A SIMPLE BUT ACCURATE MASS CONSERVATIVE, PEAK-PRESERVING, MIXING-RATIO BOUNDED ADVECTION ALGORITHM WITH FORTRAN CODE

A simplified but very accurate method for calculating advection of mix ing ratios in a mass conservative and monotonic manner is presented. T his scheme replaces the polynomial approximations of other advection a lgorithms with dual-linear segments, and employs a special treatment n ear local maxima and minima to preserve extremes very well. Before upd ating mixing ratios, fluxes at grid-cell faces are bounded to yield co nservative, monotonic, maximum-bounded and minimum-bounded solutions t o the advection equation with very little numerical diffusion, even in locally deformational Bows. ''Bounded'' here means that updated mixin g ratios never exceed local maxima or fall below local minima. If an i nitial tracer distribution is everywhere positive, the solution is pos itive-definite, but negative values can be advected. With a ''sharpeni ng'' option fully enabled, local maxima or minima are usually perfectl y preserved, and features as small as 2-3 Delta x in width are advecte d with virtually no numerical diffusion for many Courant numbers and a dvection distances. Algorithms are presented for advecting mixing rati os through variable-spaced grids in any flow, including strongly defor mational Bows. One- and two-dimensional tests of the scheme are presen ted. Relative to other advection algorithms, this scheme yields signif icantly lower peak, distribution and rms errors, especially when advec ting poorly resolved features with sizes 1-3 Delta x. Therefore this s cheme may be useful in applications where peak and minima preservation of small features is desirable. A 41-line FORTRAN advection subroutin e which can be readily applied for general advection problems is provi ded in the appendix. (C) 1998 Elsevier Science Ltd. All rights reserve d.