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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 3, 2021  REGRIDDING IN DIFFERENCE GAS DYNAMIC SCHEMES REPRESENTED AS INTERCOMPONENT EXCHANGES IN A MULTIPHASE MEDIUM
A. M. Stenin VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 320.
A global algorithm of recalculating gas dynamic quantities to a new grid (regridding algorithm) provides the calculation of contributions of the corresponding integral quantities from the old grid. To calculate the integral contributions, searching for the old/new grid overlap polygons is performed. The paper shows that such regridding algorithm can be represented as exchanges between components in some artificial multiphase medium. In this case, successive consideration of all the medium processes associated with mass, momentum, and energy exchanges and performed in a similar way, as for the continual multiphase multivelocity medium, inevitably leads to the specific internal energy calculation with amendments because of the kinetic energy deficiency in the new space grid. Key words: gas dynamics, LagrangianEulerian coordinates, global regridding algorithm, a multiphase medium, intercomponent exchanges, Sedov explosion.
 3D AND 2D NUMERICAL SIMULATION OF TURBULENT MIXING IN THE NOVA LASER FACILITY EXPERIMENT WITH A FLAT TARGET V. P. Statsenko, Yu. V. Yanilkin, O. G. Sinkova, Yu. V. Tretyachenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 2133.
In the simulation of experiments on laser facilities there occurs the need in simulating the turbulent mixing process. One of the commonlyaccepted models of turbulence is the semiempirical (κ, ε)model. There is a need in applying and testing this model under highenergy and hightemperature conditions. The paper presents results of 2D simulations with the EGAK code using the (κ, ε)model of turbulence for various experiments with a flatplate target on the NOVA laser facility (USA). These results are compared with experimental data on testing phenomenological models of turbulence used to solve the high energy density problem. Also, computations with the 3D and 2D direct numerical simulation method were carried out. There is a good agreement between these results, as well as results of computations with the (κ, ε)model. Results of computations with regard to the initial disturbances of a contact boundary specified in experiments are in a good agreement with experimental data and the approximate analytical solution to the problem also found in this work. Key words: the EGAK code, turbulent mixing, laser experiment, flat target, Xray radiography, numerical simulation, analytical solution.
 THE PROBLEM OF A CENTERED RAREFACTION WAVE REFLECTED FROM A "SOFT" PISTON V. N. Nogin VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 3441.
An exact solution has been found for the problem of a centered rarefaction wave reflected in ideal gas from a piston with constant pressure on it. The rarefaction wave is reflected from the piston as a compression wave moving along the decreasing density profile and transforming into a shock wave at some distance to the piston. The flow structure in the reflected wave is considered for the ratio of specific heat , where r is a positive integer. For r = 0, 1, 2 the solution is represented by analytical formulas. The conditions leading to a solution discontinuity have been found. It is shown that depending on the pressure at the left boundary such discontinuity occurs either in the general solution region, or in the reflected simple wave. The solution found can be used to test computational codes. Key words: a centered rarefaction wave, Riemann invariant, a characteristic.
 VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 4258. I. V. Dolzhenkov, N. A. Kravets, A. V. Soldatov, E. S. Stolmakova VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 3441.
A computational method based on the numerical solution of homogeneous 3D Maxwell´s equations in elliptic coordinates for the electrodynamics simulation in the cavity of ellipsoid of revolution is presented. The electromagnetic field sources are specified as boundary conditions on the interior surface of ellipsoid. Natural boundary conditions are used on the ellipsoid symmetry axis: 1) the electromagnetic and magnetic field components must remain limited; 2) vector components of the electromagnetic and magnetic fields oriented along axis of symmetry must not depend on the azimuthal angle. Approximating formulas for spatial derivatives have been developed on the base of integral consequences of Maxwell’s equations written for elementary differencegrid cells. For the time approximation of derivatives, the coordinatewise splitting method is used. The resultant equations in each stage are solved with the sweep method. The proposed method applicability and accuracy are demonstrated by results of computations for an informative problem having an analytical solution. Key words: ultrawideband electromagnetic radiation, elliptic system of coordinates, Makswell´s equations, numerical simulation.
