From AMS Glossary
A general methodology for constructing a smooth monotonic flux-form transport scheme.
The flux computed by a monotonic, but diffusive, low-order scheme is combined (nonlinearly) with the flux computed by an accurate, but dispersive, high-order scheme to obtain the net transport flux. The high-order scheme is locally given the greatest possible weight without introducing oscillations (ripples) to the solution.
Zalesak, S. T. 1979. Fully multidimensional flux-corrected transport algorithms for fluid. J. Comput. Phys.. 31. 335–362.