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.