A simplified but very accurate method for calculating advection of mixing ratios in a mass conservative and monotonic manner in divergent or nondivergent multidimensional flows is presented. This scheme employs a second-order-accurate, upstream approximation with monotone limiters, and uses an empirically-derived flux adjustment near local maximums and minimums that mimics and enhances the desirable behavior of higher-order advection schemes near extremes, thus greatly reducing unrealistic numerical diffusion around small features. Advection errors are reduced by a factor of 2-3 relative to higher-order schemes when advecting features with sizes smaller than 10-20 grid cells. Features larger than 10-20 grid cells in size are advected with extremely low errors that are very slightly worse than existing higher-order and computationally more expensive monotonic advection algorithms. If an initial tracer distribution is everywhere positive, advection solutions are positive-definite, but negative values can be advected with no modifications. A generalized algorithm and FORTRAN subroutine is presented for advecting mixing ratios or other conservative quantities through variable-spaced grids of one to three dimensions, including strongly deformational flows. A wide variety of one and two dimensional tests are presented and compared with other higher-order algorithms. Because of its simplicity, the number of calculations required per time step are significantly lower than higher-order schemes. For modeling applications where features smaller than 10-20 grid cells in size are being advected, this scheme will probably yield significantly more accurate advection calculations than existing higher-order, more complex numerical advection schemes
Symposium on Interdisciplinary Issues in Atmospheric Chemistry