


Since 1978 Published in Sarov (Arzamas16), Nizhegorodskaya oblast 
RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

Русский  English

Issue N^{o} 3, 1984  USING THE GODUNOV SCHEME TO SOLVE SPHERICAL HARMONICS DIFFERENTIAL EQUATIONS FOR A 1D KINETIC EQUATION
I. A. Adamskaya VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 38.
The suitabi1ity of partial solutions orthogonal running (Godunov scheme) to spherical harmonics differential equations is justified for a 1D stationary kinetic equation. It is proved that the problem boundary conditions permit to construct a complex system of linearlyindependent vectors required to use the method considered.
 NONLOCAL STABILITY CONDITIONS OF THE "CREST" DIFFERENCE SCHEME FOR ID GAS DYNAMICS WITH LAGRANDIAN VARIABLES Yu. A. Bondarenko, V. V. Zmushko, А. M. Stenin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 912.
The linearized difference scheme, "Crest", is used to describe a method for obtaining nonlocal and asymptotically exact stability conditions (with a mesh point number tending to infinity) from initial data in the presence of local inhomogeneity in the scheme coefficients. A case of regionbyregion computation and that of one small cell, compared to the rest, are considered. Smeared shock wave stability is examined for an artificial quadratic viscosity.
 AN IMPLICIT DIFFERENCE SCHEME FOR SOLVING GAS DYNAMICS EQUATIONS WITH LAGRANGIAN VARIABLES V. I. Delov, L. V. Dmitrieva, A. M. Pastushenko, S. Yu. Suslova VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 1318.
A 1D implicit unconditionally stable difference scheme is developed for solving 1D numerical problems in gas dynamics. The differential equation discretization involves the same mesh distribution as for the classical "Crest" scheme using velocity values from semiintegral times. Finitedifference equations are solved by an iteration method which does not require a time step limitation similar to the Courant condition to converge. The performonce of the scheme developed is demonstrated for two test problems.
 A DIFFERENCE SCHEME WITH NONLINEAR ARTIFICIAL VISCOSITY V. V. Bashurov, A. E. Ushakov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 1924.
A difference scheme for solving a transport equation with a nonlinear dissipative function (the so called Dviscosity) is examined. The difference equation is studied by the first difference approximation. Linearizing the first difference approximation in the vicinity of a partial solution gave uncertainty growth and its second derivative estimates. The artificial dissipative term (Dviscosity) is shown to correct the oscillations occrurring before they become fully grown and degrade the solution.
 A STABLE ALGORITHM FOR SOLVING A 2D HEAT CONDUCTION EQUATION BY REGION USING A NODE DIFFERENCE SCHEME R. M. Shagaliev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 2533.
For a 1D case, a regionbyregion algorithm is developed which approximates the conjugate conditions with 0(h^{2} + τ) order. For some limiting cases, the unconditional algorithm stability is investigated and analytically proved. The algorithm is generalyzed to a 2D case where the heat conduction equation is approximated with a nodetype scheme. The numerical results indicate that the algorithm yields a high actual accuracy and unconditional stability for a 2D heat conduction equation solved by regions on substantially nonorthogonal and nonuniform meshes with sufficiently large time steps.
 THE TIGR PACKAGE FOR SOLVING 2D PROBLEMS IN COMPUTATIONAL PHYSICS A. Yu. Bisyarin, V. U. Gribov, A. D. Zubov, N. N. Pervinenko, V. E. Neuvazhaev, V. D. Frolov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 3441.
The paper treats the issues concerning a program package development for solving 2D problems in computational physics for complicated geometry applications. This relies on reducing a complicated source problem to a sequence of simplified ones by distributing them according to geometry, physical processes, and space variables. Some aspects of deriving exchange boundary conditions are discussed for block computations. Design requirements are formulated for the programs included in a blockcomputation package. The paper gives a brief description of techniques implemented by application programs.
 NUMERICAL SIMULATION OF NONCOHERENT RADIATION TRANSPORT IN SPACECURVED OPTICAL WAVEGUIDES R. P. Tarasov, A. E. Temkin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 4248.
Transport equations are used to examine the numerical simulation of a noncoherent optical radiation energy propagation through spacecurved optical multimode waveguides. The transition from a wave equation to transport equations involves a fractional exponent of the Helmholtz operator and h^{1} pseudodifferential operator theory.
 INVESTIGATING THE DYNAMIC BEHAVIOR OF A THICK SPHERE STRESS STATE UNDER A MOBILE LOADING ON AN EXTERNAL BOUNDARY T. I. Zmushko, Yu. N. Bukharev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 4953.
A method of space characteristics is used to study elastic wave propagation and forming the highest stress regions (that is maximum stress rate regions) for a thick sphere which experiences dynamic load on its external surface h = 0,5R, h is the shell thickness, R is the external radius). Die external load is assumed to be determined by two stress tensor components (σ_{rr} normal and τ_{kθ} tangent) and its application region varies with time. The sphere being studied occupies the R^{l}≤r≤R, region within the r, θ, φ spherical coordinates, where 0≤θ≤π/2, is uniform, isotropic, and has linearly elastic properties defined by the density, ρ, longitudinal wave velocity, α, and transverse wave velocity, β. Axial symmetry requirements are assumed to be met.
