Extreme atmospheric phenomena include thunder-storms, heavy rains, hailstorms, and tornadoes. These events have much in common. They usually develop on the basis of a convective cloud of the vertical size exceeding 10 km. The width of strips of heavy rain, hailstorm, or tornado is approximately the same, seldom exceeding 1 km. In meteorology, such phenomena are called local. Tropical cyclones lasting several days and covering areas of about 100 thousand square kilometers are also considered as disastrous atmospheric phenomena. In meteorology, the phenomena of such a scale are called regional. In the present epoch, the extreme atmospheric phenomena fill a highly important place in damage to national economy. In addition to losses due to a strong wind and a hailstorm, there are forest fires, flooding, and mud flows caused by lightnings and heavy rains.

The paper presents methods of simulation of local atmospheric phenomena, which were developed in the Institute of Computational Mathematics and Mathematical Geophysics, the Institute of Water and Ecological Problems, and the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences. One of the most widespread methods is Large Eddy Simulation (LES).

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