Nonnegative, conserved scalar transport using grid-cell-centered, spectrally constrained Blackman cubics for applications on a variable-thickness mesh

Abstract

A flux-formulated advection scheme is developed based on local, grid-cell-centered cubic polynomials. The coefficients of these polynomials involve a weighted admixture of locally and globally defined derivatives and are subjected to constraints developed from spectral theory. The continuous polynomials are subsequently replaced with a multipoint representation that eliminates the possibility of negative concentrations and conserves mass exactly. The performance of this new, low-numerical-diffusion transport scheme is compared with several other transport schemes. -Author