About numerical simulation of three-dimensional convection

The problem of three-dimensional convection of the liquid in rectangular parallelepiped with stress-free isothermal horizontal boundaries, at heating from below is considered. The special spectral-finite difference method is offered with the second order aproximation on space and the first on time. The linear analysis proposed numerical method has been shown that numerical method has the good quantitative correspondence in long-wave part of spectrum and qualitative – in short-wave. As test the calculations of two-dimensional roll and three-dimensional turbulent Rayleigh–Benard convection with supercriticality is equal to 2.2 and 950, accordingly are performed with Prandtl number is equal to 10.