Convective Flux Dependence on Upstream Flow Directionality in Finite-Volume Computations

Abstract

This article investigates upstream interpolation of convection modeling in SIMPLEC finite-volume and hybrid finite volume / element formulations of incompressible flow and heat transfer. A mass-weighted interpolation of convection variables is developed and compared against conventional upwind schemes with respect to solution convergence and accuracy. A newly developed method called NISUS (Non-Inverted Skew Upwind Scheme) includes flow directionality of multiple upstream control volumes in the convection modeling. The performance of the new methodology is studied for natural convection in a tilted cavity with Rayleigh numbers between Ra = 10³ and Ra = 10⁶. Numerical results are also studied for radial heat flow in a rotating hollow sphere with varying Peclet numbers in the range 0.01 ≤ Pe ≤ 10⁴. Mass weighting with flow directionality of convective upwinding to multiple upstream cells is shown to have beneficial impact on solution accuracy, CPU runtime, and convergence.

Support of this research from the Natural Sciences and Engineering Research Council of Canada and a University of Manitoba Graduate Fellowship (E. O. B. Ogedengbe) are gratefully acknowledged.