 TIME CONSTANT ESTIMATION WITH STATISTIC SIMULATION METHODS IN PARTICLE TRANSPORT PROBLEMS D. G. Modestov VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 5969.
The asymptotic behavior of the transport equation solution at large times is determined by the transport operator eigenvalue with a maximum real part, i.e. a time constant. Accordingly, this value is an important characteristic of the radiation field dynamics. To calculate it with the statistic simulation methods that allow solving the transport equation with least approximations, the most common approach is based on solving the conditionally critical problem with an added auxiliary reaction parametrized by a trial value of time constant. The true value is obtained by selecting values according to the operator criticality condition. A restricted range of applicability is a disadvantage of the current methods based on the approach above. The paper describes the approach with an auxiliary operator which is time dependent and, at the same time, smoothly depends on the trial timeconstant value which has no such disadvantage. To solve the problem, an algorithm similar to the method of generations with a quadratic rate of convergence, in optimal case, is used. Issues of convergence are considered. Comparison between the numerical and analytical solutions is presented including the case of no convergence. Key words: particle transport equation, time constant, method of generations, statistical simulation.
 AUTOMATIC GENERATOR OF UNSTRUCTURED POLYHEDRAL MESHES ON THE BASE OF TETRAHEDRAL MESHES WITH PRISMATIC LAYERS N. V. Popova VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 7083.
In the numerical simulation of fluid flows described by Eulerian, or NavierStokes equations the computational mesh generation is performed prior to the solution of basic equations and analysis of results. The paper describes an automatic generator of unstructured meshes consisting of arbitrarilyshaped polyhedrons on the base of partitioning tetrahedrons and prisms. A 3D mesh is generated beginning from the boundaries of a surface triangular mesh approximating an arbitrary closed computational domain. There are two main stages of the process: generation of a primary isotropic tetrahedral mesh with prismatic layers and generation of a secondary polyhedral mesh using a hybrid scheme. To build a prismatic mesh, the method of stretching a surface triangular mesh at a given distance along normals is used. Intermediate nodes are calculated according to the given distribution law. To build a tetrahedral mesh, the method of a moving front is used. Local areas of concentrated, or coarsened cells are provided for. The transformation into a polyhedral mesh is primarily performed using the centroid dual scheme and the nearsurface transformation in regions with specific geometric features is performed using the median dual scheme. Classification of the primary mesh nodes and the corresponding ways of generating polyhedral cells are described. The mesh generation result is presented by the example of a joining piece of pipeline. The automatic mesh generation is used in the preprocessor of the "Logos" software package for engineering analysis and supercomputer simulation. Key words: "Logos" software package, preprocessor, unstructured meshes, arbitrarilyshaped polyhedrons, a tetrahedral mesh, a prismatic layer, Delaunay triangulation with restrictions, mediаn dual scheme, centroid dual scheme.
 A FUNCTIONAL MODULE IN TIM CODE FOR GENERATION OF UNCTRUCTURED VOLUME GRIDS USING A REGULAR ADAPTIVE REFINEMENT PATTERN V. A. Nikitin VANT. Ser.: Mat. Mod. Fiz. Proc. 2021. No 3. P. 8492.
RFNCVNIIEF has been developing the TIM code to solve multidimensional unsteady problems of continuum mechanics on unstructured moving arbitrarilyshaped grids. In complex simulations for 3D problems in Lagrangian variables, with eddy flows and jet flows, large material deformations causing distortions of the grid in three directions take place. Local corrections in a severely distorted grid may consume much time and, therefore, it is reasonable to change the grid. To generate a new grid, a functional module was developed that allows generating an unstructured locallycondensed 3D grid. Such grid can be generated both manually and automatically. A regular adaptive refinement pattern is used for the grid generation and transformed into an unstructured grid. A set of control volumes, i.e. solid geometric figures in which the grid is condensed according to the specified sizes, is used as input parameters. A brief description of input parameters and examples of the generated grids are presented, a grid generating method is described including that used in parallel mode with MPI interface, and some functional module performance data is given. Key words: generator of a volume grid, unstructured grids, an adaptive refinement pattern, the TIM code.
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