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

  • D. B. Zhakebayev al-Farabi Kazakh National University
  • Ye. Moisseyeva al-Farabi Kazakh National University
  • M. Y. Hrebtov Novosibirsk State University
  • N. V. Tsoy al-Farabi Kazakh National University


The article presents research results on dynamics of large-scale thermals influenced by buoyancyforce, turbulent mixing and adiabatic expansion. Mathematical model is based on the Navier –Stokes equations, the continuity equation, and the total energy equation. Numerical simulationrealized 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 Poiseuilleflow problem. A number of numerical experiments were carried out, with different initial conditionsfor temperature and density inside and outside the large-scale thermal.The dependence of theheight of cloud rise on the initial temperature was obtained. Dynamics of the temperature fieldpropagation is given for an initial value of 1800 ◦ K at the time instant of 5 s, 15 s, and 35 s.


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How to Cite
ZHAKEBAYEV, D. B. et al. Numerical algorithm for solving the problem of modeling the dynamics of a large-scale thermal. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 100, n. 4, p. 88-102, jan. 2019. ISSN 2617-4871. Available at: <>. Date accessed: 20 jan. 2021. doi:
Keywords large-scale thermal, Lattice Boltzmann Method, D3Q27