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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2023  THE MONOTONE METHOD OF FRACTIONAL PARTICLES FOR TWODIMENSIONAL ELASTOPLASTIC FLOWS
V. A. Shmelyev, I. E. Cherednichenko, Yu. V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 2. P. 315.
The paper describes the main algorithms of the twodimensional method of fractional particles for the simulation of elastoplastic flows in the LagrangianEulerian LEGAK code. The method is used to resolve the problem of the equation approximation accuracy in the convective transport stage for mixed cells, while eliminating the disadvantage of the classic method of particles, namely, the solution nonmonotonicity caused by the discrete transport of mass and accompanying quantities from one cell to another. The sudden fracture and compaction model and Kanel’s model have been implemented on the base of the monotone method of fractional particles. The first model was tested on the problem of adiabatic compression and expansion of a plane layer, the second one was tested on the problem of colliding copper plates. And, also, the both models were tested on the problem of a steel sphere impacting a composite barrier. The results obtained confirm that the implemented method allows improving the accuracy of describing the material elastoplastic straining and fracturing processes within the continuum mechanics on immobile meshes. Key words: elastoplastic flow, model of sudden fracture, Kanel´s model, brittle spall, damage measure, the monotone method of fractional particles, numerical simulation.
 NUMERICAL SOLUTION OF THREEDIMENSIONAL PROBLEMS OF IMPACT INTERACTION OF ELASTOPLASTIC BODIES IN EULER VARIABLES ON THE BASIS OF MODIFIED GODUNOV SCHEME M. H. Abuzyarov, E. G. Glazova, A. V. Kochetkov, S. V. Krylov, A. A. Lisitsyn, I. A. Modin VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 2. P. 1629.
The numerical method earlier developed by the team of authors for solving threedimensional coupled problems of the dynamic (highspeed) interaction of deformable bodies and media in Euler variables based on Godunov´s scheme of a higher accuracy is used to solve problems of impact interaction of elastoplastic bodies. An improved accuracy of the scheme is achieved by changing the "predictor" step. A 3D timedependent solution of the elastic Riemann problem is applied, which provides the secondorder approximation in time and space in the region of smooth solutions. Monotonicity in the region of discontinuous solutions is ensured by changing over to the "predictor" step of the firstorder scheme. A multigrid approach is used with the three types of computational grids for each body with an explicit Lagrangian selection of moving free and contact surfaces: a Lagrangian surface grid in the form of a continuous set of triangles (STL file), which is used both to set the initial geometry of a liquid and a solid body and to accompany it during the calculation, and two types of 3D volumetric grids. The results of solving test and 3D applied problems with large displacements and deformations are presented and they demonstrate the numerical method potential. The impact and penetration processes are considered, including the deformable impactor penetration through a singlelayer and a twolayer elastoplastic barrier. The impactor ricocheting during oblique impact is described. Numerical results demonstrate a good performance of the numerical models and techniques in use. Key words: numerical simulation, Godunov´s scheme, improved accuracy, multigrid approach, threedimensional problem, elastoplastic barrier, multilayered structure, deformable impactor, impact, penetration, ricochet.
 THE HISTOGRAM DATA APPROXIMATION WITH THE CONDITIONAL MINIMIZATION METHOD FOR THE LENGTH OF THE CUBIC C^{1}CLASS SPLINE WITH THE NONNEGATIVENESS AND LOCAL MONOTONICITY PROPERTIES. PART 1 S. V. Mzhachikh, N. V. Kolobyanina, Yu. N. Lapshina VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 2. P. 3044.
The paper considers the problem of processing the data which is available in the form of a function of a single variable given by a stepwise histogram. With such data approximation built in the form a cubic C^{1}class spline with the desired properties, possible, including nonnegativeness and local monotonicity, the researcher can estimate the monotonicity sites and values at the given points, both for the function itself and for its derivative. The paper presents the fundamental principles of the approximation calculation method. The problem is solved with the method of minimizing the target function, which is the spline curve length dependence on the vector quantity. For the vector in question, a region is formed, which sets the required spline properties. The problem is solved most accurately with the use of limitations in the form of nonlinear inequalities, however, in some problems linear inequalities are also permitted. In the latter case, an approximate solution can be found, quickly and with no faults. Key words: cubic spline, conditional minimization, locally monotone approximation, nonnegative approximation, the modified Lagrangian method, the gradient descent method, the Newton linearization method, intragroup spectrum.
