Numerical algorithm for solving the problem of modeling the dynamics of a large-scale thermal

Abstract

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.