channelflow.org

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% Inviscid, irrotational flow around a cylinder
% Make quiver plot of velocity and contour plot of pressure for
 
% Vx(r,theta) =  V0 (1 - a^2/R^2 cos(2 theta))
% Vy(r,theta) = -V0 a^2/r^2 sin(2 theta)
%  p(r,theta) =   2 a^2/r^2 cos(2 theta) - a^4/r^4;
 
% for a=1, V0=1, on domain -4 <= x <= 4, -4 <= x <= 4
 
%%%%%%%%% Define constants %%%%%%%%% 
V0 = 1;
a  = 1;
 
%%%%%%%%% First draw the cylinder %%%%%%%%% 
 
theta = linspace(0, 2*pi, 100);
plot(a*cos(theta), a*sin(theta), 'k-')
hold on
 
 
%%%%%%%%% Make the quiver plot of velocity %%%%%%%%% 
 
x = linspace(-4,4,21);  % quiver plots work better on coarse grids
y = linspace(-4,4,21);
[X,Y] = meshgrid(x,y);
 
R = sqrt(X.^2 + Y.^2);
Theta = atan2(Y,X);
 
% evaluate the formula for the velocity field
Vx = V0*(1 - a^2./R.^2 .* cos(2*Theta));
Vy = - V0*a^2./R.^2 .* sin(2*Theta);
 
% set Vx, Vy to zero inside the cylinder
Vx = (R > a) .* Vx;
Vy = (R > a) .* Vy;
 
% draw the quiver plot
quiver(x,y, Vx, Vy);
 
hold off
 
axis equal
axis tight
 
xlabel('x');
ylabel('y');
title('inviscid 2D flow around a cylinder')