Bifurcations of central symmetry breaking and stability of nonsymmetric states of buoyancy-driven convection in laterally heated cavities are studied numerically. The calculations are carried out using two independent numerical approaches. Stability and weakly nonlinear analysis of the calculated bifurcations are studied by the spectral Galerkin method. Time-marching calculations are carried out using the finite volume method. By applying two independent numerical approaches the subcritical steady flows, their stability, the transitions between different states and flows at small and large supercriticalities are comprehensively investigated. It is shown how these numerical techniques can be applied for interpreting a particular experimental result.