Compact high-resolution algorithms for time-dependent advection on unstructured grids

A technique for constructing monotone, high resolution, multi-dimensional upwind fluctuation distribution schemes for the scalar advection equation is presented. The method combines the second-order Lax-Wendroff scheme with the upwind positive streamwise invariant (PSI) scheme via a fluctuation redistribution step, which ensures monotonicity (and which is a generalization of the flux-corrected transport approach for fluctuation distribution schemes). Furthermore, the concept of a distribution point is introduced, which, when related to the equivalent equation for the scheme, leads to a ?preferred direction? for the limiting procedure, and hence to a new distribution of the fluctuation, which retains second-order accuracy from the Lax-Wendroff scheme, even when the solution contains turning points. Experimental comparisons show that the new method compares favourably in terms of speed, accuracy and robustness with other, similar, techniques. Copyright © 2000 John Wiley & Sons, Ltd.