Algorithm For Numerical Simulation Research Articles

О ВЛИЯНИИ ОЧИСТНЫХ РАБОТ НА ХАРАКТЕР ДЕФОРМИРОВАНИЯ ДЕМОНТАЖНЫХ ВЫРАБОТОК

The paper presents the results of numerical modeling of the geomechanical behavior of the system “lava — operational excavation — enclosing potash rock mass” during mining operations. Numerical modeling includes a forecast of the mechanical behavior of the system at all stages of the system existence: from the natural stress-strain state (SSS) of the rock mass to excavation and safety measures installation, as well as the longwall mining operations. The results of numerical experiments are verified using the data from field studies of convergence of the roof and floor of the operational excavation and the side walls of this excavation. As a result of the studies, it is established that longwall mining has a significant impact on the operational excavation at a distance of about 40 m or less. In addition, the paper describes an algorithm for numerical simulation of the geomechanical behavior of the considered geotechnical system.

The fractional non-polynomial spline method: Precision and modeling improvements

This research introduces the fractional non-polynomial spline method as a novel scheme for solving the time-fractional Korteweg-de Vries (KdV) equation. The study focuses on numerical analysis and algorithm development for simulation purposes. The proposed method involves the construction of a fractional non-polynomial spline to estimate the equation's solution, offering improved precision and modeling capabilities compared to existing approaches. To assess the stability of the proposed approach, the von Neumann method is employed, demonstrating its unconditional stability within a specific parameter range. To validate the effectiveness of our numerical analysis and simulation algorithm, contour, 2D, and 3D graphs are utilized to compare the solution obtained through our method with an analytical solution. Through rigorous comparative analysis with previous works, the superiority of our approach in terms of accuracy and efficiency is demonstrated. Norm error calculations, specifically the (L2and L∞) error norms, provide a quantitative assessment of the accuracy and reliability of our proposed scheme.

Erosion Life Prediction of Metal Mesh Screen Pipes in Oil Wells Based on Numerical Simulation of Discrete Particle Flow.

High-speed fluid-carried sand particles pose a significant challenge to oil well screen pipes, leading to sand control failure and adversely affecting the well's production and recovery rates. This research targets the commonly used metal mesh screen pipe in oil well sand production and establishes a full-sized three-dimensional structure model. A fluid-solid coupling of discrete particle flow numerical simulation algorithm is incorporated to formulate a novel method for predicting the screen pipe's erosion life. This method provides a solution to the complex task of predicting the pipe's lifespan under oil sand fluid erosion. The analysis elucidates the impact of sand particles on the velocity distribution and erosion rate of the metal mesh at varying velocities, facilitating the prediction of the mesh screen pipe's erosion life. Key findings reveal that the velocity and erosion rate vary across the different layers. The first layer screen experiences velocity and erosion rates that are 3.6-3.76 times and 2.45-2.50 times, respectively, higher than those at the inlet. The second layer screen undergoes velocity and erosion rates 2.32-2.43 times and 1.04-1.06 times, respectively, higher than those at the inlet. Erosion failure primarily occurs in the first layer screen due to velocity expansion instigated by the screen tube's structure. The discrete flow numerical simulation method proves valuable in predicting the mesh screen's erosion life at different flow rates, with a maximum error of 6.38% when compared with field monitoring life values. This method introduces a new technical approach to predicting the life span of metal mesh screens in oil wells. The study concludes by suggesting measures to extend the screen pipe's lifespan, thereby enhancing oil recovery.

Energetic and exergetic analysis of a transcritical CO2 air-source heat pump water heating system in the cold region

To analyze the energetic and exergetic performance of the transcritical CO2 air-source heat pump water heating system in the cold region, the numerical model and simulation algorithm are set up and verified with the experiments. Under the low ambient temperature (−15 °C to 0 °C) and water inlet temperature (9 °C), the performance evaluation of the system is investigated using the developed numerical model at different compressor frequency (75, 80 and 85 Hz). The results show that Qgc, COP and ηex decrease by 14.47%, 12.78% and 20.83% respectively as the ambient temperature decreases from 0 °C to −15 °C. The CO2 outlet state of the gas cooler and corresponding slope of isotherms have significant effects on COP and ηex. The COPopt and ηex,opt exist in the system but at different compressor discharge pressures. With the compressor frequency increasing from 75 Hz to 85 Hz, the increase in Qgc is at the cost of a decrease in COP, and COPopt decreases by 5.31%. The effect of the compressor frequency on ηex is different as the compressor discharge pressure elevates. Thus, a suitable operating condition, considering different needs, should be selected in the system operation.

