CFD Online Discussion Forums - Multiple solutions for Euler equations

You get a unique solution for lift around airfoils only if they have a sharp trailing edge and the Kutta condition is imposed there. If there are no sharp edges, it is not clear where the Kutta condition should be imposed. A good example is an ellipse at an angle of attack. So the lift prediction can not be made using invicid flow computations. The reason for this is quite simple (though it is often not explained along side the Kutta condition).

Inviscid flows can not produce vorticity in a flow that is initially irrotational except in the presence of baroclinic torque. Baroclinic torque can often be small or absolutely zero if the fluid has constant density. In that case, Euler equations can not produce any body force (lift or drag). If you solved the Euler equations around an ellipse, you would end up with zero lift (the flow pattern would look similar to a Hele-Shaw flow). For airfoils with sharp leading edges, you impose the Kutta condition the justification for which is the fact that no real fluid (i.e., viscous fluid) can fully turn around a sharp corner. This constraint generates vorticity around the airfoil and the lift. The condition itself has nothing to do with Euler equations. It is a physical observation based on real fluid behavior.

You would however end with non-zero drag if you the flow around ellipse shaped airfoils numerically. The trailing edge separation point would depend on the extent of truncation error (artifial dissipation) and so would the lift. So, two different Euler schemes would give two different lift coefficients.