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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2015  ARTIFICIAL VISCOSITY IN THE GODUNOV’STYPE SCHEMES AS THE METHOD OF "CARBUNCLE"INSTABILITY SUPRESSION
A. V. Rodionov, I. Yu. Tagirova VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 311.
The paper describes a new method of solving the "carbuncle"problem, its essence is the introduction of dissipative dopants in the form of righthand parts of the NavierStokes equations, where the molecular viscosity is replaced by the artificial one (i.e. the tensor of artificial viscous tension is introduced). Artificial viscosity is the second infinitesimal order quantity which, like in the artificial NeumannRichtmyer viscosity, is proportional to the velocity divergence. The principle difference here is the limiter, which prevents the additional dissipation out of the front of an intense shock. The new method of solving the carbuncleproblem, being the external relative to a certain scheme, does not change the algorithm of the nonviscous flow simulation. The efficiency of the proposed approach is proved by the examples of solving several test problems: the Kirk problem (broken onedimensionality of a plane shock wave), strong shock diffraction on the right angle and the "Double Mach Reflection". Key words: hypersonic flows, Euler and NavierStokes equations, carbuncleproblem, Godunov’stype schemes, artificial viscosity.
 INTERACTION OF SOUND WITH MATERIALMATERIAL INTERFACE IN DIFFERENCE SCHEMES OF 1D LAGRANGIAN GAS DYNAMICS. ACCURACY DEPENDENCE ON THE GRID ADJUSTMENT METHOD VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 1227.
In some difference schemes for 1D gas dynamics on Lagrangian grids (without account for artificial viscosities) the difference coefficients of sound perturbation reflection from the materialmaterial interface have been calculated and the difference laws of acoustic energy preservation have been built. It is shown that in the difference schemes on scattered special grids (the "cross" scheme and the scheme with artificial antidispersion) the difference reflection coefficient matches the analytical one (obtained for the acoustics differential equations) only when the grid on the materialmaterial interface is adjusted over the acoustic thickness. The difference coefficients of acoustic perturbation reflection in the KABARE and Godunov’s difference schemes always (independently of the way the grid is adjusted) match the analytical value, but other types of errors are indicated which are proportional to the jump of the cell acoustic thickness. The calculation of the weak shock passage through a periodical stratified medium have shown that when the grids adjusted over the acoustic thickness are used, the simulation accuracy can be improved by several times, while the running time can be reduced by more than an order of magnitude compared with the simulations on the masseven grid, provided that the preset accuracy is preserved. Key words: weak perturbations, dispersion equations, acoustic reflection coefficients, difference law of acoustic energy preservation, uneven grids, rules of grid adjustment on the materialmaterial boundaries.
 NUMERICAL MODELING OF THE DETONATION PROCESS IN 3D SPACE USING ADAPTIVEINBUILT LAGRANGIAN GRID IN THE "D" TECHNIQUE L. A. Andreevskih, I. M. Epishkov, N. V. Korepova, D. M. Linnik, O. O. Murugova, B. V. Titova, Yu. D. Chernyshev VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 2839.
The paper describes the calculation technique for 3D gasdynamics problems on adaptiveinbuilt Lagrangian grids. The main idea in solving the gasdynamics problems using adaptiveinbuilt grids is in the reduction of the initial grid cells in the course of the simulation in local areas with high gradients of gasdynamic quantities. Such approach enables, in a number of cases, to improve significantly the accuracy of the numerical solution without overloading the simulation process with an overrefined grid, and making the simulation more cost—effective. Due to its costefficiency the adaptiveinbuilt calculation technique suits well for the 3D setup problems, in particular, for the highexplosive burning numerical simulation using the MorozovKarpenko detonation kinetics models. When this model is used the issue of high requirements to the grid cell size arise, which is partly associated with the physical parameters of the applied explosive material. For example, for the penthritebased high explosive the size of the chemical zone is approximately 0.03 mm. Clearly, the computing grids with the approximately 0.1 mm cells which are usually employed for the simulation of other explosives’ detonation processes (e.g. TATBbased ones) with the MorozovKarpenko kinetics are not always applicable to the penthanitebased high explosives. Therefore the approach associated with the detonation kinetics model application to 3D simulations could not have been used because of its high requirements to the computing resources. This paper briefly describes the algorithms of the adaptiveinbuilt grids application as applied to the Lagrangian "D" technique, and shows the results of the numerical simulation of one experiment for the determination of weak shock effect on the detonation wave propagation in penthritebased highexplosive rods using the described technique. Key words: 3D Lagrangian "D" technique, gas dynamics, MorozovKarpenko detonation kinetics, adaptiveinbuilt Lagrangian grid.