Techno-Environmental Evaluation and Optimization of a Hybrid System: Application of Numerical Simulation and Gray Wolf Algorithm in Saudi Arabia

Renewable energy systems have the potential to address increasing energy demand, mitigate environmental degradation, and decrease reliance on fossil fuels. Wind and solar power are examples of renewable energy sources that are characterized by their cleanliness, environmental friendliness, and sustainability. The combination of wind and solar energy is motivated by each energy source’s inherent variability. The objective of this study is to assess the technical, economic, and environmental aspects of a hybrid system designed to provide energy. This study utilizes numerical simulation and develops a novel model using the gray wolf optimization (GWO) algorithm to assess the technical, economic, and environmental consequences of adopting a hybrid system. The evaluation focused on determining the optimal configuration of a greenhouse unit in Najran, Saudi Arabia, over a period of 20 years. The results showed that the diesel generator produced 42% of the required energy when combined with photovoltaic generators, while photovoltaics produced 58%. The wind turbine generated 23% of the required power while the remaining 77% was produced by the diesel generator. Finally, diesel generators, photovoltaics, wind turbines were observed to generate 37%, 48%, and 15% of the required energy, respectively. This outcome is consistent with current knowledge because solar and wind systems reduce pollution. However, the diesel generator–photovoltaic–wind mode is the preferred method of reducing emissions. Finally, the rate of return on investment for diesel generators is 3.4 years, while for diesel-photovoltaic generators and the triple array it is 2.5 and 2.65 years, respectively.

Electromagnetic Transient (EMT) Simulation Algorithms for Evaluation of Large-Scale Extreme Fast Charging Systems (T& D Models)

Simulation of high-fidelity models of extreme fast charging (XFC) systems and large-area power grids with many XFCs can be time consuming in traditional simulators. Traditional simulators use a single method of discretization for all the components that results in imposing a large computational burden of inverting a large matrix as well as increased computations related to single method of discretization (that is typically a trapezoidal method). To overcome the problem of simulating large-area power grids with many XFCs, in this paper, advanced numerical simulation algorithms are applied for the first time together to reduce the dimension of matrix inversion. The algorithms include numerical stiffness-based segregation, time constant-based segregation, clustering and aggregation on differential algebraic equations (DAEs), and multi-order integration approaches. These algorithms apply multiple discretization algorithms rather than a single discretization algorithm that further reduces the computational burden. The approaches mentioned here have resulted in speed-up of up to 18x in the simulation of a single distribution system with 15 XFCs and of up to 271x in the simulation of a transmission-distribution system with 300 XFCs in multiple distribution feeders with respect to conventional simulators (like power systems computer aided design [PSCAD]).

Impact of Continuous Cable-Strut Joints on the Anti-Progressive-Collapse Performance of Suspended-Dome Structures

In suspended-dome structures, cable-strut joints can be categorized into discontinuous joints and continuous joints. In calculations, the discontinuous joints can be treated as hinge joints. However, in the event of a cable breakage, the continuous joints might experience slip and detachment phenomena. Simplifying continuous cable-strut joints as hinge joints for calculation purposes can result in a significant discrepancy from the actual load-bearing state of the continuous joints. In fact, under the scenario of cable rupture, the continuous cable-strut joints might undergo slip and detachment. This could influence the formation of new tension paths within the cable support system, thereby affecting the anti-collapse performance of the suspended-dome structure. Therefore, this paper investigates the influence of the slippage and detachment of continuous cable-strut joints on the anti-progressive collapse performance of suspended-dome structures through joint tests, numerical simulations, and theoretical analyses. Firstly, two cable-strut joint test models were constructed. Apart from the difference that one uses a discontinuous cable-strut joint and the other a continuous cable-strut joint, all other conditions were kept identical. Research was conducted on the hoop cable failure test. The results indicate that the slippage and detachment of continuous joints hinder the formation of new tension paths in the lower cable-strut system. Structures using continuous cable-strut joints have lower anti-collapse capabilities compared to those using discontinuous cable-strut joints. Secondly, a simplified numerical simulation algorithm for cable-strut joints’ slippage and detachment is proposed. This algorithm only considers the support of struts to the upper structure and uses an Abaqus subroutine to achieve an equivalent simulation of the slippage and detachment phenomena of continuous joints during the finite element computation process. Then, using this algorithm, a progressive collapse analysis of suspended domes using continuous cable-strut joints was carried out. It was found that for suspended domes with continuous cable-strut joints, the slippage and detachment of the cable-strut joints are extremely detrimental to forming new tension paths, making the structure more susceptible to a progressive collapse. Lastly, using the resistance index, a quantitative analysis was conducted on the anti-collapse carrying capacity of suspended domes using both continuous and discontinuous cable-strut joints.

