A numerical analysis of the performance of linear interpolation schemes coupled with finite volume method in determining velocity distribution for confined convection-diffusion turbulent flow field

Abstract

Numerical methods are widely used to obtain solutions of fluid flow problems because they well compliment experimental methods. The numerical results obtained are however never exact due to errors emanating from the scheme used in discretizing the governing equations and the flow domain. For convection-diffusion flow, the magnitudes of these errors vary depending on the scheme used to interpolate the nodal values of the flow quantities to the interfaces. The precision level of an interpolation scheme is determined by its ability to minimize these errors hence generating results that are consistent with experimental results. This paper documents the performance of three linear interpolation schemes; upwind differencing, central differencing scheme and the hybrid scheme in obtaining velocity profiles for a convection-diffusion turbulent flow field. The field variables present in the governing equations are decomposed into a mean and a fluctuating component and averaged so as to reduce the enormous scales inherent in a turbulent flow regime. The closure problem was solved using the turbulence model. The turbulence equations have been converted into discrete form using the robust finite volume discretization technique. The discretized equations are solved using a segregated pressure-based algorithm. The numerical results were validated using the benchmark results of Ampofo and Karayiannis, (2003). The results revealed that linear interpolation schemes are not appropriate in analyzing velocity distribution for confined convection-diffusion turbulent flows because the results obtained using all the three linear schemes were inconsistent with experimental results.