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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 3, 2022  NUMERICAL SIMULATION OF 3D GAS FLOW IN GAS CENTRIFUGA. PART 1. DESCRIPTION OF THE METHOD
Yu. V. Yanilkin, V. P. Statsenko, Yu. D. Chernyshev, S. P. Belyaev, V. Yu., Kolobyanin, A. V. Kondrashenko, O. O. Toporova, I. Yu. Turutina VANT. Ser.: Mat. Mod. Fiz. Proc. 2022. No 3. P. 319.
This is the first part of the work describing the effort on 3D numerical simulation of the rarefied gas in the real gas centrifuga with the account for the physical viscosity and thermal conductivity. A numerical method is described; its realization is carried out on the basis of EGAK on a cylinder mesh in a special coordinate system using a parallel computer. A part of processes is approximated in an immobile Cartesian coordinate system, and the other part  in the inertial cylindrical system. The method is meant for the endtoend simulation of the whole process of centrifuga operation without implementation of approximated methods of linking the computation results in different regions of the centrifuga. Aiming at this, we use an approximation based on the fact that the equations of gas dynamics, thermal conductivity and diffusion are implemented everywhere. An approach based on the solution of 3D NavierStokes equations is used in all centrifuga including the regions of 2D flow in the separating chamber. Decomposition by processes is used to improve the efficiency of the program where only one process comes for the region of the 2D flow. This allows saving computational resources by orders of magnitude. Testing results for the method are given in the second part of the publication. Key words: gas centrifuga, separating chamber, sample and stripping chamber, EGAK method, viscous liquid, heat exchange, numerical method.
 NUMERICAL SIMULATION OF 3D GAS FLOW IN GAS CENTRIFUGA. PART 2. COMPUTATION RESULTS OF MODEL "IGUASSU" CENTRIFUGA Yu. V. Yanilkin, V. P. Statsenko, Yu. D. Chernyshev, S. P. Belyaev, V. Yu., Kolobyanin, A. V. Kondrashenko, O. O. Toporova, I. Yu. Turutina VANT. Ser.: Mat. Mod. Fiz. Proc. 2022. No 3. P. 2036.
This is the continuation of the first part of the effort on 3D numerical simulation of flows in gas cenrifuga by the group of authors. The second part describes test problems on the "Iguassu" model centrifuga and the outcomes of their simulation using the 3D method described in the first part. The following problems were analized: solidstate rotation of gas with constant temperature; establishing solidstate rotation; gasdynamic problem with account for thermal conductivity, for which analytical solution has been produced; onechamber model of the gas centrifuga rotor, for which analytical solution has been produced; a problem with twochamber model of the gas centrifuga rotor, where the influence of the point of linking 2D and 3D areas of the solution was studied as well as convergence of numerical solution when refining the mesh; 1D diffusion problem with an analytical solution. Acceptable agreement with analytical solutions was produced for all tests. Key words: gas centrifuga, "Iguassu" centrifuga, separating chamber, sample chamber, viscous liquid, heat exchange, numerical simulation.
 QUASISPECTRAL METHOD TO SOLVE THE KINETIC EQUATION OF RADIATION TRANSFER IN 2D AXIALLY SYMMETRIC SETUP A. D. Khmelnitskaya, N. G. Karlykhanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2022. No 3. P. 3747.
A quasispectral method is proposed to solve radiation transfer equation in 2D axially symmetric case using a rectangular mesh. The method lies in averaging the equation by spectrum and angle variables and reduction of the averaged kinetic equation of transfer to the equation of radiation heat conductivity. The value of the method is in the fact that all the complexity of the iteration is shifted to the equation of the radiation thermal conductivity, for which the problem is considerably simplified. Besides, the method allows arranging parallelization by spectrum variable and by space to compute energyaveraged paths and active radiation energy. The performance of the method is demonstrated in the second Fleck problem; the solution is compared to the spectrum computation in 1D spherical case. Key words: quasispectral method, spectral equation of radiation transfer, quasidiffusion equation, quasitransfer, radiation thermal conductivity, radiation effect.
 HIERARCHICAL PARALLELIZATION ALGORITHM WHEN COMPUTING 3D NEUTRON TRANSFER EQUATION ON HYBRID SUPERCOMPUTERS A. A. Nuzhdin VANT. Ser.: Mat. Mod. Fiz. Proc. 2022. No 3. P. 4862.
