Vol 9, No 1 (2017)

In this paper, we consider the conduction current excited in a silicon obstacle by the action of an external flux of penetrating radiation. We use quantum kinetic equations for distribution functions of conduction band electrons and holes of the valence band in the phase space of coordinates and quasi-momentums. Effective masses, densities of states, and group velocities of particles are determined on the base of band theory of a crystal. The approximation of the continuous momentum losses due to scattering on lattice defects is performed. The applicability of the model is validated by the comparison with the experimental data for the electron average-velocity dependence on the electric-field strength and on the velocity of the electron-energy transmission to the lattice. The silicon radiation conductivity excited by a free-electron current is calculated and the compliance of the results with the theoretical estimates is demonstrated.

In this paper the second order approximation method on unstructured tetrahedral mesh for solving the transport equation with the help of short characteristics is constructed. The second-order interpolating polynomial is constructed from the values at the vertices of an illuminated face with the use of the values of the integrals of the required function along the edges of the same face. The value at the unilluminated vertex is obtained by integrating along the backward characteristic interval inside the tetrahedron from the interpolated value on the illuminated face. The accuracy of the method depends on the interpolation accuracy and on the source integration along the interval of the characteristic. In the case of piecewise constant approximation of the source part, the method is of the second order, assuming the solution to be sufficiently smooth. On test problems it is shown that the convergence rate of the method is slightly smaller than two in the case of smooth solutions, while this rate is smaller than one for nondifferentiable solution.

The mathematical models and computation results for plasma confinement in magnetic traps called “Galatheyas” and for the evolution of the neutral current sheet in the vicinity of the magnetic zero line are compared. The computer simulations of plasma, magnetic field, and electric current configurations and their formation are based on solving MHD problems. Models of equilibrium configurations in the Galatheya–Belt trap and the current sheet use different dependences p(Ψ) of the plasma pressure on the magnetic flux function in the boundary problems with the Grad–Shafranov equation. Time-dependent models of the configuration formation in both setups differ by the electric current regime in the conductors producing the magnetic field.

This paper studies the reconstruction of body geometry using elements of a discrete model of the computational domain, which is important for the numerical simulation of a flow around a solid body by the immersed boundary method. Possible approaches to the solution of this problem are analyzed. Based on them, methodology has been worked out for the space reconstruction on unstructured meshes applied to the solution of a model problem.

The article is devoted to the application of the concept of sustainable development management to the task of combating the eutrophication of shallow water bodies (by the example of the Azov Sea). To describe the state dynamics of the water body, partial differential equations solved numerically by the finite difference method have been used. The dynamic problem of minimizing costs for the maintenance of the ecosystem of the water body in the defined condition, which is interpreted as the requirement for sustainable development, has been solved. The research and forecast complex, including the mathematical models of the hydrobiology of the shallow water body, environmental databases, and program library used to design scenarios of the ecological situation in the Azov Sea, has been worked out. Changes in the concentration of malicious blue-green algae due to water pollution by biogenic substances causing the rapid growth of these algae have been forecast. The influence of the spatial distribution of the temperature and the salinity on the biological treatment of the Azov Sea though the introduction of green algae, which displaced the toxic blue-green algae, has been studied. Using the designed research and forecast complex based on the materials of expeditions it is possible to investigate the key mechanisms of formation of vertical and horizontal zones in the distribution of biogenic substances, oxygen, and planktonic populations, to set the values of the parameters for management of the amount of hydrogen sulfide and hypoxemic zones, to evaluate the possibility of the biological treatment of the Azov Sea waters with the help of the introduction of the green alga Chlorella vulgaris BIN, followed by displacement of the toxic blue-algae that are most common in shallow water bodies such as Aphanizomenon flosaquae, and to rank the ecological efficiency of the factors for the management of the stability of the composition of the phytoplankton species, including the blooming of microalgae. Examples of the numerical calculations have been provided. The obtained results have been analyzed.

The unsatisfactory operation of a parallel multigrid algorithm is caused by two reasons: the imbalanced load of processors and the intensive exchanges of data between them. The further development of the parallel universal multigrid technique based on the reduction of a difference initial boundary value problem to a set of independent problems is considered. The universal multigrid technique is a single-grid algorithm, which uses the fundamental multigrid principle to minimize the number of problem-dependent components. The use of the same grid for the calculation of a correction eliminates all the difficulties produced by imbalanced loads and intensive exchanges on coarse grids. It has been shown that it is possible to decrease the volume of stored data and the time of computation and to attain nearly absolute parallelism in some cases. The results of some computational experiments with the difference six-order approximation pattern are presented.