Question

Which partial differential equation is used to define the characteristic at sonic condition?

(a) Hyperbolic partial differential equation

(b) Parabolic partial differential equation

(c) Elliptic partial differential equation

(d) Circular partial differential equation

This question was addressed to me at a job interview.

This interesting question is from Two Dimensional Irrotational Flow in portion Numerical Techniques for Steady Supersonic Flow of Aerodynamics

Answer 1

Correct option is (b) Parabolic partial differential equation

The best I can explain: At sonic condition, when Mach number is equal to 1, there is only one characteristic that passes through the flow field point. This is defined by the parabolic partial differential equation.

\(\frac {dy}{dx_{char}} = \frac {- \frac {uv}{a^{2}} ± \sqrt {M^2 – 1}}{1 – \frac {u^{2}}{a^{2}}}\)