ACCURACY AND NONUNIQUENESS ASPECTS OF NUMERICAL-SOLUTIONS OF SOME NATURAL-CONVECTION PROBLEMS

This paper examines the source of machine and mesh sensitivity and the effect of initial perturbations on the onset and development of natur al convection in fluids with unstable density stratification due eithe r to thermal or solutal gradients. Numerical simulations are presented for two problems: the liquid phase epitaxial process used to grow sem iconducting crystals and the Rayleigh Benard problem. The simulations are performed by solving the unsteady form of the momentum equations i n their stream-function vorticity form coupled with the unsteady scala r (temperature or solute) transport equation. The higher than usual me sh and round-off error sensitivity exhibited by the numerical solution s of these buoyancy-driven flows is investigated by comparing high res olution solutions on different machines and solutions on different mes hes. It is shown that flows initiated 'spontaneously', without control led perturbation, are in reality not spontaneous but rather the result of numerical noise. The onset and development of convection in such s olutions are delayed and depend on both the computational grid and the machine. It is shown that this dependency is eliminated by imposing p roper initial conditions such as controlled initial perturbations larg e enough to dominate numerical noise.