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The Lattice Boltzmann Method (LBM) is used to treat the natural convection problem. It has enabled us to demonstrate the existence of thermal and dynamic instabilities in natural convection within the cavity. Oscillatory and other regimes are revealed. Numerical simulations carried out by researchers no longer converge, and infinite calculation times are declared. A closer look and more serious investigations into the evolution of temperature and current function have enabled us to unravel the problem and affirm that it is indeed a purely periodic regime of low amplitude variation for values of aspect ratio A. Two different regimes of temperature distribution as a function of time are recorded: the stable and permanent regime, and the oscillatory and permanent regime. In this book, we have chosen to illustrate different cavity aspect ratio values. We have obtained the steady-state, permanent regime and a steady-state oscillatory regime.