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A modification of the arbitrary discontinuity breakup numerical scheme (S.K. Godunov’s scheme) is proposed for evaluating unsteady gas-dynamic processes during pressure wave supercharging using a pass-through marching calculation without shock discontinuities extraction. With the help of a new version of the scheme based on using the specifically developed system of gas-dynamic functions of unsteady flow, a numerical simulation of the pressure wave supercharging of piston engines has been carried out.

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer that interacts with a half-space of a compressible ideal fluid and in a prestrained compressible elastic half-space that interacts with a layer of an ideal compressible fluid is studied. Use is made of the three-dimensional linearized equations of the theory of elasticity of finite deformations for the compressible elastic solid and the three-dimensional linearized Euler equations for the compressible ideal fluid. A problem statement and an approach based on the general solutions of the linearized equations for elastic solid and fluid are used. The dispersion equations that describe the propagation of quasi-Lamb waves in hydroelastic systems over a wide frequency range are derived. The effect of the initial stresses and the thicknesses of the elastic layer and liquid layer on the phase velocities of quasi-Lamb modes is analyzed. A criterion of the existence of quasi-Lamb waves in hydroelastic waveguides is proposed. The developed approach and the obtained results make it possible to establish the limits of applicability of the models of wave processes based on different theories of small initial deformations, as well on the classical theory of elasticity. The numerical results are presented in the form of graphs and are analyzed.

Purpose. To create a method for mathematical modeling of wave processes in power two-winding transformers based on a substitute scheme, which takes into account the design features of power transformers. Methodology. Formation of mathematical models for the research on wave processes in power two-winding transformers and further development of the analytical method for solving the system of partial differential equations. Findings. A mathematical model for the research on wave processes in power two-winding transformers based on a substitution scheme, witch adequately takes into account both electrical and magnetic connections, is created and an improved analytical method is proposed for solving a system of partial differential equations which allows taking into account the interval time of propagation of electromagnetic waves along the entire length of the windings and the time interval, during which the voltage changes significantly from its complete change during the wave processes,. Originality. The paper proposes a mathematical model for the research on wave processes in the windings of power two-winding transformers based on its alternative scheme, which takes into account electrical and magnetic connections, and improves the Fourier method for solving a system of differential equations with partial derivatives. Practical value. A mathematical model is created for calculating wave processes in transformers, which allows analyzing the voltage distribution in the transformer windings during the action of pulse voltage on them and adjusting their insulating abilities, given that the operation of power transformers is subject to high requirements for the reliability of their work.

This paper is devoted to the study of the stability dynamics of wave processes of flat and circularelements, and also some axisymmetric problems of oscillation of an elastic layer limited by rigid or deformableboundaries when exposed to normal or rotational shear stresses are considered. Solutions to the problems underconsideration were obtained using integral transformations by coordinate or time. The work develops the dynamicstability of a round rod. The loss of stability of a round rod will be investigated on the basis of the mathematicaltheory and the transverse oscillations of a round rod, described in the work of I.G. Philippov.

The ability of numerical models to deal with wave breaking processes and dry areas is of paramount importance for applications in coastal zones and dam breaks. The mathematical models commonly used in such real problems are usually based on Boussinesq-type equations and, to a small extend, on Serre equations. However, these standard models are weakly dispersive and must be appropriately modified to deal with breaking waves and dry areas. Indeed, nearshore and dam break problems involve complex wave dynamics and highly dispersive wave processes can easily arise. In those cases, it is well known that weakly dispersive models like the ones based on classical Boussinesq or Serre equations are unreliable for an accurate simulation of the phenomena involved. In this work we extend the applicability of an improved Serre model, herein denoted by Serre α , β , to include the wave breaking process, the broken waves propagation, and dry areas. We provide a comprehensive set of numerical examples involving wave propagation over exposed and submerged structures, as well as dam break problems. The numerical experiments show the accuracy and robustness of the proposed model. Particular attention is given to bottom friction modeling, where the standard Manning’s assumption is compared with a more realistic formulation. Also noteworthy is the simulation of wave breaking problems with highly dispersive effects. The advantages of the Serre α , β model over the standard Serre model for these challenging cases are clear.

