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Issue No 4, 2023

AN ANISOTROPIC CLOSURE MODEL FOR ELASTO-PLASTICITY EQUATIONS OF A MULTI-MATERIAL MEDIUM IN MIXED CELLS

A.L. Stadnik, Yu. V. Yanilkin, O. O. Toporova
VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 4. P. 3-16.

In the Elerian-Lagrangian and Eulerian methods for the simulation of elasto-plastic flows mixed cells may contain material-material interfaces. A two-stage approach is used in the ALE methods. In the first (Lagrangian) stage, the elasto-plasticity 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 elasto-plasticity 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, multi-material medium, finite difference methods, numerical simulation, two-dimensional flows, elasto-plasticity.

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. 17-33.

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 "Gresho-Chan vortex" test is used to simulate the dynamic balance. The Rayleigh-Taylor instability is simulated for the 3D α-Group problem and an extended problem, the growth rate coefficient of bubbles is calculated. The Kelvin-Helmholtz instability with single-mode and multimode disturbances is simulated for 2D and 3D problems. The growth rate coefficient of the mixing zone is calculated. To simulate the Richtmayer-Meshkov 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, Gresho-Chan vortex, the Rayleigh-Taylor instability, the Kelvin-Helmholtz instability, the Richtmayer-Meshkov 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. 34-43.

The paper describes the method of solving systems of linear algebraic equations when simulating the heat conduction processes on distributed-memory computers. The description of the parallel preconditioner used to solve linear equation systems with iterative schemes on Krylov sub-spaces in the heat conduction block of the KORONA code is given. The preconditioner is based on the parallel multilevel incomplete LU-factorization 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 MULTI-MATERIAL 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. 44-58.

The paper proposes the generalization of the HLLEM Riemann solver earlier used for a system of 1D single-material gas-dynamic equations onto a 3D multi-material 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 multi-material gas-dynamic 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 multi-material gas-dynamic 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 two-stage Runge-Kutta method. Two plane Riemann problems were selected for testing on a 3D cubic and an unstructured mesh with the ideal gas EOS and two-term EOS. The results of testing demonstrate the proposed approach efficiency.


Key words: multi-material gas dynamics, Riemann solver, HLLEM, eigenvectors, arbitrary equation of state, three-dimensional unstructured mesh.

COMPUTATIONAL AND EXPERIMENTAL STUDY OF DEFORMATION AND FRACTURE FOR TUBULAR 09G2S-STEEL 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. 59-69.

The paper presents the results of the computational and experimental study of the features of quasi-static deformation and fracture of tubular samples made of 09G2S steel under the effect of axial tension and internal pressure. The stress-strain 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: stress-strain state, elasto-plastic 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. 70-78.

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 high-quality 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 general-purpose 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. 79-89.

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 long-distance communication cables with single-mode 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 non-intrusive methods. The general-purpose efficiency and security indexes are given for all intercept methods. The compensation radiation-intercept methods are considered for single-channel and multi-channel fiber-optic systems.


Key words: lateral radiation; devices for radiation output, collection, and input; lateral surface of optical fiber; multimode gradient and single-mode optical fiber; passive, active, and compensation intercept methods.

 
 
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