A crystal plasticity-based microdamage model and its application on the tensile failure process analysis of 7075 aluminum alloy

In this study, a microdamage model by introducing the damage of crystal is proposed. Damage variables are defined for each slip system, and the damage-coupled crystal plasticity constitutive equations are derived by virtue of the concept of effective stress and the hypothesis of strain equivalence. A function of damage driving force is proposed by analyzing failure mechanisms. The damage evolution equation is then derived based on thermodynamics. After that, a differential evolution-based method is adopted for the calibration of the parameters, and a numerical simulation algorithm is implemented for the failure process simulation of a single crystal material for verification purposes. The proposed model and the corresponding numerical method are then applied to the failure process analysis of a polycrystalline material 7075 aluminum alloy. The EBSD observation is conducted to obtain the size and orientation of grains, which combines with the Voronoi diagram method to be the basis for establishing the polycrystal finite element model. Afterwards, the numerical simulation of the failure process of specimens under tension is conducted. The predicted results are in good agreement with the experimental observations. It indicates that the proposed model can well reflect the damage-softening effect from the microplasticity to the macroscopic deformation. Finally, the two damage mechanisms of grains in 7075 aluminum alloy are investigated based on the calculated result.

Epidemic monitoring in real-time based on dynamic grid search and Monte Carlo numerical simulation algorithm.

Building upon the foundational principles of the grid search algorithm and Monte Carlo numerical simulation, this article introduces an innovative epidemic monitoring and prevention plan. The plan offers the capability to accurately identify the sources of infectious diseases and predict the final scale and duration of the epidemic. The proposed plan is implemented in schools and society, utilizing computer simulation analysis. Through this analysis, the plan enables precise localization of infection sources for various demographic groups, with an error rate of less than 3%. Additionally, the plan allows for the estimation of the epidemic cycle duration, which typically spans around 14 days. Notably, higher population density enhances fault tolerance and prediction accuracy, resulting in smaller errors and more reliable simulation outcomes. Overall, this study provides highly valuable theoretical guidance for effective epidemic prevention and control efforts.

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equation is solved at each time step usually in physical space using iterative solvers, and the resulting pressure gradient is then applied to make the velocity field divergence-free. It is generally accepted that this pressure-correction stage is the most time-consuming part of the flow solver and any meaningful acceleration would contribute significantly to the overall computational efficiency. The objective of the present work was to develop a fast hybrid pressure-correction algorithm for numerical simulation of incompressible flows around obstacles in the context of projection methods. The key idea is to adopt different numerical methods/discretisations in the sub-steps of projection methods. Here, a classical second-order time-marching projection method, which consists of two sub-steps, was chosen for the purposes of demonstration. In the first sub-step, the momentum equations were discretised on unstructured grids and solved by conventional numerical methods, here a meshless method. In the second sub-step (pressure-correction), the proposed algorithm adopts a double-discretisation system and combines the weighted least-squares approximation with the essence of immersed boundary methods. Such a design allowed us to develop an FFT-based solver to speed up the solution of the pressure Poisson equation for flow cases with obstacles, while keeping the implementation of the boundary conditions for the momentum equations as easy as conventional numerical methods do with unstructured grids. The numerical experiments of five test cases were performed to verify and validate the proposed hybrid algorithm and evaluate its computational performance. The results showed that the new FFT-based hybrid algorithm works and is robust, and it was significantly faster than the multigrid-based reference method. The hybrid algorithm opens an avenue for the development of next-generation high-performance parallel computational fluid dynamics solvers for incompressible flows.