The problem of establishing the temperature profile in a radiatively cooling-down disperse flow in the presence of external thermal radiation is considered. A comparison of the obtained analytical estimates of the speed of establishment of an equilibrium profile with the results of numerical solution is made. The amplitude of the wave phenomena accompanying the establishment of temperature has been calculated.

A mathematical model is proposed for a Kirchhoff–Love-type nonlinear elastic cylindrical shell surrounded by an elastic medium and containing a viscous incompressible liquid. The model is used to analyze wave processes both analytically and numerically. On the basis of the proposed computational algorithm, a software package is developed, which makes it possible to plot diagrams and to obtain numerical solutions to Cauchy problems with initial conditions taken in the form of exact solutions to dynamic equations of shells in the absence of the liquid.

The paper considers active wave processes in changes in the lumina of cylindrical hollow organs. A mathematical model is proposed for autowave transport of the internal contents of an organ based on mechanochemical interactions. The self-organization of changes in the shapes of organs are discussed in application to lymphatic vessels of living organisms.

Recent researches have shown that the damaged areas, calculated using various failure criteria for materials with complex heterogeneous structure are not always consistent with physical experiments and with each other. In this paper, we compare two failure criteria, i.e. the principal stress criterion and the von Mises yield criterion. Also, we compare two models of destruction formation, i.e. the model of fractures and sand model. Using the wave dynamics analysis, we explain the difference in the calculated zones of destruction. We indicate what differences in elastic wave phenomena cause the difference in the calculated fracture zones. We assume that further study of the connection between wave phenomena and destruction of materials will allow to develop more precise failure criteria. To carry out the research, we applied numerical modeling of spatial dynamic elastic wave processes in a nuclear power plant and enclosing rocks. We use the grid-characteristic method on combined regular and structural hexahedral grids to describe the complex shape of the dome of the nuclear power plant with minimal computational costs. Moreover, in this work, we consider an approach for calculating the contribution of dynamic elastic wave phenomena to seismic stability of facilities. This technique can be especially useful in the development and testing of seismic insulation of buildings. We propose a failure formation model that takes into account the contribution of static loads and dynamic loads separately.

This paper describes a method for identifying modulation effects caused by the interaction of waves with different frequencies based on regression analysis. We present examples of its application on experimental data obtained using high-precision laser interference instruments. Using this method, we illustrate and describe the nonlinearity of the change in the period of wind waves that are associated with wave processes of lower frequencies—12- and 24-h tides and seiches. Based on data analysis, we present several basic types of modulation that are characteristic of the interaction of wind and swell waves on seiche oscillations, with the help of which we can explain some peculiarities of change in the process spectrum of these waves.

Processes of wave propagation in fractured medium are studied. The medium is considered as a set of elastic blocks interacting with each other by interlayers with significantly weaker mechanical properties. For the modeling of fractured interlayer, the rheological method with non-classical element rigid contact is applied. Computational algorithm is based on the space-variable two-cyclic splitting method in combination with finite-difference monotone schemes of predictor-corrector type. Numerical results of wave propagation in fractured medium are presented.

In technological machines for various purposes, hydraulic actuators are widely used, which are constantly being improved in terms of the characteristics of power, speed and accuracy. These parameters must be stable, which requires making certain changes in the design of these actuators that allow them to withstand the operating modes of technological machines in the limits search. The authors consider results of the stability investigation of a nonlinear hydraulic actuator under the action of wave processes in its lines. They propose mathematical models of the wave process, which to some extent reflect its influence on the movement of the hydraulic motor in the form of a damping effect. For a nonlinear hydraulic actuator under the action of wave processes, a mathematical model and the results of the study of this hydraulic actuator are presented in the form of conditions, under which the stability of its operation is ensured.

A piecewise-linear problem of the effect of a wave propagating in soil on an extended underground pipeline interacting with soil according to the model of an “ideal elastoplastic body” is solved by the finite difference method. The results of calculating the velocities, strains and lateral shear stress for three waveforms: step-like, impulse and harmonic ones are presented. The analysis of the results obtained is performed and the effect of reverse outward forcing of the pipeline under the action of a displacement impulse propagating in soil in the form of sine squared is shown. An approach to the stationary mode under sinusoidal impact is considered.

