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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 1, 2023  CONSIDERATION OF THE MIXING PROCESS HYSTORY IN THE DIRECT NUMERICAL SIMULATION OF TURBULENCE FOR 2D PROBLEMS
Yu. V. Yanilkin, A. R. Guzhova, L. I. Degtyarenko, V. Yu. Kolobyanin, V. A. Shmelyev VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 315.
The paper offers a new approach to the direct numerical simulation of the turbulent mixing process for miscible and immiscible materials of different densities. The idea of this approach is that in mixed cells containing intermixing materials the states of homogeneous and heterogeneous mixtures consisting of fragments with interfaces are distinguished. The method of solving 2D problems developed to implement this approach in the EGAK code is described. The method is verified on the classic problem of turbulent mixing due to the RayleighTaylor instability under the steady acceleration of the interface between two gases of different densities. Key words: RayleighTaylor instability, turbulent mixing area, direct numerical simulation, homogeneous mixing degree, the EGAK code.
 ON STABILITY OF TVDR DIFFERENCE SCHEMES FOR SOLUTION OF THE 1D RADIATION TRANSPORT EQUATION A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 1628.
In computational physics, the transport equation is one of the fundamental equations widely accepted to describe the radiation gasdynamics processes. A lot of papers were devoted to the problem of developing numerical methods to solve the radiation transport equation. Nonlinear TVDR schemes of a higher approximation order (higher than the 1st order) constructed using the classic TVD methodology comprise a separate class of schemes. The paper describes the study of the TVDR difference scheme stability using the spectral Neumann criterion for 1D transport equation. The comparison between the stability of St and TVD schemes is presented. Conclusions concerning the stability conditions for TVD and TVDR schemes are made. Key words: transport equation, difference schemes, stability.
 THE INFLUENCE OF DISSIPATIVE ERRORS OF MIMOZA CODE ON THE RATE OF CHANGES OF KINETIC ENERGY IN THE TAYLORGREEN VORTEX DECAY PROCESS A. N. Razin, V. V. Zmushko, A. A. Sinelnikova VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 2941.
The influence of dissipative errors of the difference MIMOZA code on the numerical simulation result is studied by the example of the TaylorGreen vortex decay problem. Euler’s questions are integrated using the secondorder scheme with the reconstruction of flows across cell edges. A series of computations with the 3D initial data was performed using a succession of refined meshes containing (N+1)^{3}, (2N+1)^{3}, (4N+1)^{3}, (8N+1)^{3}, and (16N+1)^{3} cells, N = 32. To assess the influence of the initial conditions on the result, the problem with 2D initial data was simulated. The MIMOZA results obtained in the computation series are compared with each other and, also, with the data of the other authors obtained using the Euler and NavierStokes equations. Key words: TaylorGreen problem, twodimensional and threedimensional boundary conditions, laminartoturbulent transition, mathematical modeling, dissipation effect.
 THE EGIDATEST CODE FOR NUMERICAL STUDY OF THE HIGHPERFORMANCE COMPUTER PARAMETERS V. Yu. Kolobyanin, I. N. Chistyakova VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 4250.
The paper describes the EGIDATEST code with twolevel parallelization (MPI+OpenMP) developed to test highperformance computers for the numerical simulation of complex physical processes. The description of gas dynamic tests in the EGIDATEST is given, the code functionality for the analysis of the obtained results of testing is presented. Special focus is on the specifics of implementing the system part of the test code, which allows considering any test in EGIDATEST as a set of minitests having different characteristic features. The EGIDATEST code is a simplified analog to the EGAK code for the simulation of a multicomponent continuum that allows predicting the real application efficiency on a highperformance computer of interest. Key words: highperformance computers, the EGAK code,lb the EGIDATEST code, twolevel parallelization, standard paralleling scheme, memory, system of tests, test monitoring, timing.
 THE LOGOS HEAT PROGRAM MODULE: VALIDATION OF THE MODEL OF HEATING A PLATE MADE OF ALUMINUM ALLOY AMG6 BY LASER RADIATION A. E. Zaponov VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 5159.
One of the tasks to be resolved prior to the mathematical modeling for the development of modern air vehicles is to validate the model of heating a plate made of aluminum alloy AMg6 by continuous laser radiation. The plate heating process was simulated using the "Logos Heat" module of the "Logos" software package for engineering analysis and supercomputer simulation. The obtained simulation results are compared with the known experimental data. The validation demonstrates that a maximum percentage error in the temperature maximum of the rear plate surface exposed to a laser radiation is not higher than ~ 15 %. Key words: computer simulation, laser radiation, heating, metal.
 THE DEPENDENCE OF MEAN VALUES OF VERTICAL FORCES AFFECTING A RAIL ON THE TRAIN VELOCITY I. M. Anisina VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 6067.
This paper extends a series of papers on the analysis of data (collected by employees of the AllRussian Scientific Research Institute of Railway Transport) on the rutting of subgrades, when one, or several long trains pass the rail track. The mathematical model offered in these papers provides an adequate description of the soil deformation under an applied load and its subsequent relaxation, however, it does not reproduce the experimentally found dependence of the mean values of the vertical forces affecting the rail track on the train velocity. The present paper considers this problem. The model offered in the paper describes the load on rails and rutting of subgrades depending on the train load with account for the radial acceleration and damping properties of soil and provides a good agreement with the available data of experiments. The developed method allows predicting the growth of dynamic deviations in vertical plane, if long trains pass the rail track, and such predictions are required to plan the track surfacing works. Key words: rail track, subballast base, settlement of track, model of standard linear solid, radial acceleration, viscosity.
 PROCESSING OF MODELING RESULTS IN THE ScientificView SYSTEM USING 3D STRUCTURED MESHES AND ADAPTIVELY NESTED SUBMECHES A. L. Potekhin VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 6875.
The generality of the ScientificView parallel postprocessing system, which provides visualization of the computer modeling results, requires supporting different data representation types: 2D and 3D data on structured and unstructured meshes, as well as data given on sets of material points (clusters, molecules, particles). Structured meshes along with adaptively nested submeshes are used in a number of modeling programs to provide a detailed local description of the geometry, or going physical processes. The paper describes the specific features of the algorithms implemented in ScientificView for graphically postprocessing these types of 3D data. Key words: scientific visualization systems, postprocessing of results, mathematical modeling, adaptively nested submeshes.
 AN ALGORITHM OF BUILDING DUAL MESHES WITH PARALLELIZATION TO SOLVE COMPUTATIONAL HYDROGEOLOGY PROBLEMS M. L. Sidorov, T. S. Agapova VANT. Ser.: Mat. Mod. Fiz. Proc. 2023. No 1. P. 7688.
The paper describes a capability of building dual meshes in parallel mode, which has been implemented in the mesh generator of the "Logos Hydrogeology" digital product. A dual mesh of polyhedral cells is considered, such mesh is built on the base of the primary mesh, which cells are tetrahedrons, prisms, hexahedrons, and pyramids. The program conception is considered and the mesh generator algorithm of building dual meshes is described. The specific features of the mesh generator operation in the parallel mode of generating mesh models and possible cases of the dual mesh generation method limitation are emphasized. Resultant mesh models are demonstrated by examples of the test and realworld models of territories. Results of building mesh models both in the parallel and serial modes are given. Key words: "Logos Hydrogeology", subsurface hydrodynamics, unstructured mesh, dual mesh, polyhedrons.
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