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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2023  AN ANISOTROPIC CLOSURE MODEL FOR ELASTOPLASTICITY EQUATIONS OF A MULTIMATERIAL MEDIUM IN MIXED CELLS
A.L. Stadnik, Yu. V. Yanilkin, O. O. Toporova VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 316.
In the ElerianLagrangian and Eulerian methods for the simulation of elastoplastic flows mixed cells may contain materialmaterial interfaces. A twostage approach is used in the ALE methods. In the first (Lagrangian) stage, the elastoplasticity equations without convective terms are considered, the convective transport equation is taken into account in the second stage. The paper describes a new anisotropic closure model used in the Lagrangian stage for the elastoplasticity equations in mixed cells containing two, or more components of the medium. The model is implemented in the 2D EGAK code. Problem setups and results of computations for the 2D and one 1D test problems demonstrating the new method advantages are presented. Key words: closure model, mixed cell, multimaterial medium, finite difference methods, numerical simulation, twodimensional flows, elastoplasticity.
 COMPARISON BETWEEN WPH AND DISPH METHODS OF PARTICLES IN SIMULATION OF INSTABILITIES F. A. Sapozhnikov, V. S. Rykovanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 1733.
Two methods of particles  the WPH and DISPH methods  are compared on the problems with instability generation and growth. To find errors induced by the methods, test problems having exact solutions are solved. The "Cube transport" test is used to simulate the static balance and the "GreshoChan vortex" test is used to simulate the dynamic balance. The RayleighTaylor instability is simulated for the 3D αGroup problem and an extended problem, the growth rate coefficient of bubbles is calculated. The KelvinHelmholtz instability with singlemode and multimode disturbances is simulated for 2D and 3D problems. The growth rate coefficient of the mixing zone is calculated. To simulate the RichtmayerMeshkov instability, the "Inverse chevron" problem has been selected, for which experimental results are available. In all test problems simulated with the WPH method we obtained a less error and observed a higher computation speed, as compared to the DISPH method. So, the conclusion is made that is reasonable to use the WPH method for the simulation of problems requiring the instability growth to be described. Key words: hydrodynamics of smoothed particles, the SPH method, hydrodynamics of weighted particles, the WPH method, the Molokh code, GreshoChan vortex, the RayleighTaylor instability, the KelvinHelmholtz instability, the RichtmayerMeshkov instability.
 A PARALLEL PRECONDITIONER FOR SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS TO SOLVE THE NONLINEAR RADIANT HEAT CONDUCTION EQUATION IN THE "KORONA" CODE S. V. Chebotar VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 3443.
The paper describes the method of solving systems of linear algebraic equations when simulating the heat conduction processes on distributedmemory computers. The description of the parallel preconditioner used to solve linear equation systems with iterative schemes on Krylov subspaces in the heat conduction block of the KORONA code is given. The preconditioner is based on the parallel multilevel incomplete LUfactorization of sparse matrices in combination with incomplete block decomposition of an inverse matrix. The idea of the method is in recursively building the hierarchy of Schur complement addition matrices with successively reducing the number of processes. There has been implemented a possibility of stopping the recursion at a given level and building for the next matrix the Schur complement of incomplete block approximation of inverse matrix. The results of computational experiments obtained in solving problems with the KORONA code in parallel mode are presented. For comparison, there have been implemented several commonly used preconditioners using the ILU(t)factorization as the basis: the block Jacobi method, the restricted additive Schwarz method, as well as the Spike family method using the reduced matrix. Key words: parallel computations, systems of linear algebraic equations, preconditioner, the KORONA code, heat conduction.
 THE HLLEM RIEMANN SOLVER FOR 3D MULTIMATERIAL GAS DYNAMICS WITH AN ARBITRARY EQUATION OF STATE I. V. Glazyrin, A. V. Ershova, N. A. Mikhailov VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 4458.
