ETBFCT: a solver for one-dimensional transport equations

A robust numerical technique for solving a wide class of one-dimensional transport-dominated problems is presented. The method is a finite-difference technique called flux-corrected transport (FCT) that preserves stability without sacrificing accuracy by exploiting the property of positivity. The specific algorithm, ETBFCT, developed by Boris at the Naval Research Laboratory, has been vectorized for execution on the Cray Computer. A single call to ETBFCT solving a transport equation on a 100 node mesh typically takes less than 0.001 cpu second on the Cray. ETBFCT has been modularized to be used as a library routine. The methodology and theory of FCT is discussed, enabling the potential user to make an informed judgment as to the usefulness of the method. The routines comprising the FCT algorithm and the mechanics for their use are then described. Finally, two example transport problems are solved to illustrate the use of ETBFCT. Fortran listings of the algorithm are included