This paper describes a class of explicit, Eulerian finite-difference algorithms for solving the continuity equation which are built tive features such as stability and exact conservation. For around a technique called ''flux correction.'' These flux-corrected finite-difference methods of a given order, typically the transport (FCT) algorithms are of indeterminate order but yield realfirst or second, the distinguishing qualitative features are istic, accurate results. In addition to the mass-conserving property determined by the error terms. The crucial importance of of most conventional algorithms, the FCT algorithms strictly mainthe form of the error becomes painfully apparent in regions tain the positivity of actual mass densities so steep gradients and inviscid shocks are handled particularly well. This first paper concenwhere and/or อณ is of order unity, that is, in many problems trates on a simple one-dimensional version of FCT utilizing SHASTA, of physical interest. a new transport algorithm for the continuity equation, which is
In regions where the mass density (x) and the flow described in detail. แฎ 1973 Academic Press velocity v(x) of Eq. ( 1) are smooth, most second-order schemes such as Lax-Wendroff [3, 4] or leapfrog [1,[4][5][6] treat the continuity equation quite adequately. In shocks