 MODIFIED KINETIC MODEL OF BRITTLE SPALLATION O. A. Tyupanova VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 4048.
The kinetic model of brittle spallation (NAG type) has been modified for the accounting of the temperature factor effect on the metal resistance to pulse tension. The modification has been carried out by the introduction of the temperature dependences of three model parameters. Previously these parameters  threshold presures of microcrack nucleation and qrowth, as well as viscosity  were considered as constants. The paper shows that using the modified model enables the correct description of the pure iron spallation process within the temperature range of T = 273÷1 025 К and within the shock range σ = 1÷13 GPa, where the change of the fracture character is registered (from brittle to viscous). Key words: brittle spallation, temperature effect, modified model, iron.
 ACCELERATION METHODS FOR INPUT DATA CALCULATION UNDER THE 3DRND PROGRAM COMPLEX AT THE PARALLEL NUMERICAL SIMULATION OF MATHEMATICAL PHYSICS PROBLEMS K. K. Olesnitskaya, A. L. Potekhin, E. V. Potekhina, V. I. Tarasov VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 4958.
The paper describes the phases and methods of the parallel calculation efficiency improvement under the 3DRND complex for the input data calculation of the mathematical physics problems in the 3D setting. In the first method we use the computing load balancing basing on the estimation of the grid cell complexity, according to which they are distributed over the processors. In the second method the whole scope of the сells is divided into big amount of portions (blocks) and their dynamic distribution between the processors. To preserve the computed data in the 3DRND program complex the EFR library is used, which provides the effective access to the file data on the multiprocessor computers. We describe, for the methods, the basic algorithms of calculation and input data preservation, the comparative analysis of the input data calculation rate parameters for a number of problems. Key words: 3DRND program complex, EFR library, {it parallel} computations, matrix decomposition, computation load, computation load balancing, computation efficiency.
 GeomGrid2 UNIFIED SYSTEM FOR PREPROCESSING OF 2D MATHEMATICAL MODELING PROBLEMS O. V. Belomestnykh, S. V. Gagarin, D. V. Mogilenskikh, E. A. Prib, A. A. Ushkova VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 5968.
For a long time RFNCVNIIEF has been developing program complexes for numerical simulations in the field of continuum mechanics. The role of efficient methods for data preparation for calculations is constantly growing. The GeomGrid2 system has been developed to provide the required functionality of the initial data preparation process for 2D problem calculations. It has modern ergonomic interface. Due to the developed efficient algorithms and functions for visual and numerical analysis of geometry, grids and particles, this system enables the comprehensive control of the initial data preparation for 2D problems. This paper describes the GeomGrid2 system user interface, its main functionality which enables forming the 2D geometry “from scratch” or uploading it from dwg/dfxfiles (AutoCAD) and hdf4/hdf5files with standard 2D crosssections, building blocks and domains within the problem, building and optimizing computing grids (structured and nonstructured ones), generating particle fields, setting materials for domains and distributing them between the grid cells. The formed input data is downloaded from the system into variousformat files, which then are used to start 2D problem calculations by RFNCVNIIEF mathematical simulation program complexes. Key words: RND, initial geometry, SDR format, crosssection, XML format, AutoCAD, computed domain, physical subdomain, structured grid, nonstructured grid, physical values.
 RAMdisk LinuxBASED OPERATING SYSTEM OPTIMIZED FOR HIGHPERFORMANCE CALCULATIONS E. V. Eremin, N. N. Zalyalov VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 6977.
The paper describes the basic milestones of the core resident Linuxbased Operating System development to control the operation of diskless computer nodes of a multiprocessor computer complex. We consider the procedures of the system building to enable the change of the software suit by adding and removing program packages, forming various operating system images for different parts of the heterogenic computer complex. We discuss in detail the processes of twostep downloading over the communication network of the computer complex, which accelerates the whole complex loading. We also provide several estimations of the operating system effect on the parallel code, which we have obtained using local tests, collective exchanges and profiling data. There is also a short review of related work. Key words: multiprocessor computer complex, core resident Operating System, Linux core, descending loading, profiling, parallel code, hot spot, Operating System noise.
 USING VARIOUS COMPUTING GRID TRANSFORMATIONS IN THE TIM2D TECHNIQUE A. I. Panov, A. V. Shurygin VANT. Ser.: Mat. Mod. Fiz. Proc. 2015. No 2. P. 7887.
The algorithms used for various transformations of unstructured polygonal grid in the TIM2D technique and for preparation of initial data for this technique are described. The provided examples show the way the transformations are performed both separately and in composition. We also provide practical recommendations on the use of different transformations depending on the type of the structure and special features of the problem solving. Key words: TIM2D technique, nonstructured grid, geometric transformations, initial data calculation.
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