A barely implicit correction for flux-corrected transport

In virtue of adding one elliptic equation that must be implicitly solved, the 'barely implicit correction' method presented removes the stringent sidestep limit imposed by sound speed in the explicit methods. The barely implicit method is presently combined with a flux-corrected transport algorithm, which has been rendered fourth-order by the appropriate subtraction of corrected fluxes, in order to accurately represent the sharp gradients in subsonic flows. The multigrid MGRID technique (DeVore, 1984) is used to efficiently solve the elliptic pressure equation.