A hierarchical parallelization algorithm is described in the paper, which is based on distinguishing the levels of the architecture of the hybrid supercomputer with GPU and implementation of the principle of geometric decomposition at every level. Inside a compact group of threads parallelization by the elements of the hyperplane of a fixed size is used; it consists of mesh cells. KBAalgorithm on the basis of 2D decomposition by columns and hyperplanes is used between the blocks of one GPU. KBAalgorithm on the basis of 3D decomposition is used between different GPU. The program is realized on the example of PAUK miniapp using CUDA technology. The efficiency of adaptation of the PAUK miniapp for one GPU is confirmed with the results of profiling and comparison with the performance of CPUversion of the program. Scalability of PAUK miniapp in the mode of multiGPU is studied with multiplication method. Key words: GPU, CUDA, Snmethod, sweep algorithm, KBAalgorithm.
 OPTIMIZATION OF ALGORITHMS IN APPLIED TECHNICAL MD TEST FOR EFFICIENT GPU IMPLEMENTATION A. M. Erofeev, M. V. Vetchinnikov VANT. Ser.: Mat. Mod. Fiz. Proc. 2022. No 3. P. 6372.
Algorithms of molecular dynamics (MD) benchmark are described that allow completing the transfer of all computations on GPU in such a way that we get rid of a constant need of particle information exchange between the devices. As a result, interaction between GPU and CPU is necessary only to send boundary information between separate GPU using MPI to CPU, and this is much less than sending in the initial code; that is proven by the test measurement of the performance. The speedup of the algorithm on one GPU compared to the initial one is from 8,7 to 12,5 times in case of problems different in their size. When two GPUs were involved in this work, the speedup was from 6,6 to 12,5 times. The parallel efficiency on two GPUs V100 was 76,379,6 % in case of problems with the number of particles from 4 mln; on two GPUs А100 it was 77,381,8 % in case of problems with the number of particles from 13,5 mln. Key words: molecular dynamics, performance, GPU, CUDA, algorithms.
 QUALITY IMPROVEMENT OF THE FACETS OF 3D CELLS WHEN GENERATING UNSTRUCTURED MESHES IN "LOGOS" SOFTWARE PACKAGE O. N. Borisenko, M. V. Kuzmenko, M. V. Cherenkova, A. G. Giniyatullina, N. V. Chukhmanov, D. N. Smolkina, T. E. Timaeva, K. A. Blazhnova VANT. Ser.: Mat. Mod. Fiz. Proc. 2022. No 3. P. 7385.
The ways to improve the quality of the facets of 3D cells in case of automatic generation of unstructured meshes in "Logos" software package are described; they are used in numerical simulation of the problems of aero and hydrodynamics. This is a modification of cells with partially coinciding facets, integration of facets with the account for their shape, cutting of the curved facets, cutting of notconvex facets with adding a new node having a possibility to delete a small edge, cutting of the curved facets into the multiple plane ones in the transfer regions of the notsmooth regions into the smooth area, and deleting extra nodes. Implementation of the integrity of these ways allows improving the shape of the facets of the cells produced by the cuttingoff method and, as a result, the layer of the cells generated on their basis, where a strong flow velocity gradient is characteristic. Eventually, the quality of the computational mesh in general is improved. Key words: "Logos" software package, unstructured meshes, mesh quality improvement, surface facets, boundary layer.
 POSSIBLE IMPLEMENTATION OF VECTOR FONTS FOR ADDITIVE PRODUCTION REALIZED IN "VIRTUAL 3DPRINTER" SOFTWARE COMPLEX M. A. Titov VANT. Ser.: Mat. Mod. Fiz. Proc. 2022. No 3. P. 8696.
A possibility to use vector fonts in the integrating frame of the "Virtual 3Dprinter" software package is shown. It provides application of the text, symbols or a logotype of the company on the structures and items produced in the process of additive production using the method of layerbylayer laser sintering of a metal powder mixture. SVGformat of computer scalable vector fonts is considered. Its brief description is provided in the language of commands of 2D Scalable Vector Graphics. An approach is proposed to produce the coordinates of the points that lie on the boundary of delineating the symbol of the vector font. A syntactical SVGanalyzer (a parcer of glyphs of the font symbols) and the rasterization library of quadratic and cubic Bezier curves realized for these purposes are described. There is an example of using developed programs to form a 3D scene from the line of symbols produced with a vector font. There are photos of the 3D text produced in the process of additive production. Key words: SVGformat of vector fonts, Bezier curves, a parcer of glyphs of symbols, rasterization library, additive production.
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