Question

Which of these is the compatibility equation along C– characteristic line?

(a) du + \(\frac {dp}{ρa}\) = 0

(b) du – \(\frac {dp}{ρa}\) = 0

(c) \(\frac {dpu}{ρa}\) = 0

(d) \(\frac {du}{ρa}\) = 0

I got this question during an online interview.

This key question is from Philosophy of Method of Characteristics topic in division Numerical Techniques for Steady Supersonic Flow of Aerodynamics

Answer 1

Right option is (b) du – \(\frac {dp}{ρa}\) = 0

To elaborate: C– characteristic line is the path along which the governing partial equation can be reduced to the ordinary differential equation. The compatibility equation along C– line is:

du – \(\frac {dp}{ρa}\) = 0

The compatibility equation along C+ line is:

du + \(\frac {dp}{ρa}\) = 0