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A method for calculating the nonstationary thermal interaction between a viscous gas flow and a solid body is presented. The method consists in direct joint integration over time of the equations of gas dynamics of a multicomponent mixture and the heat equation in a solid on multi-block unstructured meshes. To calculate one time step, the system of governing equations is split into hyperbolic and parabolic subsystems. The numerical method provides approximation of the matching condition (continuity of temperature and the normal component of the heat flux) at the interface between gas and solid and is efficient for nonstationary calculations. The comparison with the analytical solution of the model problem of the interaction of a high-speed flow and a heated plate confirm the efficiency of the method. [ABSTRACT FROM AUTHOR]

An approach to numerical simulation of three-dimensional electrical and thermal fields in high-temperature superconductors is described. In such a semiconductor, the phenomena of superconductivity are observed at high temperatures above the temperature of liquid nitrogen. The absence of a generally accepted theory of superconductivity leads to the need to study physical processes in semiconductor structures using mathematical simulations. The main attention is paid to the calculation of temperature and electric current distributions in large-size mesas with a self-heating effect. An efficient algorithm for solving the equations describing these distributions is constructed. The basis of the algorithm is an adaptive multigrid method on structured Cartesian grids. The adaptability is based on the Chebyshev iterative method for constructing the smoothing procedures at each grid level and for solving the coarsest grid equations. The adaptive technique allows us to realistically simulate the anisotropic phenomena. The functionality of the algorithm is demonstrated along with an example of solving an anisotropic model problem with discontinuous coefficients. [ABSTRACT FROM AUTHOR]

The article describes a robust technology for numerical simulation of multicomponent flows in the presence of strong shock waves, for example, in the flight of a high-speed vehicle with a ramjet/scramjet engine. This takes into account the phenomena of turbulence, multicomponent diffusion and heat transfer. High-temperature phenomena that occur when moving at a high supersonic speed and are associated with dissociation and ionization of the gas environment are not considered, although they fit well into the framework of the general model of a multicomponent reacting gas. The advantage of the algorithm proposed in this article is its adaptability to both the simulation of strong shock waves and to the simulations on small scales, as well as a high potential for parallelization. Illustrative examples of simulations based on the developed method are given. [ABSTRACT FROM AUTHOR]