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RUSSIAN FEDERAL NUCLEAR CENTER 
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Issue N^{o} 2, 1990  MIMOZA SOFTWARE SYSTEM FOR SOLVING MULTIDIMENSIONAL CONTINUUM MECHANICS PROBLEMS ON THE ELBRUS2 COMPUTER
I D. Sofronov, E.A. Afanaseva, O.A. Vinokurov, A.I. Voropinov, V.V. Zmushko, F.A. Pletenev, P.V. Rybachenko, V.A. Saraev, N.V. Sokolova, B.N. Shamraev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 39.
The paper describes the MIMOZA software system for solving 2D and 3D continuum mechanics problems. Methods of splitting in physical processes and dividing the solution domain into computational domains are used. Regular grids are constructed in each computational domain, which consist of quadrangles in a 2D case and hexahedrons in a 3D case. The mutual influence of domains is taken in account using internal boundary conditions. The grid motion doesn’t always coincide with the material motion. The solution of 3D equations is based on representing them in Eulerian Lagrangian coordinates with one Eulerian and two Lagrangian variables. Problemoriented languages are used for data setting, management of computations, and result output.
 NUMERICAL STUDY OF THE MEDIUM COMPRESSIBILITY EFFECT ON THE RAYLEIGHTAYLOR INSTABILITY DEVELOPMENT N.N. Anuchina, M.G. Anuchin, V.I. Volkov, A.E. Guseva, N.S. Eskov, V.N. Ogibina, A.V. Polionov, I.A. Potanina VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 1016.
The medium compressibility effect on the RayleighTaylor instability development is studied on the base of twodimensional nonstationary gas dynamic computations using program complexes MAX and MECH. It is demonstrated that the medium compressibility leads to an increasing perturbation growth rate and an increasing mixing zone width and, in some cases, may drastically change the phenomenon character. The higher are the pressure gradients in the original flow, the more significant is the compressibility effect. The interpretation of the calculated results is given, which explains the physical mechanism of the compressibility effect.
 METHODS OF INCOMPLETE FACTORIZATION. PART 1. EXPLICIT ALGORITHMS V.P. Ilin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 1724.
This is the first one in the series of three papers on the iterative methods of incomplete factorization for solving linear grid equations. It describes different approaches (grid and algebraic) to the construction of wellknown and some new explicit iterative methods of incomplete factorization.
 METHODS OF INCOMPLETE FACTORIZATION. PART 2. IMPLICIT ALGORITHMS V.P. Ilin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 2529.
This is the second one in the series of three papers on the iterative methods of incomplete factorization for solving linear grid equations. It presents the comparative analysis of the grid principles of constructing implicit schemes of incomplete factorization and modern approaches, which consist in directly constructing preconditioning matrices. The unified algebraic apparatus used to study known algorithms and create new iteration processes is described.
 AN IMPROVED P_{0}TRANSPORT APPROXIMATION USED TO DESCRIBE THE ANGULAR DISTRIBUTION OF NEUTRONS IN INTERGROUP TRANSITIONS DUE TO SCATTERING V.P. Gorelov, Yu.V. Petrov, G.G. Farafontov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 3034.
The paper suggests three forms of approximately describing the angular distribution of neutrons in transitions between groups due to neutron scattering. The first of them called the P_{0}transport approximation is preferable for application in practice. It allows reducing the collision integral of the transport equation written for a 2D, or a 3D region to the single one with the D_{2}approximation characteristics being preserved and the collision integral positivity being ensured, in contrast to the latter.
 ARRANGEMENT OF ITERATIVE ACCESS TO THE CENTRALIZED I/O SYSTEM OF HETEROGENEOUS COMPUTER COMPLEX V.I. Samoylov, S.I. Sapronov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 3538.
The paper presents a general description of the TEX system, which performs its service functions on the arrangement of iterative access to the BSO centralized I/O system resources in the heterogeneous computer complex environment. The capabilities, functional structure, and system operation logics, as well as the BSO system interaction principles are considered. The system was developed to satisfy the need in broadening the scope of services for the remote access to the net resources of the computer complex. The main purpose of the system is to provide realtime access from terminal units to output files of jobs, which are processed in the BSO system. In addition to the conventional capabilities, the TEX system provides a number of unique capabilities developed owing to a high functionality of the BSO system.
 RIEMANN PROBLEM ON THE INTERFACE BETWEEN AN ISOTHERMAL GAS AND A HETEROGENEOUS MIXTURE OF THE OTHER TWO ISOTHERMAL GASES O.V. Buryakov, V.F. Kuropatenko, V.K. Mustafin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 3942.
