Ay. Gelfgat et I. Tanasawa, NUMERICAL-ANALYSIS OF OSCILLATORY INSTABILITY OF BUOYANCY CONVECTION WITH THE GALERKIN SPECTRAL METHOD, Numerical heat transfer. Part A, Applications, 25(6), 1994, pp. 627-648
The Galerkin spectral method with basis functions previously introduce
d by Gelfgat [1] is applied for analysis of oscillatory instability of
convective flows in laterally heated rectangular cavities. Convection
of water and air in a square cavity, and convection of a low-Prandtl-
number fluid in a square cavity, and a cavity with a ratio length / he
ight of 4 are considered Patterns of the most unstable perturbations o
f the stream function and the temperature are presented, and mechanism
s of oscillatory instability are discussed. Comparison with other nume
rical investigations shows that the Galerkin method with divergent-fre
e basis functions, which satisfy all the boundary conditions, needs fe
wer modes than other methods using discretization of the flow region.