Finite element analysis of eigenvalue problems in the stability of fluid motions - Du Toit, Helena (Not Specified, 2024)
Variational eigenvalue problems for linear and energy stability theory of buoyancy-driven flow are studied. Critical Rayleigh numbers are determined by the finite element method. The penalty method is used to approximate the incompressibility condition. We consider the stability of Boussinesq flows in a two-dimensional box in which internal heat sources are present. The influence of side walls are studied for various boundary conditions and width-to-height ratios. The temperature boundary conditions include fixed heat flux at the side walls, fixed temperature and fixed heat flux at the bottom surface, and a general convective exchange at the upper surface which includes fixed temperature and fixed heat flux as special eases. The velocity boundary conditions include rigid side walls and rigid and free upper and lower surfaces.