NUMERICAL-ANALYSIS OF OSCILLATORY INSTABILITY OF BUOYANCY CONVECTION WITH THE GALERKIN SPECTRAL METHOD

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.