Issue No 2, 1997
METHODS OF CONNECTION RECONSTRUCTION FOR ARBITRARY POLYHEDRAL COMPUTATIONAL GRID
V.V. Rasskazova, I.D. Sofronov, A.N. Shaporenko
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 3-16.
A method of 3-D irregular grid local reconstructions has been proposed along with its program implementation algorithm. The method is based on two grid reconstruction operations — pasting two meshes having one common face and cutting a certain mesh into two by a given plane.
The criteria of either operation application are given and analyzed.
Two test calculations with a program of 3-D irregular grid local reconstructions used have been carried out; the computed results are given.
|CALCULATION OF SMOOTH GRIDS WITH COMPLEX COMPOSITION BY DIRECT MINIMIZATION OF VARIATIONAL FUNCTIONALS
R.N. Antonova, G.P. Prokopov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 17-23.
Method of construction block-regular 2-D grids in one-connected and multiply-connected regions is considered. The method is based on direct minimization of variational functionals by means of descent in directions not connected with the functional gradient vector. The method is oriented to multiprocessor systems and may be extended to the spatial case.
|SOME STATIONARY SOLUTIONS FOR THERMONUCLEAR BURNING WAVE
M.M. Basko, N.I. Efanova, E.A. Zabrodina, N.A. Krasnoborov, M.D. Churazov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 24-30.
It was considered the stationary method of the calculations for the thermonuclear wave in the magnetized plasma channels.
In this approximation it was obtained the velocity of the wave D ≈ 42,43 ⋅ 107cm/s in DT-fuel with ρ = 10g/cm3 and D ≈ 69,44 ⋅ 107cm/s for D0,93He0,1 - fuel with the density ρ = 100g/cm3. The radious of the fuel channel was equal R0 = 0,0050cm. The results of the calculations by the another methods were compared.
As conclusion it is advisable to elaborate the further improvement of the numerical methods.
|COMPARISON OF COMPUTATION TIME FOR EOS POTENTIAL COMPONENTS HAVING VARIOUS ANALYTICAL REPRESENTATIONS
L.F. Gudarenko, M.K. Sarayeva, I.I. Tukmakova
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 31-35.
The paper is aimed to compare computation time for EOS potential components — pressure, energy and pressure derivative with respect to relative compression — expressed in different analytical forms that are used in EOS models of condensed materials. To compute energy and pressure derivative with respect to relative compression 16 analytical pressure representations and relevant dependencies are considered. The example of EC-1066, i486/DX2/66MHz and Pentium/133MHz computations illustrate that the most complicated dependencies require computation time about 6 times greater than that of the most economical functions represented by polynomials.
The given data is of reference character and might be useful in EOS model development and in massive computation programs.
|APPLICATION OF DYNAMICALLY ADAPTIVE GRIDS IN PLAN PROBLEMS OF SHALLOW WATER THEORY
V.B. Barakhnin and G.S. Khakimzyanov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 36-44.
The paper describes some algorithms of constructing dynamically adaptive grids for 2-D (plan) problems of wave hydrodynamics to be numerically calculated. The algorithms are based on a 1-D equidistribution method modification. The problem of solitary wave oblique flow on the vertical wall calculated in frames of shallow water theory of the first and second approximation is used as an example to show the advantage dynamically adaptive grids over stationary ones.
|EFFICIENCY ESTIMATION OF IMPLICIT EULERIAN-LAGRANGIAN METHOD OF COMPUTING 2-D GAS DYNAMICS PROBLEMS WITH HEAT CONDUCTION FOR DISTRIBUTED-MEMORY MULTIPROCESSOR SYSTEMS
O.I. Butnev, B.L. Voronin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 45-54.
Computation modules of implicit Eulerian-Lagrangian method for 2-D axisymmetric gas dynamics problems with regard to non-linear heat conduction are studied in terms of parallel computations. The possibilities of algorithm parallelizing in computation modules, the operation number distribution within algorithms, the demand to distribute data among algorithm parallel branches are analyzed and the costs for data redistribution are estimated.
The problem to transpose the matrices of information about calculation points is encountered when the implicit Eulerian-Lagrangian method is parallelized on distributed-memory multiprocessor system. Transposition algorithms are proposed for “ring”-and-“tore”-configurated multiprocessors; the efficiency of method parallelization is estimated.
|SOME INTEGRABILITY CASES OF FACTOR-EQUATIONS FOR POLYTROPIC GAS 1-D DYNAMICS
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 55-65.
The paper studies cases of integrability in factor-equation quadratures relevant to 1-D subalgebra optimum system of symmetry algebra for polytropic gas 1-D dynamics in Lagrangian equations.
The factor-equations are reduced to Abelian equations, for which cases of reducibility to linear and Bernoulli equations are studied. This allows to find new analytical solutions of gas dynamics equations.
|CALCULATION OF ANGULAR AND RADIAL DISTRIBUTIONS OF ACCELERATED ION REPEATED SCATTERING IN MATERIAL
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 66-70.
The paper presents a method of angular and radial distributions of accelerated ion repeated scattering on material atoms. The method is designed to be used with interatomic interaction potentials of Thomas-Fermi type, whose screening function is a linear exponent combination. A classical theory in pulse approximation is used to calculate the differential cross-section of one-time scattering. Calculated distributions, experimentally compared to those measured, showed a good agreement. Some dicrepancies with the known tables calculated on Lindhard approximation base for the differential cross-section of one-time scattering have been found. An area of interatomic interaction potential applicability is illustrated using the experimental mea-surement results of ion beam radial scattering in rarefied gas targets.
|INTERPOLATION OF FUNCTIONS AND SMOOTH RECONSTRUCTION OF CURVES RETAINING THE MONOTONICITY AND CONVEXITY
G.P. Prokopov, O.I. Sofronova
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 71-78.
The elementary but important for applications problem of construction of spline passing through the giving set of support points is under consideration. The rational splines construction approach allowing to retain the monotonicity and convexity of constructing curve of C class is suggested. The advantage of the algorithm is automatized definition of all parameters of splines.
|CONCEPTIONS OF PROGRAM ARRANGEMENT FOR MP-3 MULTIPROCESSOR COMMUNICATION SYSTEM
V.M. Vikharev, S.I. Sapronov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 2. P. 79-84.
MP-3 multiprocessor communication system conceptions are described in this paper. The multiprocessor is a MIMD machine with distributed memory.
Hardware communication components description is minimized. Careful consideration is given for software components.
Communication system has three layers architecture. Layers interfaces are separated.
Channel layer controls the communication hardware, performs message fragmentation and routing.
Representation layer performs management of internal communication components which have been created specially for high level message passing requests support.
Application layer contains service functions for specific purposes. The layer provides NX and MPI message passing standards and packet of functions for system purposes. Message passing libraries provide Fortran and С calling interfaces.
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