 THE EGAK CODE ADAPTATION TO COMPUTATIONS ON HYBRID COMPUTERS WITH GRAPHIC ACCELERATORS A. M. Erofeev, E. A. Sizov, I. Yu. Turutina, I. N. Chistyakova VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 2. P. 4558.
The paper presents results of efforts on the EGAK code adaptation to computations on parallel hybrid computers with graphic accelerators (GPUs). The EGAK code is used for the numerical simulation of multidimensional continuum mechanics problems using an immobile computational mesh. The code uses an adaptively refined mesh that introduces irregularity to the mesh structure. The approaches to resolving the problems that arise in the development of the program for computations of GPUs are described. The paper considers the issues of selecting the program implementation, when adapting the existing algorithms of the code, the issues of data transfer in case of several GPUs used in the computation. The problem of simultaneously enabling all computing resources of the node (concurrent computations on all available CPU cores and all available GPUs) is considered. The speedup values gained on a hybrid computing node with GPUs using the test problems typical for the code are shown in comparison with the node having only CPUs. Key words: the EGAK code, EGIDATEST, GPU, speedup, parallelization, CUDA, MPI, OpenMP, efficiency, gas dynamics, adaptive refined mesh.
 CREATION OF A UNIFORM LASER RADIATION FLOW OF PICOSECOND DURATION ON THE INNER SURFACE OF THE TARGET WITH INVERSE CORONA USING THE DESIGNFORM REFLECTOR V. M. Yamshchikov VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 2. P. 5964.
The idea of adding to the inversecorona target design a reflector, which scatters, as uniformly as possible, laser energy from its surface over the inner surface of the target is considered. It was supposed in the theoretical study that the scattered radiation indicatrix consists of the summarized mirrored and Lambertian parts. For such indicatrix, the reflector surface form was designed, which provides absolutely uniform distribution of the mirrored component of the scattered energy over the inner surface of the target with inverse corona. The gas dynamic plasma spread from the reflector surface is not taken into account, it is shown that it can be neglected for some realistic parameters of the target and laser radiation. The radiation distribution is described in the geometric optics approximation. Key words: target with inverse corona, mirror reflector, indicatrix, Lambert law, laser plasma.
 CORRECTION OF OVERLAPS IN SURFACE TRIANGULAR MESHES IN THE LOGOS SOFTWARE PACKAGE PREPROCESSOR DURING PREPARATION OF AERO AND HYDRODYNAMICS PROBLEMS E. O. Evstifeeva VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 2. P. 6576.
The paper describes an algorithm of correcting overlaps in surface triangular meshes of different types. The algorithm is used in the computational model preparation chain in the "Logos" software package preprocessor, when solving problems in aerodynamics and hydrodynamics. In contrast to the most part of existing approaches oriented to a certain type of the original mesh and using the global reconstruction of the mesh to correct it, the proposed algorithm has no limitations on the input data and changes the mesh in local regions only, where overlaps have been detected. The algorithm includes two stages: first, the detected overlaps are corrected using local operations with elements of the mesh (triangular cells and their vertices) and then, if noncorrected overlaps are present, the region of triangular cells is removed, the hole is filled out with new triangles, and the new mesh region optimization is performed to improve the mesh quality. Key words: "Logos" software package, preprocessor, generator of a surface triangle mesh (surface generator), cell overlaps, quality of mesh.
 TRUNK SECURED FIBEROPTIC TRANSMISSION SYSTEMS V. V. Shubin VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 2. P. 7786.
The paper considers multiwavelength secured fiberoptic transmission systems with optical amplifiers and the corresponding technology of modern optic transport networks. A new engineering solution is proposed to build such systems. It is shown that trunk secured fiberoptic transmission systems can be built with the intermediate points located outside of the control area. The proposed trunk secured fiberoptic transmission system consists of the information, monitoring, and data security components. For the monitoring of systems with optical amplifiers, coherent reflectometers are used, which take a part of the protection functions based on the reverse scattering method. The information security is provided by a specially introduced device based on the direct detection method. So, two methods are used for the data protection. In trunk fiberoptic transmission systems, the security of data with the use of technical means can be provided by the transocean fiberoptic system technologies. Key words: trunk secured fiberoptic transmission system, optic transport network technology, optical activefiber amplifiers, monitoring system based on coherent optical reflectometers, engineering solutions for trunk fiberoptic transocean transmission lines.
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