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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 3, 2018  STUDYING THE "SPH" METHOD APPLICABILITY TO THE 2D SIMULATION OF GAS DYNAMIC PROCESSES WITH DETONATION
I. M. Epishkov, I. V. Zalyalova, D. M. Linnik, S. Yu. Suslova VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 3. P. 313.
The paper describes the study into the feasibility of using the classic SPH method for the 2D simulation of gas dynamic processes with detonation. The main formulas of the method are presented, as well as results of gas dynamics simulations with the detonation wave rate control and using the MorozovKarpenko kinetic model. The calculated results are compared with the available experimental data and also with similar results obtained using the twodimensional D code. Key words: gas dynamics, the MorozovKarpenko model of detonation kinetics, detonation wave, the SPH method, interpolation core, smoothing length.
 THE PHASE METHOD TO SOLVE THE EIGENVALUE PROBLEM FOR THE DIRAC EQUATION M. A. Vronskii, V. M. Povyshev, S. Yu. Polyakova, E. S. Stolmakova VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 3. P. 1431.
We propose a version of the phase method for the solution of the eigenvalue problem for the radial Dirac equation. The potential with Coulomb behavior at the origin is considered. Our method is applicable to both finite and infinite interval. The regular solution at the origin is obtained as a solution of the derived Volterra equation. We prove the comparison theorem for the solutions of the phase equation. This theorem underlies the effective algorithm to find the eigenvalues. We determine the correspondence between the quantum numbers and the rightboundary values of the phase function for the eigenstates. We highlight the eigenfunction calculation problems and describe two ways to solve them. Several test calculations are presented. Key words: the Dirac equation, the eigenvalue problem, the SturmLiouville problem, the phase method, the Sturm comparison theorem, the potential with Coulomb behavior at the origin.
 THE "PI" TECHNIQUE FOR THE SIMULATION OF PROTON IMAGES K. L. Mikhaylyukov, I. V. Khramov, A. V. Skobeyev, S. V. Potapov, N. V. Frolova, M. D. Romanova VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 3. P. 3243.
The paper describes the proton imaging (PI) technique for the mathematical simulation of a proton beam passing through various objects and magnetic optics in order to simulate the proton images of these objects. The software implementation of this technique is required for managing the available and future proton radiography devices and consists of two modules for the simulation using the beam summation and Monte Carlo methods. The last version of the software implementation of the PI technique has been supplemented with the API subsystem for computerbased job preparation and running. The API subsystem provides the computerbased parameter setting, viewing, editing, and checking out, an ability of reinterpolating the grid values of quantities and running jobs on the simulation of proton images using the beam summation and Monte Carlo methods. API provides the user´s webinterface for entering and editing simulation parameters via a webbrowser. The paper briefly describes the code validation results and gives some examples of the simulated proton images. Key words: simulation of proton images, Geant4, webinterface, proton passage through a substance.
 THE ARTIFICIAL VISCOSITY FOR SUPPRESSING THE "CARBUNCLE"TYPE NUMERICAL INSTABILITY IN 3D PROBLEM SIMULATIONS A. V. Rodionov VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 3. P. 4451.
Generalization of the artificial viscosity method to suppress the "carbuncle"type instability in the simulation of 3D problems is described. The firstorder schemes (Godunov, Rowe, and HLLC schemes, AUSM+ and Safronov scheme) are considered as applied to the simulation of 3D problems using smooth structured grids. The efficiency of this method is demonstrated by the example of wellknown test problems.n the TIM code. Key words: hypersonic flows, Eulerian and NavierStokes equations, numerical instability, artificial viscosity, 3D problem simulations.
 GEOMETRIC PROBLEMS OF SIMULATING PARTICLE TRAJECTORIES IN THE C007 CODE V. I. Roslov, A. G. Mal´kin, A. V. Gorbunov VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 3. P. 5262.
The paper describes the principles of setting geometric objects in the C007 code for solving linear transport problems with the Monte Carlo method. The way of constructing the problem geometry is described and the geometric block types are given. The derivation of formulas to calculate the distance to a surface is shown by the example of an axially symmetric block. Special attention is paid to the calculation of the distance to torus. Key words: the Monte Carlo method, geometry, the distance to torus.
 PLESTIMATES OF FLOW AT POINT TO CALCULATE THE ABSORBED DOSE GENERATED BY RADIONUCLIDES IN AIR E. N. Donskoy VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 3. P. 6369.
The local assessment of the radiological situation caused by radionuclides distributed in atmosphere is the task of a higher importance for the radiation safety analysis. If a radionuclide emits gamma photons, it is required to solve the problem of gammaradiation transport in a homogeneous air medium with a source of radionuclides, which size (as well as the size of detecting area) is several orders higher than the range of influence of a point source of gammas. (The radionuclide source size is about 100 km, the range of influence of a point source of gammas with energy below 10 MeV doesn´t exceed several hundred meters.) Such situation causes difficulties in solving the problem with traditional methods using local flow estimates at a point. At the same time, this situation is favorable to apply PLestimates of flow at a point. Key words: distribution of radionuclides in atmosphere, radiation safety, model of a source of gammas, local estimate of flow at a point, PLestimate of flow at a point, the absorbed dose calculation method.
 SOFTWARE SYSTEM FOR DIAGNOSING MULTIPROCESSOR NODES OF A COMPUTING SYSTEM A. B. Kiselev VANT. Ser.: Mat. Mod. Fiz. Proc. 2018. No 3. P. 7074.
The paper describes the software system for the automatized diagnosing (checking) of faulty multiprocessor nodes in a computing system. Sources of hardware and software failures have been identified, the methods used in the system to restore serviceability of computing nodes controlled by the JAM batched job processing system are described. Key words: batched job processing system, restoration of serviceability of a computing system´s multiprocessor node.
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