 A SCALING TECHNIQUE FOR GAS DYNAMIC QUANTITIES IN THE CASE OF MESH VARIATION B. L. Voronin, O. M. Kozlova VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 5457.
A method is presented for scaling gas dynamic quantities due to the variation of a mesh which is used to solve 2D numerical timedependent problems in gas dynamics. The method peculiarity is that a 2D mesh reconfiguration and gas dynamic quantities scaling reduce to progressively performing 1D reconfiguration and scaling operations. The method capabilities are illustratied by a 2D gas dynamics problem.
 EQUILIBRIUM SORPTION DYNAMICS PROBLEM STUDIES IN TERMS OF LONGITUDINAL DIFFUSION A. V. Lukshin, T. G. Sysoeva VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 5861.
A numerical solution dependence on the problem parameters is studied. A selfsimilar analytical solution is derived. The numerical solution obtained from an infinite column simulation is compared to a selfsimiiar one. The isotherm is recovered using an approximate concentration front.
 STABILITY CONDITIONS FOR A 2D GAS DYNAMICS SOLVED USING LAGRANGIAN VARIABLES ON ARBITRARY RECTANGULAR MESHES Yu. A. Bondarenko, A. M. Stenin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 6269.
The paper describes a linearly approximated estimation of the Cresttype difference scheme stability for solving 2D gas dynamics equations with Lagrangian variables on arbitrary rectangular meshes in terms of artificial viscosity in the case where a pressure for the first boundary part and a normal velocity component for the second are given. For a time step, sufficient stability conditions close to exact ones are obtained in the form of inequalities to efficiently account the cell shapes, the grid nonuniformity, viscosity and sound speed variability along with boundary condition types. A weak instability is revealed which depends on the grid configuration near the boundary and a scheme modification is given with such instability removed.
 SOME ISSUES RELATED TO THE BESM6 MODIFICATION FOR SUPPORTING THE ELBRUS1 SERVER SYSTEM N. E. Balakirev, Yu. G. Bartenev, V. A. Erzunov, S. A. Zeldinova, N. A. Mustaeva, V. F. Tyurin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 7073.
The adaptation of the DISPAK OS to the Elbrus1 multiprocessor server is discussed. The reasons for creating a single OS for the BESM6 and the server are examined. Adequate multiprocessor architecture mapping оп the operation system is analyzed. The DISPAK is the first opergtfon system implemented for a server. It provides the BESM6 environment and the server compatibility, which permits the latter to use the software resources developed during the BESM6 life time. However, the Elbrus1 multiprocessor nature encourages one to further improve the operation system. Implementations, discussed here (multicomputer and multiprocessor) progressively bring us close to an operation system for multiprocessing. Multicomputer/multiprocessor combination allows to unify a multiprocessor efficiency and multicomputer reliability. The DISPAK OS utilization demonstrated it to be functionally complex and to have a high performance.
 EXPERIMENTAL DATA PROCESSING SYSTEM V. A. Zherebtsov, M. I. Kaplunov, V. G. Podvalny VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 7479.
Experimental data processing has the feature of both business (information capacity) and scientific (complicated problems) applications. Individuals involved in this sphere have variouslevel programmer skill. Therefore the data processing system proposed contains a wide range of data and processing mode description facilities  from the simplest to extremely complicated ones. The primary system purpose is to formalize and to automate experiment processing applications by sharing operations between experiment makers, mathematicians and computers.
 CENTRALIZED SYSTEM OUTPUT IMPLEMENTATION FOR A N0NH0M0GENE0US COMPUTER COMPLEX Yu. I. Akutin, N. N. Vyskubenko, A. S. Maksimov, V. I. Samoylov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 8083.
The paper presents a general description of the BSO system implementing centralized output functions within a nonhomogeneous computer complex. The system purpose, main capabilities, functional structures, and operation logic are examined. The background for creationg the system is elucidated. New possibilities, provided by the BSO, are discussed. The system design has taken into acount some disadvantages of earlier local output subsystems. Some new capabilities were also provided including failed output repeatability during several hours after an output process has been completed; detailed systemstatus information for the operator; simplicity of system function extensions (maintainance of new machine types and new classes of output files). The BSO operation showed that it successfully performs the functions assigned.
 MULTIDIMENSIONAL ANGULAR FUNCTION TECHNIQUES IN THEORETICAL PHYSICS A. A. Sadovoy VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1984. No 3. P. 8493.
Mathematical basis of multidimensional angular function techniques is analyzed. The paper compares hyperspherical functions, generalized hyperspherical functions, used in atomic nucleus theory, relativistic and nonrelativistic multidimensional angular Coulomb functions for evaluating quantum mechanics system properties with longrange interaction. Sturm representations of Green functions for several multiple particle system were derived to illustrate the efficiency of using mathematical capabilities of multidimensional angular functions. The issues related to using these computation techniques in technical physics are discussed.
 [ Back ] 






