What is the best method now to solve advection equation?

I am solving the advection equation which is hyperbolic. Some basic techniques (shown on the page  http://www.cse.illinois.edu/iem/pde/discadvc/) are either of large oscillation or numerical diffusion.

I am striving to find a method without or with little of these problems. Or is there any post correction method to use?

Thank you all!