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The article is devoted to the numerical study of shock-wave flows in inhomogeneous media–gas mixtures. In this work, a two-speed two-temperature model is used, in which the dispersed component of the mixture has its own speed and temperature. To describe the change in the concentration of the dispersed component, the equation of conservation of “average density” is solved. This study took into account interphase thermal interaction and interphase pulse exchange. The mathematical model allows the carrier component of the mixture to be described as a viscous, compressible and heat-conducting medium. The system of equations was solved using the explicit Mac-Cormack second-order finite-difference method. To obtain a monotone numerical solution, a nonlinear correction scheme was applied to the grid function. In the problem of shock-wave flow, the Dirichlet boundary conditions were specified for the velocity components, and the Neumann boundary conditions were specified for the other unknown functions. In numerical calculations, in order to reveal the dependence of the dynamics of the entire mixture on the properties of the solid component, various parameters of the dispersed phase were considered — the volume content as well as the linear size of the dispersed inclusions. The goal of the research was to determine how the properties of solid inclusions affect the parameters of the dynamics of the carrier medium — gas. The motion of an inhomogeneous medium in a shock duct divided into two parts was studied, the gas pressure in one of the channel compartments is more important than in the other. The article simulated the movement of a direct shock wave from a high-pressure chamber to a low–pressure chamber filled with a dusty medium and the subsequent reflection of a shock wave from a solid surface. An analysis of numerical calculations showed that a decrease in the linear particle size of the gas suspension and an increase in the physical density of the material from which the particles are composed leads to the formation of a more intense reflected shock wave with a higher temperature and gas density, as well as a lower speed of movement of the reflected disturbance reflected wave.

The article reports the findings of an investigation into pollution migration processes at the municipal solid waste (MSW) landfill located in the water protection zone of Lake Seliger (Tver Region). The distribution of pollutants is investigated and migration parameters are determined in field and laboratory conditions at the landfill site. A mathematical model describing physical and chemical processes of substance migration in soil strata is constructed. Pollutant migration is found to be due to a variety of factors. The major ones, having a significant impact on the migration of MSW ingredients and taken into account mathematically, include convective transport, diffusion and sorption processes. A modified mathematical model differs from its conventional counterparts by considering a number of parameters reflecting the decrease in the concentration of ammonium and nitrate nitrogen ions in ground water (transpiration by plant roots, dilution with infiltration waters, etc.). An analytical solution to assess the pollutant spread from the landfill is presented. The mathematical model provides a set of simulation models helping to obtain a computational solution of specific problems, vertical and horizontal migration of substances in the underground flow. Numerical experiments, analytical solutions, as well as field and laboratory data was studied the dynamics of pollutant distribution in the object under study up to the lake. A long-term forecast for the spread of landfill pollution is made. Simulation experiments showed that some zones of clean groundwater interact with those of contaminated groundwater during the pollution migration from the landfill, each characterized by a different pollutant content. The data of a computational experiments and analytical calculations are consistent with the findings of field and laboratory investigations of the object and give grounds to recommend the proposed models for predicting pollution migration from a landfill. The analysis of the pollution migration simulation allows to substantiate the numerical estimates of the increase in $NH_4^+$ and $NO_3^-$ ion concentration with the landfill operation time. It is found that, after 100 years following the landfill opening, toxic filtrate components will fill the entire pore space from the landfill to the lake resulting in a significant deterioration of the ecosystem of Lake Seliger.

The paper reviews possibilities to predict buckling of thin cylindrical shells with non-destructive techniques during operation. It studies shallow shells made of high strength materials. Such structures are known for surface displacements exceeding the thickness of the elements. In the explored shells relaxation oscillations of significant amplitude can be generated even under relatively low internal stresses. The problem of the cylindrical shell oscillation is mechanically and mathematically modeled in a simplified form by conversion into an ordinary differential equation. To create the model, the researches of many authors were used who studied the geometry of the surface formed after buckling (postbuckling behavior). The nonlinear ordinary differential equation for the oscillating shell matches the well-known Duffing equation. It is important that there is a small parameter before the second time derivative in the Duffing equation. The latter circumstance enables making a detailed analysis of the obtained equation and describing the physical phenomena — relaxation oscillations — that are unique to thin high-strength shells.

It is shown that harmonic oscillations of the shell around the equilibrium position and stable relaxation oscillations are defined by the bifurcation point of the solutions to the Duffing equation. This is the first point in the Feigenbaum sequence to convert the stable periodic motions into dynamic chaos. The amplitude and the period of relaxation oscillations are calculated based on the physical properties and the level of internal stresses within the shell. Two cases of loading are reviewed: compression along generating elements and external pressure.