An exact solution to the Riemann problem on the interface between two media, with an isothermal gas on one side of the interface and a mixture of the other two isothermal gases on another side, has been constructed. Shock waves and rarefaction waves in the homogeneous isothermal gas, regions of a continuous flow in the mixture and homogeneous medium, as well as multiplewave configurations in heterogeneous mixtures are used as the solution components. Four Riemann problem types depending on the isothermal gas parameters are possible. The shock wave processes in a heterogeneous mixture are described with the assumption of local equilibrium of pressure components.
 NUMERICAL ANALYSIS OF THE TWO METHODS OF CALCULATING THE NEUTRON MULTIPLICATION TIMECONSTANT λ A.N. Grebennikov, G.G. Farafontov, V.F. Yudintsev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 4347.
The numerical analysis of the two methods of finding the neutron multiplication timeconstant, λ the direct iteration and quasistationary methods  has been performed. The obtained results of computations demonstrate that the direct iteration method requires almost two times smaller number of iterations to find the λ parameter values than the known Kellogg method. The costeffectiveness of finding parameter λ with the quasistationary method is higher, in terms of memory requirements, in comparison with the relaxation method and, sometimes, provides a certain gain in the number of iterations.
 SOLUTION OF DIFFERENTIAL S_{N} AND DS_{N} EQUATIONS IN SOLID SPHERE V.P. Gorelov, Yu.V. Petrov, Z.V. Travin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 4853.
The paper suggests an approach to solving a system of ordinary differential equations, which are the result of S_{N} or DS_{N} transformations applied to the equation of neutron transport in a solid sphere. The procedure of accelerating successive approximations without any significant increase of the amount of computations is described. The approach discussed in the paper is not associated with the use of the original equations in their finite difference form and reduced to the use of stepbystep methods (RungeKutta, predictorcorrector, etc.) of solving problems with the specified initial conditions.
 SOME INEQUALITIES FOR DETERMINANTS OF LEADING SUBMATRICES A.A. Maleev VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 5457.
Some properties of matrices and leading submatrices are studied, expressions describing the relation between elements of a matrix, determinants of leading submatrices, and algebraic complements are derived. These relations contain new nontrivial estimates for the determinants of leading submatrices. For matrices with an irreducibly dominant diagonal, the nondegeneracy of their leading submatrices is proved.
 MODAL TRANSFORMATION OF THE MULTIGROUP NEUTRON TRANSPORT EQUATION CORRESPONDING TO THE USE OF P_{0}TRANSPORT APPROXIMATION V.P. Gorelov, G.G. Farafontov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 5862.
The paper suggests the transformation simplifying the multigroup neutron transport equation corresponding to the use of the P_{0}transport approximation when describing the angular neutron distribution in transitions between groups due to scattering. The transformation is called “modal” and allows writing the transport equation in the form corresponding to the assumed isotropic angular distribution of scattered neutrons. The specific features of using the modal transformation in problems with sources and in problems of finding various eigenvalues are discussed.
 INTERRELATION OF DIVERGENCY AND CONSERVATIVENESS OF DIFFERENCE SCHEMES FOR GAS DYNAMIC EQUATIONS V.F. Kuropatenko VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 6370.
The issue concerning the interrelation of the form and conservativeness of difference gas dynamic equations is considered. An attempt of further developing means for a priory examination of the properties of difference schemes for systems of linear equations in partial derivatives is made. Theorems of convertibility of the form of difference equations have been proved. The paper introduces and substantiates the notions of М and Sconservativeness, thermodynamic correctness, and strong/weak dissipativity of difference schemes. Properties of many known difference schemes have been examined and it is demonstrated, which of them have the given properties. All verbal proofs in the paper concern the differential forms of difference equations.
 ABOUT ONE VERSION OF THE METHOD OF SELETING DIAGONAL ELEMENTS A.A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 7175.
The paper considers the solution of the radiation transport equation in multigroup P_{1} approximation jointly with the energy equation. To accelerate the iteration process convergence when solving a nonlinear system of radiation transport equations and energy equation, the method of selecting diagonal elements with the linearization of all nonlinear terms with respect to temperature, which provides a high iteration convergence speed, both in optically dense and optically transparent media, is used. The paper suggests one of methods to linearize the absorption constant in a simplified form leading to the reduction of computation costs in problems with complex absorption constants.
 ABOUT COMPARISON PRINCIPLES FOR 2D GRID GENERATING ALGORITHMS AND PROGRAMS A.Ya. Filatov, A.G. Tsitsin VANT. Ser.: Mat. Mod. Fiz. Rroc. 1990. No 2. P. 7677.
The paper suggests some criteria to compare algorithms and programs used to generate twodimensional grids: an amount of input data, a rated number of grid nodes, machine (processor) time consumed to generate a grid, geometric gridquality criteria, graphical (machine) representation of a grid. It is noted that the grid generating algorithms should be classified prior to the comparison of grid generators.
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