Numerical Analysis of Transient State Heat Transfer by Spectral Method Based on POD Reduced-Order Extrapolation Algorithm

In order to meet the requirements of high accuracy and fast algorithm for numerical heat transfer simulation, an iterative scheme of Proper Orthogonal Decomposition (for short, POD) dimension reduction based on the classical central difference Galerkin spectral method is proposed for solving two-dimensional transient heat conduction problems. The POD dimension reduction spectral method model is constructed by taking the calculation results of classical central difference Galerkin spectral method as sample data. The numerical algorithm characteristics of flow and heat transfer are studied by using a partial differential equation as a mathematical model, and the error estimation is given. Finally, different time intervals are used as parameters to simulate experiments. The results show that the POD method is applicable to transient nonlinear heat conduction problems, and the maximum average relative error of the reconstructed temperature field is 0.89675%. Moreover, the POD method not only has a high calculation accuracy, but also has an average calculation speed as high as 310.25 times that of the central difference Galerkin algorithm. It can be seen that under the condition that the error between the solution of POD dimension reduction extrapolation algorithm and the solution of classical central difference Galerkin spectrum method is small enough, the POD method can greatly reduce the calculation amount, shorten the running time, and ensure a high accuracy of the calculation results, thus verifying the effectiveness and feasibility of the algorithm.

Stress prediction of heated crude oil pipeline in permafrost region via fully coupled heat-moisture-stress numerical simulation and SVM algorithm

Large diameter crude oil transmission pipelines in unstable permafrost areas have been put into operation in China in recent dozen years. The perennial positive temperature operation of buried heating transmission pipelines leads to freeze–thaw of the soil around pipelines, and the axial stresses generated by thawing settlement of permafrost may induce fracture failure of weld crack. However, there are many shortcomings in existing frozen soil thawing settlement analysis and pipeline stress assessment methods, which makes it difficult to accurately analyze and predict the axial additional stress of pipelines induced by thawing settlement. Based on heat conduction and permafrost thawing consolidation settlement theory, numerical inversion analysis of centrifuge test was conducted to verify the accuracy of the finite element method. The key influencing factors such as wall thickness, insulation layer thickness, buried depth of pipe, and length of thawing settlement zone on the axial stress and strain state of buried pipeline under the condition of double pipe operation of Mo-da line were investigated. The results show that: Pipeline with an insulation layer, larger wall thickness and smaller buried depth is beneficial to improve the bearing capacity of buried pipeline under thawing settlement of permafrost. The axial stress varies nonlinearly with the increase of the thawing settlement zone length. Based on support vector regression (SVR) model, the axial stress prediction model of pipe crown and invert at different positions in the thaw settlement area was proposed and verified by field monitoring data of buried pipeline. The relative error between the prediction results and the field monitoring results is less than 15 %. This study can provide some theoretical support for the structural design of pipelines in thaw settlement area.

P- and S-wave energy current density vectors dot product imaging condition of source time-reversal imaging

SUMMARY Source time-reversal imaging (TRI) based on decoupled elastic wave equation can utilize vector P- and S-wave time differences and achieve high-precision source location in complex geological models. The imaging condition is critical for TRI. However, because of the orthogonally polarized properties of P and S waves, traditional vector dot product imaging condition directly applied to TRI will decrease the effective imaging values. In contrast, the energy current density vectors of P and S waves represent the propagation directions of the wavefields and are almost parallel. Their dot product can result in the maximum imaging energy. Based on this principle, we propose a P- and S-wave energy current density vectors dot product imaging condition (PSEDPIC), which uses the propagation direction information of P and S waves at the source point to suppress imaging artefacts generated by waves with inconsistent propagation directions. Numerical tests reveal that PSEDPIC can (1) reduce the image artefacts, (2) improve the imaging spatial resolution and (3) allow a shallower imaging region. In addition, if the numerical simulation algorithm used in TRI can reconstruct the seismic wavefield accurately in the presence of surface topography, the impact of an observation system with elevation differences on imaging can be eliminated automatically. For this reason, we use the curvilinear grid finite-difference method to directly reconstruct the wavefield in TRI to solve the problem of data elevation correction. The test results of 3-D synthetic and field data for microseismic monitoring demonstrate the effectiveness of the proposed method.