A mathematical model is proposed which describes the interrelated processes of unsteady elastoplastic deformation of stacks of woven metal wire mesh and wave processes in pore gas in a two-dimensional axisymmetric approximation. The nonlinear equations of the dynamics of two interpenetrating continua are solved numerically using a modified Godunov’s scheme. The problem of explosive loading of a multilayer shell with an internal permeable deformable layer is solved. The results of numerical solutions are compared with experimental data. The influence of the gas-permeable layer on shell deformation is determined.

Wave processes in an isotropic hollow cylinder located in an inhomogeneous prestress field are studied. The dispersion equation of the problem is investigated, and some features of the structure of the dispersion curves in relation to the type of prestressed state are identified. Formulas describing the behavior of the dispersion curves in the neighborhood of radial resonances are derived using the perturbation method.

Background The study of the processes of propagation of pressure waves in liquid-saturated porous media is associated not only with solving practical problems of underwater acoustics, seismics, object protection, non-destructive testing, etc., but it is also necessary to understand the fundamental foundations of wave processes. in such environments. Aims and Objectives Investigation of the evolution of a pulse of finite duration in a porous medium saturated with a gas-liquid mixture. Analysis of two situations of the location of bubbles in a porous medium. The first, when the bubble envelopes several pores, and the second situation - gas bubbles are much smaller than the pore sizes and are located on the pore walls. Results The dynamics of linear waves in a porous medium filled with a gas-liquid mixture has been studied. The influence of the determining factors of a bubbly liquid (volumetric content, dispersion of bubbles) and a porous medium on the shape and decay of impulse disturbances is analyzed.

To determine the wave or ice load on offshore hydraulic structures, calculation methods and modern mathematical models are used, as well as field observations and laboratory studies. Each of these methods has advantages and disadvantages. Sharing existing methods provides an approach called “hybrid or composite modeling.” Hybrid modeling provides the most reliable approach for designing safe facilities. However, the interaction of the individual components of hybrid modeling requires further research. This article is devoted to the study of the problems that arise when verifying the results of numerical modeling of wind waves using field and laboratory model measurements. The experience of studying the projects of the port-shore protection complex in Imeretinka, Sochi, the LNG terminal in the Ob Bay and the port in the East Bay of the Sea of Japan is used.

A method is proposed for the numerical simulation of acoustic processes and the motion of solids in gases based on the representation of media in the form of multiple particles. The behavior of particles is described by Newton’s equations of motion, and the strength of the interaction between particles depends on the distance between them. For gas particles, only the repulsive force is considered, and for particles of a solid force interaction ensures the equilibrium existence of a body-centered cubic lattice. The model allows one to calculate the propagation of acoustic waves and their effect on solids in a gaseous medium.

Dispersion characteristics of wave processes in collapsible elastic biovessels with the biofluid flowing through them are presented. The possibility of the existence of fixed flow structures in the vessels is shown. The possibility of applying the results to the study of biological systems is considered.

For a hyperbolic model of a one-velocity viscous heat-conducting mixture, a modifi ed Godunov method with approximate Riemann solvers is developed. Using this method, we studied wave processes in frothing and bubble media. It is shown that the fl ow picture is signifi cantly infl uenced by heat transfer processes, which are manifested to a greater extent for bubble liquids.

It is demonstrated that pump complexes pipeline networks are characterized by a high degree of breakdown rate because of leakages accompanied by complicated wave processes in the hydrosystem. It is found out that pipeline network wave processes depend on localization place and amount of the leakage, hydronetwork structural parameters as well as the properties of the transported liquid. Leakage influence on technological, electromechanical and energy characteristics of the pump complex is determined. It is stated that to identify the leakage it is expedient to use a signal of hydraulic power, whose frequency analysis makes it possible to obtain a wider spectrum of diagnostic signs of non-stationary condition. It is shown that leakage is accompanied by growth of hydraulic power variable component, in particular, its sine component.

