Fully multidimensional flux-corrected transport

An alternative formula is proposed for the flux limiting phase of the flux-corrected transport (fct) algorithms of Boris and Book. The advantages of the proposed new formula are three: trivial generalization to multidimensions without resort to time-step splitting; elimination of the clipping phenomenon for vanishing velocity; and reduction of the clipping phenomenon in a finite velocity field. The new method makes possible for the first time multidimensional FCT calculations for problems not amenable to time splitting, such as those involving incompressible or nearly incompressible flow.