High order “ZIP” differencing of convective terms

The ZIP flux form for differencing the term (wv)_x, where w is a convected quantity and v is a convective velocity, is observed to be equivalent to differencing the alternative expression wv_x + wx_v using centered second order finite differences. The advantage of this form is that one class of nonlinear computational instabilities is eliminated. Based on this observation, the extension of the ZIP flux concept to arbitrarily high order accuracy is given. Computational examples show the advantage both of the ZIP flux concept itself and of its higher order forms within the context of flux-corrected transport (FCT) algorithms.