It is highlighted that if external forces vary in time according to the harmonic law, the periodic oscillation of the shell (nonlinear resonance) is a combination of slow and stick-slip movements. Since the amplitude and the frequency of the oscillations are known, this fact enables proposing an experimental facility for prediction of the shell buckling with non-destructive techniques. The following requirement is set as a safety factor: maximum load combinations must not cause displacements exceeding specified limits. Based on the results of the experimental measurements a formula is obtained to estimate safety against buckling (safety factor) of the structure.

Corrosion damage to metals and alloys is one of the main problems of strength and durability of metal structures and products operated in contact with chemically aggressive environments. Recently, there has been a growing interest in computer modeling of the evolution of corrosion damage, especially pitting corrosion, for a deeper understanding of the corrosion process, its impact on the morphology, physical and chemical properties of the surface and mechanical strength of the material. This is mainly due to the complexity of analytical and high cost of experimental in situ studies of real corrosion processes. However, the computing power of modern computers allows you to calculate corrosion with high accuracy only on relatively small areas of the surface. Therefore, the development of new mathematical models that allow calculating large areas for predicting the evolution of corrosion damage to metals is currently an urgent problem.

In this paper, the evolution of the corrosion front in the interaction of a polycrystalline metal surface with a liquid aggressive medium was studied using a computer model based on a cellular automat. A distinctive feature of the model is the specification of the solid body structure in the form of Voronoi polygons used for modeling polycrystalline alloys. Corrosion destruction was performed by setting the probability function of the transition between cells of the cellular automaton. It was taken into account that the corrosion strength of the grains varies due to crystallographic anisotropy. It is shown that this leads to the formation of a rough phase boundary during the corrosion process. Reducing the concentration of active particles in a solution of an aggressive medium during a chemical reaction leads to corrosion attenuation in a finite number of calculation iterations. It is established that the final morphology of the phase boundary has a fractal structure with a dimension of 1.323 ± 0.002 close to the dimension of the gradient percolation front, which is in good agreement with the fractal dimension of the etching front of a polycrystalline aluminum-magnesium alloy AlMg6 with a concentrated solution of hydrochloric acid. It is shown that corrosion of a polycrystalline metal in a liquid aggressive medium is a new example of a topochemical process, the kinetics of which is described by the Kolmogorov–Johnson– Meil–Avrami theory.

There are conditions of uneven combustion for tubular powder elements of large elongation used in artillery propelling charges. Here it is necessary to consider in parallel the processes of combustion and movement of powder gases inside and outside the channels of the powder tubes. Without this, it is impossible to adequately formulate and solve the problems of ignition, erosive combustion and stress-strain state of tubular powder elements in the shot process. The paper presents a physical and mathematical formulation of the main problem of the internal ballistics of an artillery shot for a charge consisting of a set of powder tubes. Combustion and movement of a bundle of powder tubes along the barrel channel is modeled by an equivalent tubular charge of all-round combustion. The end and cross-sectional areas of the channel of such a charge (equivalent tube) are equal to the sum of the areas of the ends and cross-sections of the channels of the powder tubes, respectively. The combustion surface of the channel is equal to the sum of the inner surfaces of the tubes in the bundle. The outer combustion surface of the equivalent tube is equal to the sum of the outer surfaces of the tubes in the bundle. It is assumed that the equivalent tube moves along the axis of the bore. The speed of motion of an equivalent tubular charge and its current position are determined from Newton’s second law. To calculate the flow parameters, we used two-dimensional axisymmetric equations of gas dynamics, for the solution of which an axisymmetric orthogonalized difference mesh is constructed, which adapts to the flow conditions. When the tube moves and burns, the difference grid is rearranged taking into account the changing regions of integration. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the Godunov problem of decay for an arbitrary discontinuity. The developed technique was used to calculate the internal ballistics parameters of an artillery shot. This approach is considered for the first time and allows a new approach to the design of tubular artillery charges, since it allows obtaining the necessary information in the form of fields of velocity and pressure of powder gases for calculating the process of gradual ignition, unsteady erosive combustion, stress-strain state and strength of powder elements during the shot. The time dependences of the parameters of the internal ballistics process and the distribution of the main parameters of the flow of combustion products at different times are presented.

