)=1.0 A(N,N)