A Discussion On Finite-difference Schemes
For Low Prandtl Number Rayleigh-Bénard
Convection
Author(s)
X. Luo & W.-K. Chen
Abstract
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
Keywords
Rayleigh-Bénard convection, low Prandtl number fluid,
two-dimensional roll, finite-difference scheme, QUICK scheme.
Related Book
Other papers in this volume
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