1. The problem statement, all variables and given/known data I need to model the streamlines for an incompressible, irrotational flow about various symmetric bodies, starting with an ellipse 2. Relevant equations for a uniform flow in the positive x direction, psi =y for a source/sink of strength K at (xn,yn) psi = Karctan((y-yn)/(x-xn)) at any point along the body, there must be no flow across it, and hence psi = 0 3. The attempt at a solution the stream function for the whole flow = Uy+ SUM Knarctan(y/(x-xn)) (no ydisplacement as all sources are on axis) this = 0 at each of the control points y(m) (and everywhere else along the surface of the sphere, but a number of control points = to the number of sources should be appropriate) hence Knpsin(m) - Uy(m) = 0 and so I should be able to get the strengths from the following matlab code (taking U =1) Code (Text): n = 10; L = 1; D = 0.5; dx = 2*L/(n+1); xs = -L+dx:dx:L-dx; % uniformly distributed xb = -L+dx:dx:L-dx % uniformly distributed % % definition of body geometry % yb = D*sqrt(1-xb.^2./L^2); % ellipse % % plot control points % figure plot([-L xb L],[0 yb 0],[-L xb L],[0 -yb 0]) axis equal % % compute source strengths % % K = strength % for i=1:n for j=1:n a(i,j) = atan(yb(i)./(xb(i)-xs(j))); end b(i,1) = -yb(i); end K = a\b However this, results in all negative values for K, meaning a huge total removal of volume from the system instead of the expected no (or approximately no) change, and hence a set of funky streamlines that look nothing at all like a flow around an ellipse. EDIT: realised I made a mistake, should be b(i,1) = yb(i) (not -yb(i)) however this just results in all strengths being positive, so I get what looks like a funky superposition of flows around multiple semi-infinite bodies.