A new general convective boundedness criterion (GCBC) is proposed for the construction of composite high-resolution schemes with boundedness. It is shown that the conventional convective boundedness criterion (CBC) proposed by Gaskell and Lau and the extended convective boundedness criterion (ECBC) proposed by Yu et al. are two extreme cases of the newly proposed GCBC. A new scheme based on the GCBC is proposed and tested by two problems: (1) pure convection of a stepwise profile in an oblique uniform velocity field; and (2) pure convection of a double-step profile in an oblique uniform velocity field. The numerical tests show that the new scheme (SBGCBC) is capable of capturing steep scalar gradients while maintaining boundedness of solutions.
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