Question

The condition that the flux limiter of a scheme should satisfy to be TVD is __________

(a) Ψr=min⁡(0.5r,r) & if r>0; Ψr=0 & if r<0

(b) Ψr=min⁡(r,1) & if r>0; Ψr=0 & if r≤0

(c) Ψr=min⁡(2r,r) & if r>0; Ψr=0 & if r≤0

(d) Ψr=min⁡(2r,2) & if r>0; Ψr=0 & if r<0

The question was posed to me in a national level competition.

This is a very interesting question from High Resolution Schemes in division High Resolution Schemes of Computational Fluid Dynamics

Answer 1

The correct answer is (c) Ψr=min⁡(2r,r) & if r>0; Ψr=0 & if r≤0

For explanation I would say: Similar to the Convection Boundedness Criterion, a flux limiter should satisfy the following criterion to be a TVD. There is a list of conditions which has to be satisfied. Simplifying and combining all of them, we get

\(\Psi = \left\{\begin{matrix}

min(2r,r) & r>0 \\

0 & r\leq 0

\end{matrix}\right\}.\)