The processes of changing the mechanical characteristics of the material, intensive plastic deformations and the entrainment of material from the working surfaces are studied at high-speed sliding of loads along the rail guides of the rocket track.

The effective viscous inertia properties exhibited by suspensions in the presence of oscillatory wave processes are considered. A cell model of a concentrated suspension is used to derive the dependence for the complex density, whose real and imaginary parts characterize the effective inertia and the bulk viscous resistance to oscillatory motion, respectively. From hydrodynamic models of low-frequency and high-frequency translatory oscillations of spherical inclusions in the host liquid, estimates are obtained for the internal dynamic parameters of the suspension, namely, the apparent mass factor and the inclusion relaxation time, which specify the general formulas for the complex density.

The modeling of a layered structure in a finite element Ansys complex is considered. The model is an imitation of a layered pavement design. The design consists of 10 layers, each of which has a certain fixed list of properties. We consider the simulation in the form of a simplified, flat statement of the problem. Simulated dynamic analysis under shock. The wave field of displacements in a certain part of the structure is analyzed. The correlation between the amplitude of the field displacement in a certain region of the surface layer and the variation of its elastic modulus is considered. Based on a numerical experiment, an approach to estimating the characteristics of a layer is constructed.

The paper considers large-scale 3D wave motion of weakly compressible and perfectly conducting inhomogeneous inviscid liquid subject to a magnetic field and the Coriolis force, with due account the spherical topography of bounding surfaces. The results of the studies can be used in geophysics and astrophysics, and in particular, in the study of dynamical processes occurring in the Earth liquid core and in stellar interiors. Moreover, they can be also employed in evaluation of magnetohydrodynamic characteristics of a liquid medium and for estimation of the parameters of the wave disturbance in the electromagnetic field induced by the corresponding hydrodynamic excitement. In addition, the above results can be used in the study of magnetohydrodynamic processes in engineering devices and in the study of foreground energy materials.

Introduction. The method of scales distortion in physical modeling of wave processes is considered. Distortion of scales is applied in practice, but has an insufficient theoretical basis in relation to researching of the waves impact on hydraulic structures. Development of theoretical basis and practical recommendations for the conversion of model data at the construction site in hydraulic modeling with distortion of scale will allow exploring the extended constructions under the circumstances of laboratory with a limited size, and reduce the building costs of hydraulic models. The prospects of development and application of the method of the scales distortion of physical models have been estimated. Materials and methods. The available methods of the scales distortion of hydraulic models are considered. To estimate the errors arising from the scale distortion of the model, a mathematical modeling of the three typical sections at the coastal area of the sea, subjected to different degrees of the scale distortion has been performed. The parameters of waves in the water area were calculated using the regulatory methodology of the Russian Federation, followed by an analysis of changes in the wave situation caused by distortion of scale. Results. The estimation of existing mathematical apparatus, allowing to deviate from strictly geometric similarity of model and the full-scale object, was given. The parameters of waves on twelve mathematical models with different degrees of the scale distortion were obtained, allowing to explore the impact of method on the results obtained in the modeling. Conclusions. Usage of existing provisions on the scales distortion of hydraulic model at exploring of wave processes in the most cases leads to essential errors in results, or to their full discrepancy of reality. Affine transformations can serve as a basis for the development of the scales distortion on hydraulic models technique. Experimental research can play a crucial role in the development of methodology, estimating the errors and degree of permissible scale distortion. At the moment, without a validated procedure, it is recommended to make a preliminary analysis of refraction plans and wave transformation parameters for determining the degree of permissible scale distortion and estimating the errors that arise.

The aim of this study was to analyze distribution and development of stress-stress state in struc- tured rock specimens subject to uniaxial and biaxial loading to failure using digital speckle corre- lation method. Within the experimental analysis of wave processes in the block-hierarchy struc- ture of geomedia (uniaxial and biaxial compression and shearing of prismatic geomaterial speci- mens), the authors revealed the fact of initiation of low-frequency micro-deformation processes under slow (quasi-static) disturbances. The estimation of the deformation-wave behavior of geo- materials as the "summed" contributions made by elements of the scanned surfaces with differ- ent-oriented (in-phase and anti-phase) oscillations has been performed using the energy ap- proach that is based on the scanning function R, analogous to the "center of mass" in the classical mechanics.

