Abstract
A multidimensional finite volume gas-kinetic BGK scheme for obtaining nu-merical solutions to the compressible Navier-Stokes equations with external source terms is outlined in this thesis. This scheme is applied to the case of a perfect gas with constant dynamic viscosity and thermal conductivity confined in a cube whose upper and lower boundaries are maintained at fixed temperatures. The resulting convection problem has been studied. The on-set of 2D roll has been reproduced and compared with the analytical results. The effect of varying some characteristic parameters on the steady properties of the 2D convection have been tested. Good results were obtained.