Question: How would you go about calculating aerodynamics

Daniel Bearup answered on 29 Jan 2020:

Well, aerodynamics involve the movement of a fluid (air) around a structure (a plane, car, or building). So the starting point is the system of partial differential equations called the Navier-Stokes equations (https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations). These equations are so complicated that they cannot be solved algebraically.

However, it is often not necessary to use the full set of equations, we can simplify them by making assumptions about the real world system that we are interested in. Then we might be able to work with them algebraically. Alternatively we would need to find an approximate solution using a numerical algorithm.

One problem, is that it isn’t known if these equations always have a well-behaved solution, it might be possible for the solution to go to infinity. If that happens the result isn’t particularly meaningful to aerodynamics and it might result in a dangerous problem. So one of the major challenges in maths is to work out whether the Navier-Stokes equations do have well-behaved solutions.