Although the convective boundedness criterion proposed by Gaskell and Lau (G/L-CBC) has been proven effective by many numerical cases and accepted as a sufficient condition for a convective scheme with boundedness, there is still some confusion in its derivation. A more rigorous analysis of the convective boundedness criterion is presented based on a newly proposed four-node normalized variable analysis method. The greatest improvement of the presented study is amending the interpolative boundedness condition proposed by Gaskell and Lau (from “the face value \(\phi_{i-1/2}\) lies inside the bounds of its adjacent values at nodes i and i-1” to “the node value \(\phi_i\) lies inside the bounds of its adjacent faces’ values  \(\phi_{i-1/2}\) and \(\phi_{i+1/2}\)”) based on the nature of the finite volume method (FVM). The newly obtained boundedness region on the normalized variable diagram (NVD) is consistent with G/L-CBC within \(0\leq\tilde{\phi}\leq1\), but wider than G/L-CBC in the range of \(\tilde{\phi}<0\) and \(\tilde{\phi}>1\). Numerical practice proves that the convective boundedness criterion proposed in this work is more appropriate than the ones in previous studies. In addition, the stability of a convective scheme can also be indicated directly in the four-node NVD for a convection-diffusion case.
 

Computational fluid dynamics,Convective boundedness criterion,Convective discretization scheme,Normalized variable diagram