Flame dynamics in wide tubes with ideally adiabatical and slip walls is studied by means of direct numerical simulations of the complete set of hydrodynamical equations including thermal conduction, fuel diffusion, viscosity, and chemical kinetics. Stability limits of curved stationary flames in wide tubes and the hydrodynamic instability of these flames (the secondary Darrieus-Landau instability) are investigated. The stability limits found in the present numerical simulations are in a very good agreement with the previous theoretical predictions. It is obtained that close to the stability limits the secondary Darrieus-Landau instability results in an extra cusp at the flame front. It is shown that the curved flames subject to the secondary Darrieus-Landau instability propagate with velocity considerably larger than the velocity of the stationary flames.