A numerical study of the complete system of reaction-diffusion-convection equations that govern the dynamics of Belousov-Zhabotinsky (BZ) reactive fluid has been carried out in order to better understand the interaction of chemical waves with thermally driven buoyant convection in the BZ system, It was shown by direct numerical simulation that such convection may be responsible for inducing the abrupt and continuous changes of chemical wave velocity which have been routinely observed in experiments using magnetic resonance imaging techniques, Distortions of chemical waves propagating in upright cylindrical tubes, by the axisymmetric mode of convection, were predicted by the numerical simulation that strongly resemble those observed experimentally.