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

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.