Overshoot/Undershoot behaviour predicted by some high-resolution composite schemes following G/L CBC

Byline: Jin-Jia Wei, Bo Yu, Wen-Quan Tao, Yasuo Kawaguchi Analysis of a discretised scalar equation shows that high-resolution composite schemes containing a characteristic line of ˆφf = 1 on the Normalised Variable Diagram (NVD), although following the Convective Boundedness Criterion (CBC) proposed by Gaskell and Lau, may result in numerical results dependent on initial field, and thus may predict overshoot/undershoot behaviour. The finding is confirmed by testing a case of pure convection of a double-step profile in an oblique uniform velocity field. A slightly revised CBC is proposed by excluding the line of ˆφf = 1 from the CBC region, and can predict bounded numerical results without losing accuracy.