This article continues our studies of the development of an MHD, waveguide, centrifugalresonance instability as a possible mechanism for the formation of solar magnetic arcades; here, we take into account the non-isentropic nature of this process associated with the presence of dynamical radiative cooling. In contrast to the results of our previous study, our computational data show that five, rather than two, waveguide-resonance families of unstable modes are able to develop in a cylindrical, rotating layer of magnetized plasma. This substantially expands the spectrum of associated wave processes, so that the joint action of all these growing wave harmonics can lead in the non-linear stage of their development to morphologies close to those observed in solar magnetic arcades—to the formation both of the magnetic arcades themselves and of fine structure in such arcades.

New results of experimental studies performed at the Scientific Center of Nonlinear Wave Mechanics and Technology of the Russian Academy of Sciences (NTs NVMT RAN) on the investigation of wave processes in dispersed media, aimed at the application of wave effects for processing and obtaining microheterogeneous emulsions, are presented. The possibility of controlling the drop sizes of the dispersed phase due to variations in the wave processing mode is shown using the example of cosmetic creams. The energy efficiency of the wave method for processing and obtaining the microheterogeneous emulsions is presented.

Wave processes in a 2D blocky medium are under investigation. Considered continuum consists of rectangular elastic blocks divided by fluid-saturated porous interlayers. The interlayers are described in terms of modified Biot’s porous-flow model. Porous skeleton in the model has viscoelastic properties and takes pore collapsing effect into account. In order to analyse the fluid behavior in nodes between blocks, a hydrodynamic analogue of Kirchhoff’s law is used. To implement presented model nu-merically, a computational algorithm, based on a two-cyclic splitting by spatial variables, is developed. For the blocks equations Godunov’s gap decay scheme is used; for the interlayers equations a hybrid numerical method, based on the dissipationless Go- dunov’s and Ivanov’s schemes, is applied. Parallel software is designed for analysing stresses and velocity fields in a 2D blocky medium. Comparative study of the model with elastic interlayers and the model with fluid-saturated porous interlayers is carried out. I...

This study applies the numerical model GPUSPH, an implementation of the weakly compressible smoothed particle hydrodynamics (SPH) method on graphics processing units, to simulate nearshore tsunami processes. Two sets of laboratory experiments that involve violent wave breaking are simulated by the three-dimensional numerical model. The first set of experiments addresses tsunamilike solitary wave breaking on and overtopping an impermeable seawall. Comparison with free-surface profiles and laboratory images shows that GPUSPH satisfactorily reproduces the complicated wave processes involving wave plunging, collapsing, splash-up, and overtopping. The other set of experiments investigates tsunamilike solitary wave breaking and inundation over shallow water reefs. The performance of GPUSPH is evaluated by comparing its results with (1) experimental data including free-surface measurements and cross-shore velocity profiles, and (2) published numerical results obtained in two mesh-based wave models: the n...

The single- and multi-wave processes in the elastoplastic solids are modeled based on the approximate approach proposed. We consider one- and two-dimensional problems on propagation of the longitudinal waves arising at normal impact on the boundary of an isotropic half-space, the problem of shock-wave reflection from a free surface of a plate and the problems on two-dimensional fracture of a plate, produced by a cylindrical impactor. The proposed approach allows one to simplify considerably the analysis of these and others similar problems taking into account the elastoplastic behavior of the solid.

The influence of localization of vibrations on film exfoliation from an elastic basis is investigated. A model is suggested that makes it possible to find an approximate analytical solution and to analyze the conditions of increasing and decreasing exfoliation.

The results of investigations of wave processes in dispersed media for application of wave effects in the development of a new class of wave machines, including the mixer-activator to produce modifying additives, are presented. The results of experimental investigations into the wave effect on various types of dry multicomponent dispersed systems to apply similar wave machines and aggregates in various branches of industry are presented.

Results of numerical simulations of the evolution of disturbances in a hypersonic shock layer on a flat plate at high Mach numbers (M∞ = 21) and moderate Reynolds numbers (ReL = 1.44 · 105) are analyzed by an adapted method of bispectral analysis. All basic types of nonlinear interactions are obtained. The calculated results are compared with experimental data.

