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Rational techniques for verifying the congruence of complex matrices are discussed. An algorithm is said to be rational if it is finite and uses only arithmetical operations. An important part in verifying the congruence of nonsingular matrices play their cosquares. The verification gets complicated if there are eigenvalues of modulus 1 in the spectrum of cosquares; this is especially true if such eigenvalues are defective. In this direction, the most advanced result is the rational algorithm for matrices A and B whose cosquare is the direct sum J_m (1) ⊕ J_m (1). Here, this algorithm is extended to the case where the cosquare is the direct sum of two Jordan blocks of distinct orders. This extension is heavily dependent on additional facts concerning the solutions to the matrix equation X - J^Τ_m(1)XJ_m(1) = 0. found in the present paper.

Traditionally, to solve the hydrodynamic equations a Godunov method is used, whose main component is the solution of a Riemann problem to compute the fluxes of the conservative variables through the interfaces. Most numerical Riemann solvers are based on partial or full spectral decompositions of the Jacobian matrix with the spatial derivatives. However, when using complex hyperbolic models and various types of equations of state, even partial spectral decompositions are quite difficult to find analytically. Such hyperbolic systems include the equations of special relativistic magnetic hydrodynamics. In this paper, a numerical Riemann solver is constructed by means of a viscosity matrix on the basis of Chebyshev polynomials. This scheme does not require information about the spectral decomposition of the Jacobian matrix, while considering all types of waves in its design. To reduce the dissipation of the numerical solution, a piecewise parabolic reconstruction of the physical variables is used. The behavior of the numerical method is studied by using some classical test problems.

A process of searching on the sphere for the best (in a sense) cubature formulas that are invariant under the transformations of different dihedral rotation groups is described. The parameters of the new cubature formulas of the 6th, 10th, and 12th order of accuracy are given to 16 significant digits. A table which contains the main characteristics of all the best to date cubature formulas of the dihedral rotation group up to the 29th order of accuracy is given.

For the case of two spatial variables, a finite-difference scheme of the predictor--corrector type is constructed for solving nonlinear dispersion equations of wave hydrodynamics with a higher order of approximation of the dispersion relation. The numerical algorithm is based on splitting the original system of equations into a hyperbolic system and a scalar equation of the elliptic type. Two methods of approximating the elliptic part are considered. For each of the variants of the difference scheme, dissipation and dispersion analysis is performed, stability conditions are obtained, formulas for the phase error are analyzed, and the behavior of the harmonic attenuation coefficient is studied. A comparative analysis is carried out to identify the advantages of each of the schemes.

Numerical simulation is performed for a cylinder-bound two-component liquid flow. Simulation model is based on the method of lattice Boltzmann equations (LBM). The collision integral in this model is defined from the MRT approximation. The interaction between liquid components is described by the diffusion interface model with the pseudopotentials approximation. The main deficiency of this known approach is disbalance for discrete forces of two-component interaction; this would generate a pseudo-current in the transition zone. The presented numerical study offers a qualitative view for the pseudopotential function providing a smallest value for intercomponent interaction coefficient. This means the low pseudo-currents and the smallest size for the diffusive transition. The example simulation is presented for a problem of rotation of two components in a cylinder. The simulation gives also the Reynolds number rage and the cylinder aspect ratio that ensure the start of flow recirculation at the cylinder axis. It was demonstrated that simulation results comply with experimental data with a high accuracy.

Results of numerical investigations of the characteristics of a turbulent boundary layer in the case of air injection through a smooth flat perforated surface with a single hole and also through a similar surface with a group of staggered holes 0.18 mm in diameter (d/δ) in a low-velocity flow are reported. The Reynolds number Re** based on the momentum thickness δ^** ahead of the perforated region is 2600. The blowing coefficient C_b is varied in the interval from zero to 0.0438. The influence of some geometric parameters, in particular, the distance between the hole centers, on the properties of the transverse shear flow for identical intensities of blowing in situations with one hole and with a group of holes is analyzed. All observations reveal stable reduction of local friction whose value varies depending on the number of holes and their arrangement on the surface.

An experimental study of heat transfer and hydraulic losses in a channel with one wall being a surface with trench dimple, was carried out. The working surface had four rows of dimples located alternately at angles of 45° and -45° to the channel axis. In the laminar regime, the transfer of heat and the losses of pressure turned out to be close to the parameters of a smooth channel. In the turbulent regime, a 1.5-fold intensification of heat transfer with respect to the transfer of heat in a smooth channel was obtained. The dependence of the increase in pressure losses on the Reynolds number qualitatively agreeing with the dependence for the channels with sandy roughness is obtained.

The experimental results on the effect of longitudinal ribs on the antitorque moment for Couette-Taylor flow between two rotating cylinders are presented. The tangential Reynolds number in the experiments was varied by varying the cylinder speed and the working fluid viscosity (water-glycerin solution). The experiments covered laminar, transient and turbulent flow regimes (Re = 200 - 1·10⁵). It is shown that the ribs have an amplifying effect on the drag torque and mechanical energy dissipation only in the region of small Reynolds numbers (Re < 2000) in the laminar regime and in the presence of Taylor vortices in the gap. The intensification effect can reach two and more times and is caused by intensive turbulence of the flow by longitudinal ribs. In the turbulent regime, the heat release intensification is not observed, which is confirmed by the data available in the literature.

A nonisobaric supersonic jet of vibrationally excited carbon dioxide exhausting from converging axisymmetric nozzles with the diameter ranging in a wide interval (from 0.03 to 114 mm) is studied experimentally and numerically. Numerical simulations are performed within the framework of the two-temperature approach with the use of the Landau-Teller relaxation equation for each vibrational mode of carbon dioxide molecules. The simulations reveal that vibrational nonequilibrium of molecules affects the gas-dynamic structure of the jets in the temperature range of 300 - 900 K, and this effect is verified experimentally. Vibrational excitation of molecules in the experiment is ensured by means of gas heating. The effect of vibrational nonequilibrium is manifested as reduction of the amplitude of the static pressure in wave structure cells and as reduction of the longitudinal size and number of wave structure cells as compared to the case of an equilibrium supersonic flow. It is shown that the maximum effect of nonequilibrium is observed in jets exhausting from the nozzle with a diameter of ≅ 3 mm.

The modern aviation industry has many applications for honeycomb composite panels (HCP). The HCP-manufactured product line becomes more extended. This dictates a need for most effective and inexpensive methods for nondestructive inspection for HCP integrity that can ensure a high level of flight safety. One of promising methods for nondestructive inspection is the thermal technique. This paper presents and analyses the method feasibility of revealing the delamination of outer skin from an HCP filling. This task is performed by numerical simulation and the paper presents a pictorial test with a sample of HCP typical for aircraft engineering. Our results demonstrate how the thermal imaging tools can be used for the fact of skin delamination with account for technical restrictions found in real experiments with a physical sample of HCP.