Tag Archives: mathematics

Aerodynamics Myths

This engineering talk discusses aerodynamics, lift generation, and a couple of common myths that persist in the aviation community. The talk was presented at the July meeting of the Texas Flying Club (http://www.texasflyingclub.com/). As a general guideline, the audience was comprised of pilots, such that the mathematics and physics are not presented as a formal proof but presented with the intent to convey understanding. One key point made is that any discussion of aerodynamics concepts must be consistent with continuity of mass, momentum, and energy. A simple freestream, source/sink, and vortex model was presented to explore a consistent understanding of aerodynamics for aviation.

One Vortex to rule them all, One Vortex to find them,
One Vortex to bring them all and in the darkness bind them
In the Land of Aerodynamics where the Myths lie

Solving a Convection PDE

The problem under consideration is a linear convection PDE.

\(\) From Farlow’s “Partial Differential Equations for Scientists and Engineers”, chapter 15 problem 3 is $$u_t = -2u_x \quad -\infty < x < \infty \quad 0<t<\infty $$$$ u(x,0)=e^{-x^2}$$

Intuition

We see that the governing equation is a linear convection problem. The characteristic velocity is 2. We expect the solution to be a shifted initial condition $$u(x,t)=e^{-(x-2t)^{2}}$$

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