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Application of differential quadrature method to simulate natural convection in a concentric annulus
Author(s) -
Shu C.
Publication year - 1999
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19990830)30:8<977::aid-fld873>3.0.co;2-j
Subject(s) - annulus (botany) , quadrature (astronomy) , concentric , mathematics , grid , fourier series , rayleigh scattering , natural convection , mathematical analysis , computer science , geometry , convection , physics , mechanics , optics , materials science , composite material
In this paper, the Fourier expansion‐based differential quadrature (FDQ) and 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 studied in detail. It was found that both PDQ and FDQ can obtain accurate numerical solutions using just a few grid points and requiring very small computational 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 applied to a non‐periodic problem (half of annulus), it can achieve the same order 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. However, its efficiency is greatly reduced for the high Rayleigh numbers. The benchmark solution for Ra= 10 2 , 10 3 , 3×10 3 , 6×10 3 , 10 4 , 5×10 4 are also presented in the paper. Copyright © 1999 John Wiley & Sons, Ltd.