The article presents the developments of the kinetic consistent approach of solution of the magneto gas dynamics problems on the high performance computing systems with massive parallelism. The main idea is to derive the magneto gas dynamic equations from the Boltzmann equation using a complex distribution function, including the electromagnetic terms. The derived equations were used for the formulation of the explicit numerical method of solution for the high performance parallel computing systems. The numerical experiments were performed for the veri cation of the chosen method.The main consideration of the development of the novel algorithms for the high performance parallel computing systems should follow from the optimization of few items. Among them there are two important ones which are the advanced mathematical model and the simplicity and e ciency of the computation algorithms.The choice of the mathematical model is dictated by the nature of the physical process to be simulated, by the objectives of the numerical study and by the available computing resources. As a rule of thumb, the mathematical models should be as detailed as possible without making the computations to expensive in the plane of computational systems.The important requirement for the algorithms at high performance parallel computation systems is the need of logical simplicity and high e ciency. The importance of these requirements is determined by the rapid development and change of the generation of the high performance parallel computing systems, in particular future exascale computing systems [11].Explicit algorithms are considered as the perspective for the future large scale parallel computing systems as they are easy to code/parallelize, require a modest amount of computer memory and no linear or nonlinear systems of equations required to be solved. However, the stability conditions of the explicit algorithms are the price to be paid for algorithmic simplicity of the explicit schemes. The cost of a single solution update is minimal but a very tine time discretization may be required to perform simulation over a given interval of time. The time steps may not exceed a certain threshold that depends on the stability conditions on the detailed space mesh.The present study leads to a mathematical model based on the kinetic approach of the hyperbolic type of the magneto gas dynamic equations and explicit kinetic scheme. The used explicit algorithm allows to include a regularization mechanism through hyperbolic terms of the equations on the ne spatial meshes. This mechanism improves the stability of the algorithm with a consequent relaxation of the time discretization on the high detailed spatial mesh.

A formulation (different from those adopted earlier) of the problem of numerical modeling of the altitude-time behavior of vibrationally excited molecular nitrogen has been presented. A conservative and absolutely stable difference scheme for the continuity equation with allowance for convective transfer has been proposed. The results of numerical calculations of the altitude-time behavior of different ionospheric parameters obtained on a mathematical model of ionospheric-plasmaspheric interactions have been given. The important role of vibrationally excited molecular nitrogen for such conditions has been noted. The times of establishment of the disturbed to background values of the concentrations of the excited components and the electrons and their temperatures have been determined.Introduction. The role of metastable components in both gas lasers [1, 2] and ionospheric processes [3] is known fairly well at present. Their energy may decrease due to de-excitation, producing visible emission lines from whose measurements one determines the concentration of particles. It may also become the kinetic or vibrational energy of their molecules and may pass into the environment in endothermic reactions. The processes of deactivation of such components in chemical reactions occur with much higher rates than those for neutral components. Mathematical modeling is currently one basic method of investigation of different processes natural experiments for which are very laborious. Numerical experiment based on a physicomathematical model has a significant advantage, which lies in the possibility of calculating situations repeatedly and obtaining numerical results.In this work, we present a physicomathematical model for calculation of ionospheric parameters along the geomagnetic tube of force for disturbed conditions such as the temperatures of the O + and H + (T i ) ions and electrons (T e ), the components of the neutral-wind velocities (v nx and v ny ), the concentrations of the excited components O

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The influence of zonal and meridional components of the neutral wind under anthropogenic impacts of water molecules on the ionosphere's electron concentration distributed along a magnetic field tube is considered. Computer simulation method based on a mathematical model of the F2 region along a field tube is used. SHORT COMMUNICATIONS