A Fully Two-Dimensional, Nonoscillatory Advection Scheme for Momentum and Scalar Transport Equations

Abstract

The advection scheme developed in this study is a fully two-dimensional and nonoscillatory extension of the one-dimensional Crowley-type mass-conserving schemes. The fully two-dimensional scheme includes new cell-to-cell fluxes directed along the local flow direction, which explicitly treat the exchange of the transported variable between all neighboring cells. Further, the distribution of the advected variable within each cell is approximated by a fully two-dimensional polynomial. Several polynomial formulations are tested. and a second-degree Chebyshev polynomial is found to he most efficient. Compared to time splitting, the fully two-dimensional approach is more accurate and more computationally efficient due to higher convergence order. Furthermore, it removes the instability associated with the use of standard time splitting in deformational flows. It is also directly applicable to momentum advection in incompressible flows.