This paper is a review of studies of wave phenomena in biological tissues at the cellular level. Autowave processes of mechanicochemical deformation of cells are examined, related to activation of calcium ion sources in muscle and other cells. The collective effects arising during cell fusion are described. Possible self-organization methods and dissipative restructuring of cell shapes and microvessels are discussed.

Spatiotemporal distributions of local components of the distortion tensor of quasi-plastic materials—saliferous rocks (sylvinite)—have been studied under active compressive straining conditions using double-exposure speckle photography techniques. The strain localization patterns are presented and the features of macroscopic strain inhomogeneity are considered for inelastic behavior of the material. Results obtained for the slow wave processes in deformed saliferous rocks are compared to analogous data available for ionic crystals.

The paper explains a number of phenomena that are observed in the surface vibrational treatment of oil and gas reservoirs based on the thriving theory of pendulum waves, e.g., a ring-shape response of a productive stratum and a time lag in the response, seismic luminescence and its spectrum, etc. The authors give data on velocity groups of pendulum waves in stressed block hierarchy of rock masses and substantiate the choice of the wave velocity group to be generated by the powerful surface vibro-sources designed at the Institute of Mining. The theoretical and phenomenological formulas given in the paper are of assistance in the development and improvement of the surface vibrational technologies for the enhancement of oil and gas recovery.

The impact of a liquid drop in the region between rivulets on the surface of a locally heated falling liquid film and the effect of this disturbance on the development of wave processes in the film have been studied. It is established that perturbations caused by the incident drop are spreading downstream and not going beyond the region bounded by the adjacent side rivulets. The maximum increase in the amplitude of waves in the film is observed in the same region between rivulets. At a distance of 70 mm downstream from the site of impact, the amplitude of waves in this region exhibits a 40–60% increase in comparison to the undisturbed film.

The deformation and wave processes induced by collisions of an impactor with deformable layered targets of various configurations are analyzed. The numerical solution of such problems is associated with an adequate treatment of wave processes in a continuous medium, which is an especially difficult task in the case of layered targets. To deal with the former problem, it is proposed to use adaptive Lagrangian triangular meshes. Wave processes are simulated using the grid-characteristic method, which can serve as a basis for algorithms that do not fail near the boundary of the computational domain and at numerous material interfaces. Additionally, hybrid and hybridized grid-characteristic schemes are applied that substantially improve numerical solutions with steep gradients (discontinuous solutions). These methods provide an adequate treatment of wave processes in layered targets (wave reflection and refraction at contact surfaces, secondary-wave interaction, changes in the conditions on these boundaries, etc.).

The dispersion relations for localized plastic strain autowaves are considered for some metals at the stages of easy slip and linear strain hardening. The quadratic form of this relation, the type of the dependences of the phase and group velocities of such autowaves on the wavenumber, and the quantitative relation between the characteristics of plastic flow localization wave processes and elastic wave parameters in solids being deformed are established and explained. An invariant for strain effects at micro- and macroscopic levels is introduced.

The propagation of stress waves in a column of rods of a rocker machine during a lift is considered at an arbitrary time instant. Using an integral transformation of time, the second-degree differential equation for displacement is solved where the force of the column dead weight is taken into account. It is shown that the stress variation is of a pulsating type; parameters and a form of the pulsation cycle are given. The fatigue strength of a thread in the union joint of rods and the lifetime of rods having an initial fracture are determined.

The paper generalizes results of study of the intermittency pattern in some wave processes of the burst type in the high-latitude magnetosphere of the Earth. Based on the analysis of distributions of amplitudes and interpeak intervals, it is shown that generation regimes of magnetic impulse events, ipclpulsation burst series, and Pi3 pulsations possess the properties of intermittent processes and are associated with the development of plasma turbulence in their generation regions. The degree of turbulence of the high-latitude magnetosphere plasma is estimated at a qualitative level. Burst-type structures whose behavior corresponds to a typical intermittent process are discovered in variations of the ancient geomagnetic field.