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We developed a physicomathematical model to predict volcanic explosion-induced gasdynamic phenomena and the dynamics of the distribution of particles of ash and dust that precipitate onto the earth’s surface and that remain in the atmotsphere. We investigated the factors and processes that exert an influence on the transport of dust particles in the atmosphere. On the basis of the physicomathematical model developed, numerical simulation of volcanic explosions of specified power and space scale is done, and results on the dynamics of gasdynamic flows of air and the distribution of dust particles for different instants of time are analyzed.

Physical and mathematical models for computation of the energy release of an electron beam in a homogeneous magnetized plasma are developed. Profiles of the energy release in a carbon plasma as functions of various parameters of the beam and the plasma state are obtained.

Equations of convection in a gas are analyzed and a computational algorithm that is efficient when the condition μgh/RT≪1 is satisfied for an arbitrary (fairly large) temperature drop is proposed. Calculations of convection occurring in steady nonuniform heating of walls are performed for axisymmetric argoncontaining volumes of different shape. Results of these calculations demonstrate the establishment of steady and periodic motions of the gas.

Numerical simulation of the flow of air originating as a result of volcanic eruption is carried out with the parameters corresponding to those figuring in the eruption of the Krakatau volcano in 1883 (with an energy of 100–1000 Mton of TNT equivalent). The results of the calculation are compared with the consequences of the disaster known from the literature.

A generalization of the Harten TVD-scheme in the form of a predictor-corrector-type scheme of second-order accuracy in time and space is proposed for the flows with spherical and cylindrical symmetry. The scheme does not require introducing components with artificial viscosity and describes discontinuities in the solution without the appearance of nonphysical oscillations for a Courant number less than 0.8.