The convection-dominate problem is an important problem of Computational Fluid Dynamics, which is ubiquitous in science and engineering, such as plasmas simulation in nuclear fusion, semiconductor device simulation, numerical weather prediction, etc. The numerical schemes of the convection-dominate problem have been greatly developed in both theory and applications, but there is still a lot of room of improvements in the design of numerical schemes. For instance, many existing explicit schemes are subject to the stringent time-stepping constraint; it is still a lot room of improvements in designing schemes that can capture the complex structure (such as discontinuity) accurately and robustly; it is still extremely expensive to compute some practical largely multi-scale problems.