Abstract
Totally one-sided first-order and second-order schemes are presented employing a numerically calculated characteristic speed direction and are combined into a transportive, monotonicity-preserving hybrid scheme using the method of flux correction. The first-order scheme is free of expansion shocks and artificial extrema. The hybrid scheme computes a provisional update from the first-order scheme, and then filters the second-order corrections to prevent occurrence of new extrema. Computed versus analytic results are compared for two different N-wave shocks and for a third case involving linear advection of a square wave. Results are given with and without the second-order correction. The second-order results are always superior to first-order results, with the most dramatic difference occurring in the case of linear advection. The results suggest that higher than second-order upwind differences could be substituted in the hybrid scheme to reduce truncation error even further.
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