Question

The Riemann invariants are constant along the characteristic line.

(a) True

(b) False

I got this question by my college director while I was bunking the class.

I would like to ask this question from Philosophy of Method of Characteristics topic in section Numerical Techniques for Steady Supersonic Flow of Aerodynamics

Answer 1

Correct choice is (a) True

Best explanation: Riemann invariants are obtained by integrating the two compatibility equations obtained along the characteristic lines C+ and C–. These are as follows:

J+ = u + ∫\(\frac {dp}{ρa}\) = const

J– = u – ∫\(\frac {dp}{ρa}\) = const

J+ and J– are hence constant along the characteristic lines.