1.

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 r0; 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

Answer»

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\}.\)



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