The discussions of relationship between the bpundedness of connective schemes and Convection Boundedness Criterion (CBC)

There exists a conflicting issue of accuracy and boundedness among the convective schemes. The paper discusses the relationship between boundedness of the numerical solution and convection boundedness criterion by analyzing the characteristic of two high-order schemes, the SMART scheme and Zhang Hanxin's third-order scheme, where the SMART scheme meets convection boundedness criterion and Zhang's scheme does not. The conclusions have been drawn: (1) the CBC is a sufficient but unnecessary condition for achieving a solution of boundedness (2) Zhang Hanxin's third-order scheme does not meet convection boundedness criterion.