


Since 1978 Published in Sarov (Arzamas16), Nizhegorodskaya oblast 
RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2019  COMPARISON BETWEEN THE PROPERTIES OF GRID SCHEMES FOR SOLVING THE TRANSPORT EQUATION ON UNSTRUCTURED TETRAHEDRAL GRIDS
O. V. Nikolaeva, A. S. Kazantseva VANT. Ser.: Mat. Mod. Fiz. Proc. 2019. No 1. P. 318.
The paper presents results of testing the grid schemes used to solve the transport equation on unstructured tetrahedral grids. Schemes constructed using two different methods – the method of characteristics and the finite element method – are considered. The grid solution convergences have been tested with the use of refined angular and spatial grids for the deeply penetrating radiation problems. The grid solutions are compared to the Monte Carlo solutions. The problem runtimes are given. Key words: the transport equation, tetrahedral grids, grid schemes, the method of characteristic, the finite element method.
 NUMERICAL SIMULATION WITH THE "EGAK" CODE OF MOVING RIGID PENETRATORS IN ELASTOPLASTIC MEDIA USING A STATIONARY COMPUTATIONAL GRID A. A. Krayukhin, A. L. Stadnik, Yu.V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 2019. No 1. P. 1932.
Results of simulations for several problems of rigid penetrators moving in elastoplastic media are presented. The numerical simulation was performed with the EGAK code using a stationary computational grid and an ideal solid body approximation to describe the penetrator. The medium flow was simulated using the noninertial frame of reference with respect to a fixed penetrator. The EGAK simulation results are in a good agreement with results of similar simulations in Lagrangian variables and data of experiments. Key words: penetration, an ideal solid body, elastoplastic medium, noninertial frame of reference, stationary computational grid, the EGAK code.
 ERRORS IN THE NUCLEAR FUEL BURNUP SIMULATIONS WITH THE USE OF STATISTICAL METHODS D. G. Modestov VANT. Ser.: Mat. Mod. Fiz. Proc. 2019. No 1. P. 3343.
The fuel burnup problem is a Cauchy problem for some system of ordinary differential equations, where the righthand side of equation is a set of the transport equation solution functionals. To estimate such functionals, the statistical methods of simulation are often used, which require the least number of physical and technical approximations in comparison with other methods. Errors in estimating functionals lead, in turn, to errors in the calculated results for the nuclear composition of fuel, which are classified as statistical and systematic errors. The paper describes the asymptotical behavior of the latter at small integration steps. It is also demonstrated that statistical errors are slightly dependent on these integration steps. This property allows mitigating, to some extent, the pessimistic prediction of impossibility to construct higherorder schemes, which was discussed in an earlier published article by the author. The paper presents results of methodological simulations for a simple thermalneutron reactor model, which are in a good agreement with theoretical estimates. Key words: nuclei kinetics, numerical methods, Cauchy problem, integration scheme, the particle transport equation, the generation method.
 NUMERICAL EFFECTS IN THE HEAT TRANSPORT SIMULATION A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2019. No 1. P. 4456.
In the numerical simulation of the heat transport problems, sometimes there occur effects, which are not described by the physics of simulated processes and hamper a proper understanding of these processes. The most commonly encountered among them are the grid effects caused by discretizing the space using a difference grid. The grid effects disappear with the use of stable and converging difference schemes with smaller sizes of the discrete grid cells. However, not only grid effects may become the cause of errors in solutions. There are also some other specific features of numerical simulation, which are weakly dependent on, or independent of the difference grid in use and in most cases they do not disappear with a decreasing size of cells. During the numerical simulation both the grid and nongrid effects may occur simultaneously, or in different combinations with each other. Their analysis is important for finding the ways of eliminating them. The paper describes some nongrid numerical effects for the heat transport problems. Key words: radiation transport, numerical simulation.
 COUPLING OF 1D AND 3D THERMALHYDRAULIC MODELS IN THE "KORSAR/CFD" COMPUTER CODE Yu. V. Yudov, I. G. Danilov, S. S. Chepilko, D. S. Kasterin VANT. Ser.: Mat. Mod. Fiz. Proc. 2019. No 1. P. 5768.
The paper presents a method for coupling 1D and 3D thermalhydraulic models in the KORSAR/CFD system code. The KORSAR/CFD code is designed for safety analysis of pressurized water reactors. The onedimensional approach is based on a twofluid model. Conservation equations are discretized by the semiimplicit numerical scheme on a staggered grid. A singlephase liquid is modeled with a 3D approach using the immersed boundary method. Time integration is performed by the secondorder accurate implicit scheme on the collocated grid. The models are coupled using the semiimplicit scheme. In the 1D model, mass and energy fluxes at the interface are written as sums of corresponding fluxes in the 3D model. The fluxes are expressed implicitly with respect to the velocities, thus ensuring the coupling of Poisson equation matrices in 1D and 3D domains when calculating the combined pressure field at each new time level. To improve the convergence of the iterative procedures for the Poisson equation, a multigrid method with a set of cells in the whole computational domain is used. The proposed coupling method was verified on a natural convection loop test problem in which parts of the natural convection loop were simulated using 1D and 3D approaches. The calculation of the loop heatup dynamics and natural convection development has demonstrated the fulfillment of coolant mass and energy balance. Key words: 1D model, 3D model, immersed boundary method, natural convection loop.
 SPECIFIC FEATURES OF ALGORITHMS IN THE "EVKLID/V2" CODE FOR NUMERICAL SIMULATION OF MOVING MOLTEN MATERIALIN FAST REACTOR DURING A SEVERE ACCIDENT E. V. Usov, A. A. Butov, V. I. Chukhno, I. A. Klimonov, I. G. Kudashov, N. A. Pribaturin, N. A. Mosounova, V. F. Strizhov VANT. Ser.: Mat. Mod. Fiz. Proc. 2019. No 1. P. 6977.
To justify safety of advanced reactor plants with a liquidmetal coolant, there is a need in a set of computer codes to simulate severe offdesign accidents with core melting. For these purposes, the integral EVKLID/V2 code has been developed at the RAS IBRAE. Its current version allows simulating the behavior of fastneutron reactors with liquidmetal coolants under stationary and transient operation conditions, as well as their behavior during different designbasis accidents, by carrying out coupled neutronphysical, thermomechanical, and thermalhydraulic simulations. The SAFR/V1 module has been developed for the simulation of severe accidents in a fast reactor. The module can be run either separately to simulate the melting process for a single fuel element, or within the EVKLID/V2 code that allows simulating the reactor core breakdown with regard to the molten material leakage to a coolant, the transport of components of the broken fuel element to the upper mixing chamber, melting of the fuel assembly can, and the flow passage blocking. Mathematical algorithms of the EVKLID/V2 code used to simulate the thermal breakdown of core are represented in the paper (5 figures, 12 references). Key words: SAFR/V1, HYDRAIBRAE/LM, the EVKLID/V2 code, fuel element, core, mathematical modeling, molten mass.
 RADIAL WAVE MOTIONS OF RING ELEMENTS OF MACHINES S. V. Seryogin VANT. Ser.: Mat. Mod. Fiz. Proc. 2019. No 1. P. 7883.
The paper presents results of studying the dynamic characteristics of solidstate wave gyroscopes by the example of a nonrotating circular ring which is deformed in its plane. Radial waveforms have been found in the lowest frequency spectrum corresponding to bending modes. It has been concluded that the frequency of radial motions depends on the physical parameters of the ring and doesn’t depend on the geometric parameters and the type of boundary conditions (2 figures, 1 table, 30 references). Key words: ring, bending modes, radial wave motions, frequency spectrum, resonance.
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