Question

According to the Godunov’s theorem, any linear monotonic scheme will be maximum ____________

(a) first derivative

(b) first-order accurate

(c) second-order accurate

(d) second derivative

I had been asked this question during an interview.

The origin of the question is High Resolution Schemes topic in portion High Resolution Schemes of Computational Fluid Dynamics

Answer 1

Right answer is (b) first-order accurate

The best I can explain: Godunov theorem proved that any monotonic linear scheme cannot be higher-order. It will always be first order. Therefore, all the higher-order linear schemes will be non-monotonic. This is why limiters are used to construct high resolution schemes.