The paper proposes the generalization of the HLLEM Riemann solver earlier used for a system of 1D singlematerial gasdynamic equations onto a 3D multimaterial case for an arbitrary unstructured mesh. Similarly to the 1D case, arbitrary equations of state (EOSes) of the materials are possible. The discontinuity is spread over a number of computational cells and in this domain the model of mixtures based on mass concentrations is used. The 3D multimaterial gasdynamic equation system is solved in Eulerian variables in Cartesian coordinate system. The equation system is simulated in its conservative form with the isothermal closure condition, i.e. equal temperatures of the materials are assumed. To implement the HLLEM solver, the right and left eigenvectors of the Jacobian matrix have been derived for the 3D multimaterial gasdynamic equation system with an arbitrary EOS. The proposed HLLEM solver has been implemented within the 3D Euler "Fokus" code using the finite volume method. The fluxes of conservative variables across faces of cells are calculated using the mean formula. The values of the fluxes of conservative quantities at the centers of cell faces can be found by considering 1D Riemann problems along normals to faces of cells. The reconstruction of the quantity values on the cell faces is performed using the TVD slope limiters. The time solution is found using the twostage RungeKutta method. Two plane Riemann problems were selected for testing on a 3D cubic and an unstructured mesh with the ideal gas EOS and twoterm EOS. The results of testing demonstrate the proposed approach efficiency. Key words: multimaterial gas dynamics, Riemann solver, HLLEM, eigenvectors, arbitrary equation of state, threedimensional unstructured mesh.
 COMPUTATIONAL AND EXPERIMENTAL STUDY OF DEFORMATION AND FRACTURE FOR TUBULAR 09G2SSTEEL SAMPLES UNDER TENSION AND INTERNAL PRESSURE CONDITIONS USING THE "LOGOS MECHANICAL" COMPUTATIONAL MODULE A. A. Ryabov, V. N. Rechkin, V. A. Baryshev, R. A. Barabanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 5969.
The paper presents the results of the computational and experimental study of the features of quasistatic deformation and fracture of tubular samples made of 09G2S steel under the effect of axial tension and internal pressure. The stressstrain state of the samples under large deformations up to fracture is numerically simulated on the base of experimental diagrams of the material deformation using the Logos Mechanical computational module. The threshold plastic strain intensity values of the material samples are studied under the conditions of a varying stress state described by various parameters. Key words: stressstrain state, elastoplastic deformation, fracture, strength criterion, the finite element method, "Logos" software package, "Logos Mechanical" computational module.
 THE LOGOS SOFTWARE PACKAGE: THE SURFACE MESH GENERATION CAPABILITIES TO SOLVE AERO AND HYDRODYNAMICS PROBLEMS E. O. Evstifeeva, O. N. Borisenko, D. M. Pankratov, T. V. Tsalko, A. I. Shavkhitdinova VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 7078.
The paper describes the "Logos" software package capabilities for automatically generating surface triangular meshes. It is shown that the generation of surface meshes is performed by preliminarily setting a minimum number of parameters and its purpose is to prepare highquality computational meshes to solve aero and hydrodynamics problems. Examples given in the paper demonstrate that the mesh generating technology of the "Logos" automatic mesh generator is a generalpurpose technology and allows broadening the sphere of its application. Key words: the "Logos" software package, a surface mesh, an automatic mesh generator, aero and hydrodynamics problems.
 SIGNAL INTERCEPT FROM THE LATERAL SURFACE OF OPTICAL FIBER IN DATA TRANSMISSION SYSTEMS V. V. Shubin VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 7989.
The paper considers the methods of data intercept from the lateral surface of optical fiber: passive, active and compensation methods. It is shown that passive methods are used for multimode fibers only. Active and compensation methods are typical for longdistance communication cables with singlemode fibers to intercept a signal from the fiber core. The paper presents the analytical dependence for active radiation intercept methods and experimental and literary data for intrusive and nonintrusive methods. The generalpurpose efficiency and security indexes are given for all intercept methods. The compensation radiationintercept methods are considered for singlechannel and multichannel fiberoptic systems. Key words: lateral radiation; devices for radiation output, collection, and input; lateral surface of optical fiber; multimode gradient and singlemode optical fiber; passive, active, and compensation intercept methods.
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