The paper proposes a new mathematical model to study the interaction dynamics of the longitudinal wall of a narrow channel with its end seal. The end seal was considered as the edge wall on a spring, i.e. spring-mass system. These walls interaction occurs via a viscous liquid filling the narrow channel; thus required the formulation and solution of the hydroelasticity problem. However, this problem has not been previously studied. The problem consists of the Navier–Stokes equations, the continuity equation, the edge wall dynamics equation, and the corresponding boundary conditions. Two cases of fluid motion in a narrow channel with parallel walls were studied. In the first case, we assumed the liquid motion as the creeping one, and in the second case as the laminar, taking into account the motion inertia. The hydroelasticty problem solution made it possible to determine the distribution laws of velocities and pressure in the liquid layer, as well as the motion law of the edge wall. It is shown that during creeping flow, the liquid physical properties and the channel geometric dimensions completely determine the damping in the considered oscillatory system. Both the end wall velocity and the longitudinal wall velocity affect the damping properties of the liquid layer. If the fluid motion inertia forces were taken into account, their influence on the edge wall vibrations was revealed, which manifested itself in the form of two added masses in the equation of its motion. The added masses and damping coefficients of the liquid layer due to the joint consideration of the liquid layer inertia and its viscosity were determined. The frequency and phase responses of the edge wall were constructed for the regime of steady-state harmonic oscillations. The simulation showed that taking into account the fluid layer inertia and its damping properties leads to a shift in the resonant frequencies to the low-frequency region and an increase in the oscillation amplitudes of the edge wall.

The viscoelastic fluid flow model across a porous medium has captivated the interest of many contemporary researchers due to its industrial and technical uses, such as food processing, paper and textile coating, packed bed reactors, the cooling effect of transpiration and the dispersion of pollutants through aquifers. This article focuses on the influence of variable viscosity and viscoelasticity on the magnetohydrodynamic oscillatory flow of second-order fluid through thermally radiating wavy walls. A mathematical model for this fluid flow, including governing equations and boundary conditions, is developed using the usual Boussinesq approximation. The governing equations are transformed into a system of nonlinear ordinary differential equations using non-similarity transformations. The numerical results obtained by applying finite-difference code based on the Lobatto IIIa formula generated by bvp4c solver are compared to the semi-analytical solutions for the velocity, temperature and concentration profiles obtained using the homotopy perturbation method (HPM). The effect of flow parameters on velocity, temperature, concentration profiles, skin friction coefficient, heat and mass transfer rate, and skin friction coefficient is examined and illustrated graphically. The physical parameters governing the fluid flow profoundly affected the resultant flow profiles except in a few cases. By using the slope linear regression method, the importance of considering the viscosity variation parameter and its interaction with the Lorentz force in determining the velocity behavior of the viscoelastic fluid model is highlighted. The percentage increase in the velocity profile of the viscoelastic model has been calculated for different ranges of viscosity variation parameters. Finally, the results are validated numerically for the skin friction coefficient and Nusselt number profiles.

In single-photon emission computed tomography (SPECT), patients with bone disorders receive a radiopharmaceutical (RP) that accumulates selectively in pathological lesions. Accurate quantification of RP uptake plays a critical role in disease staging, prognosis, and the development of personalized treatment strategies. Traditionally, the accuracy of quantitative assessment is evaluated through in vitro clinical trials using the standardized physical NEMA IEC phantom, which contains six spheres simulating lesions of various sizes. However, such experiments are limited by high costs and radiation exposure to researchers. This study proposes an alternative in silico approach based on numerical simulation using a digital twin of the NEMA IEC phantom. The computational framework allows for extensive testing under varying conditions without physical constraints. Analogous to clinical protocols, we calculated the recovery coefficient (RC_max), defined as the ratio of the maximum activity in a lesion to its known true value. The simulation settings were tailored to clinical SPECT/CT protocols involving ^99mTc for patients with bone-related diseases. For the first time, we systematically analyzed the impact of lesion-to-background ratios and post-reconstruction filtering on RC_max values. Numerical experiments revealed the presence of edge artifacts in reconstructed lesion images, consistent with those observed in both real NEMA IEC phantom studies and patient scans. These artifacts introduce instability into the iterative reconstruction process and lead to errors in activity quantification. Our results demonstrate that post-filtering helps suppress edge artifacts and stabilizes the solution. However, it also significantly underestimates activity in small lesions. To address this issue, we introduce post-reconstruction correction factors derived from our simulations to improve the accuracy of quantification in lesions smaller than 20 mm in diameter.

Physical-mathematical model of drying of coal particles in the gas stream and the results of calculating the drying of the particles of brown coal in a drying tube are presented. It is shown that for the drying of coal can be used superheated water vapor. Thermodynamic model of drying of a particle in a drying tube are proposed. It allows to conduct a preliminary assessment of parameters of drying process.

Comparative analysis of two models of porous medium (Dacry and Brinkman) on an example of mathematical simulation of transient natural convection in a porous vertical cylindrical cavity with heat-conducting shell of finite thickness in conditions of convective cooling from an environment has been carried out. The boundary-value problem of mathematical physics formulated in dimensionless variables such as stream function, vorticity and temperature has been solved by implicit finite difference method. The presented verification results validate used numerical approach and also confirm that the solution is not dependent on the mesh size. Features of the conjugate heat transfer problems with considered models of porous medium have been determined.