(untitled) (Journal of Mathematics Mechanics and Computer Science, 2019)
The article presents research results on dynamics of large-scale thermals influenced by buoyancy force, turbulent mixing and adiabatic expansion. Mathematical model is based on the Navier – Stokes equations, the continuity equation, and the total energy equation. Numerical simulation realized by finding solution of three dimension Lattice Boltzmann Equations appling D3Q27 model. First approximation of the solution of Boltzmann equation leads to the hydrodynamic Navier – Stokes equation.Numerical verification of the algorithm was carried out using benchmark Poiseuille flow problem. A number of numerical experiments were carried out, with different initial conditions for temperature and density inside and outside the large-scale thermal.The dependence of the height of cloud rise on the initial temperature was obtained. Dynamics of the temperature field propagation is given for an initial value of 1800 ◦ K at the time instant of 5 s, 15 s, and 35 s.