Coupling effect of critical properties shift and capillary pressure on confined fluids: A simulation study in tight reservoirs

Critical properties shift and large capillary pressure are important contributors for the phase behavior altering of nanopore fluid. However, the effects of critical properties shift and large capillary pressure on the phase behavior are ignored in traditional compositional simulators, leading to inaccurate evaluation results of tight reservoirs. In this study, phase behavior and production of confined fluid in nanopores are studied. First, we developed a method for coupling the effect of critical properties shift and capillary pressure into the vapor-liquid equilibrium calculation base on Peng-Robinson equation of state. Second, a novel fully compositional numerical simulation algorithm considering effect of critical properties shift and capillary pressure on phase behavior is accomplished. Third, we have discussed the alterations of critical properties shift effect, capillary pressure effect and coupling effect on the composition of oil and gas production in detail. The critical properties shift and capillary pressure effects on oil and gas production in tight reservoirs are analyzed quantitatively through four cases, and the influences of the two effects in oil/gas production are compared. Based on the fully compositional numerical simulation, the simulator can rigorously simulate the impacts of component changes during production. The simulation results show that both the critical properties shift effect and the capillary pressure effect reduce the bubble point pressure of Changqing shale oil, and the influence are more prevalent in pores of smaller radius. In pores is larger than 50 nm, the phase behavior altering of the fluid can be ignored. In addition, we devised four cases to comprehensively investigate the effects of critical properties shift and large capillary pressure on production performance of tight reservoirs. The comparisons between the four cases show that the capillary pressure effect impacts the reservoir production performances greater than the critical properties shift effect, such as higher oil production, higher GOR, and lower content of lighter component and higher content of heavier component in the residual oil/gas. The results of coupling effects indicate that the critical properties shift effect would suppress the effect of the capillary pressure effect. In particular, the difference between the simulation results of the coupling effects and the base case is smaller than that between the simulation results of the capillary pressure effect and the base case.

Expanding Measuring Range of LWD Resistivity Instrument in High Permittivity Layers

The effective measuring range of an electromagnetic wave resistivity instrument used in logging while drilling (LWD) is small, and the resistivity measurement is greatly influenced by the dielectric constant, especially in high-dielectric-constant formations. In this paper, the response characteristics of the instrument under a high dielectric constant are investigated by a numerical simulation algorithm, and the resistivity conversion method is determined. The results show that the higher the working frequency of the electromagnetic wave resistivity instrument while drilling, and the greater the formation of background resistivity, the greater the influence of the dielectric constant on the logging response. The existence of the dielectric constant will cause the phase shift and amplitude attenuation of the measured signal to migrate, and this migration is proportional to the formation resistivity and the dielectric constant. According to this rule, the resistivity–permittivity response library is established, and the formation permittivity is calculated by the inversion of the library. On the basis of obtaining the formation permittivity, the migration of the logging signal permittivity is corrected, the influence of the dielectric constant is eliminated, and the measuring precision and measuring range of the instrument in the high-dielectric-constant formation are enlarged.

Study on Perforation Behavior of PTFE/Al Reactive Material Composite Jet Impacting Steel Target

To study the penetration and cratering effect of reactive material composite jets, a series of experiments are carried out for the shaped charge (SC) with different composite liners damaging steel targets. The inner layer of composite liners is metal and the outer one is a polytetrafluoroethylene/aluminum (PTFE/Al) reactive material. Copper (Cu), titanium (Ti) and Al inner liners are used in this paper. The reactive material liner is composed of 73.5 wt.% PTFE and 26.5 wt.% Al powder through mass-matched ratios. Reactive material composite liners are prepared through machining, cold pressing and a sintering process. The SC mainly consists of a case, a composite liner, high-energy explosive and an initiator. The steel target is steel 45#, with a thickness of 66 mm. A standoff of 1.0 CD (charge diameter) is selected to conduct the penetration experiments. The experimental results show that when the inner layer of the composite liner is composed of Ti and Al, the hole diameters on the steel target formed by the reactive material composite jet are significantly larger than that of the inner Cu liner. By introducing the initiation delay time (τ) and detonation-like reaction model of PTFE/Al reactive materials, an integrated numerical simulation algorithm of the penetration and detonation-like effects of reactive material composite jets is realized. Numerical simulations demonstrate that the initial penetration holes on the steel targets are enlarged under the detonation-like effects of PTFE/Al reactive materials, and the simulated perforation sizes are in good agreement with the experimental results.

