Question

Which of these conditions should be satisfied for a model to be realizable?

(a) Bessel’s inequality

(b) Cauchy-Schwarz inequality

(c) Holder’s inequality

(d) Jensen’s inequality

The question was asked during an interview.

The question is from Turbulence Modelling topic in section Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Correct choice is (b) Cauchy-Schwarz inequality

The explanation is: Other than the non-negativity condition, a realizable model should also satisfy the Cauchy-Schwarz inequality. According to this, the term \((\overline{u_{i}^{‘} u_{j}^{‘}})^2 ≤ \overline{u_{i}^{‘2} u_{j}^{‘2}}\). This inequality becomes important as the realizable k-ε model is non-linear.