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)