Application of differential quadrature method to simulate natural convection in a concentric annulus

In this paper, the Fourier expansion-based differential quadrature (FDQ) an d the polynomial-based differential quadrature (PDQ) methods are applied to simulate the natural convection in a concentric annulus with a horizontal axis. The comparison and grid independence of PDQ and FDQ results are studi ed in detail. It was found that both PDQ and FDQ can obtain accurate numeri cal solutions using just a few grid points and requiring very small computa tional resources. It was demonstrated in the paper that the FDQ method can be applied to a periodic problem or a non-periodic problem. When FDQ is app lied to a non-periodic problem (half of annulus), it can achieve the same o rder of accuracy as the PDQ method. And when FDQ is applied to the periodic problem (whole annulus), it is very efficient for low Rayleigh numbers. Ho wever, its efficiency is greatly reduced for the high Rayleigh numbers. The benchmark solution for Ra = 10(2), 10(3), 3 x 10(3), 6 x 10(3), 10(4), 5 x 10(4) are also presented in the paper. Copyright (C) 1999 John Wiley & Son s, Ltd.