A Discussion On Finite-difference Schemes For Low Prandtl Number Rayleigh-Bénard Convection
Free (open access)
X. Luo & W.-K. Chen
The natural convection in a horizontal fluid layer heated from below has complex dynamic behaviour. For the Rayleigh-Bénard convection of low Prandtl number fluids, the calculated flow and temperature fields are very sensitive to the truncation error of numerical algorithms. Different kinds of finite-difference schemes might yield different numerical results. In the present work the error analysis of the upwind scheme and QUICK scheme for the Rayleigh-Bénard convection of low Prandtl number fluid was conducted. It shows that the upwind scheme will introduce numerical dispersion. This effect enlarges the viscosity term of the momentum equations and therefore no oscillation could be predicted. The QUICK scheme has higher calculation accuracy. However, it introduces an additional third-order differential term which might overestimate the oscillation effect. Keywords: Rayleigh-Bénard convection, low Prandtl number fluid, two-dimensional roll, finite-difference scheme, QUICK scheme. 1 Introduction The natural convection in a horizontal layer confined by two rigid boundaries and heated from below is well known as Rayleigh-Bénard convection. This phenomenon reveals series non-linear characteristics and complex dynamic behaviour and has been well investigated [1−2]. The studies of low Prandtl
Rayleigh-Bénard convection, low Prandtl number fluid, two-dimensional roll, finite-difference scheme, QUICK scheme.