Analysis and achievement for fractional optimal control of Hepatitis B with Caputo operator

Deciphering the effect of long memory on dynamic behavior is important for controlling disease transmission. Employing fractional order calculus, here, we propose a model with Caputo operator to emphasize the regulation effect of the long memory on the optimal control of Hepatitis B. Considering four different health classes of populations, susceptible, acute infections, chronic infections, and recovered, we try to elucidate the existence of the optimal solution of the fractional optimal control problems (FOCP) by applying a strategy of isolation, treatment, and vaccination. Initially, we discuss the locally asymptotically stability of the equilibrium solutions of the fractional differential model. Sensitivity analysis and numerical simulations are also carried out to verify how parameter changes affect the system dynamics, that is, the threshold effect depending on the basic reproduction number, which provides inspiration for constructing the controlled system. After that, the necessary conditions for the optimality of the Hepatitis B system are derived to focus on the Caputo fractional operator with a singular kernel. An effective numerical simulation algorithm based on trapezoidal approximation is used to validate the control effect in the sense of the transient response by comparing the difference between the fractional-order and integer-order derivatives, and the numeric results can vividly show the attenuation effect of memory on control. This study may provide a powerful rationale for uncovering the importance of the long-memory effects in disease control.

Effect of Tilted Uniaxial Electrical Anisotropy Parameters on Signals of Electric and Electromagnetic Logging Soundings according to Results of Numerical Simulation

Abstract —To study the effect of tilted uniaxial electrical anisotropy parameters on electric and electromagnetic logging signals, their numerical simulation and comparative analysis in homogeneous and layered models have been performed. An algorithm for three-dimensional numerical simulation of resistivity logging signals in spatially heterogeneous models with tilted principal axes of the electrical conductivity tensor, based on the finite-element method, was used in the calculations. The obtained results indicate the potential for a more accurate estimation of electrophysical properties of fractured carbonate reservoirs of the pre-Jurassic basement of West Siberia, which are characterized by the tilt of the electrical conductivity tensor principal axes.

Control of spacecraft by using multiple model algorithms

Abstract. An effective scheme for fault detection and identification (FDI) and adaptive reconfigurable control (ARC) for controlling a spacecraft under conditions of actuator failures, saturation of control inputs and large external disturbances is proposed. The obtained results increase significantly the autonomy of the spacecraft. The control scheme, based on a general methodology of multiple models, switching and tuning, is designed in the context of nonlinear spacecraft dynamics. The results obtained by using the proposed scheme are illustrated by using numerical simulation algorithms. Keywords spacecraft control, multi-model approach, nonlinear dynamics of spacecraft, numerical simulation algorithm

Формирование криптографического ключа в сопряженных приемо-передающих атмосферных лазерных системах

The security of transmission and retrieval depends on the encryption of information sent over public networks. At present, approaches to data protection based on cryptography methods using one-way mathematical functions are widely used. Symmetric and asymmetric methods of key transmission over open communication channels have been developed. The stability of information protection methods using one-way mathematical functions is based on the algorithmic complexity of their hacking for modern computers. The emergence of quantum computers of sufficient power will radically change the situation. Therefore, at present, the question of developing methods for distributing cryptographic keys based on new principles is acute. Such methods include quantum cryptography and cryptography based on stochastic physical processes. In this work, a brief review of the key generation methods based on the principles of quantum physics is carried out, and then the possibility of using fluctuations of the received radiation power caused by atmospheric turbulence to generate keys is investigated. Numerical and experimental modeling of the process of wave propagation in a system of two coupled transceivers operating in a turbulent medium (atmosphere) has been performed. For this purpose, appropriate algorithms for numerical simulation of the characteristics of optical fields distorted by the atmospheric propagation channel have been developed. An experimental setup has been developed and a model experimental study of the formation of correlated random signals in transmit-receive laser systems has been carried out. The need to use low-frequency filtering of the received signals was found. The efficiency of this filtration has been studied. The results of the work allow us to conclude that the use of atmospheric turbulence as a random signal generator makes it possible to form an almost identical cryptographic key in two communication channels directed towards each other.