%
%  w06conf.m -- (djm:  11 feb 2004)
%

%  initialize workspace
clear;  %close all

%  set x & y-vectors &  grid matrices ("help meshgrid")
L = 4.0;  ds = 2*L/101;
x = -L:ds:+L;  y = -L:ds:+L;
[xx,yy] = meshgrid(x,y);  
zz = xx + i*yy;  rr2 = xx.^2 + yy.^2;

%  flow around cylinder
Phi = (zz + 1./zz);

%  plot level curves of Phi in z-plane
figure(1);  clf
subplot(2,2,1);  hold on
axis([-1 1 -1 1]*L);  grid on;  axis square
title('\bf z-plane')
contour(x,y,real(Phi),[-2.0:0.5:2.0],'g--')
contour(x,y,imag(Phi),[-1.5:0.5:1.5],'k--')

th=0:2*pi/100:2*pi;
fill(cos(th),sin(th),'w')
plot(cos(th),sin(th),'m','linewidth',2)

plot(1,0,'rx')
plot(-1,0,'ro')
plot(0,1,'bx')
plot(0,-1,'bo')
plot(0,(1+sqrt(5))/2,'b*')

%  plot Phi-plane
subplot(2,2,2);  hold on
axis([-1 1 -1 1]*L);  grid on;  axis square
title('\bf \Phi-plane')
contour(x,y,real(zz),[-2.0:0.5:2.0],'g--')
contour(x,y,imag(zz),[-1.5:0.5:1.5],'k--')

contour(x,y,imag(zz),[0 0],'k')
plot([-2 2],[0 0],'m','linewidth',2)
plot(2,0,'rx')
plot(-2,0,'ro')
plot(0,0,'bx')
plot(0,0,'bo')
plot(0,1,'b*')