Issue No 1, 1987 |
CONSERVATIVE AND INVARIANT DIFFERENTIAL AND DIFFERENCE REPRESENTATIONS OF GAS DYNAMICS EQUATIONS IN AN AXISYMMETRIC GASE
V. I. Delov, V. N. Isaev, I. D. Sofronov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 3-10.
We propose an approach to constructing conservative and invariant differential and difference representations of gas dynamics equations in Lagrangian variables. As shown, a numerical solution may be invariant when a special type of kinetic energy in elementary volume is chosen. Test results are given which illustrate the feasibility of the approach formulated here.
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| SELF-SIMILAR RAREFACTION WAVE FOR A MODEL OF A HETEROGENEOUS TWO POLYTROPIC GASES MIXTURE O. V. Buryakov, V. F. Kuropatenko
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 11-14.
For a commonly used model of a heterogeneous medium accounting component velocity nonequilibrium, an exact solution is derived for a piston pulled out with a sufficiently high speed from a heterogeneous mixture of two polytropic gases. The derivation is carried out assuming the component pressures to be locally equivalent.
The resulting solution together with a similar one previously obtained for another commonly used heterogeneous medium model allowed to compare these types of models on one class of solutions.
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| COMPUTER IMPLEMENTATION OF-KINETICS EQUATIONS FOR PLASMA PARTICLE IONIZATION AND EXCITATION V. P. Bashurin, G. V. Dolgoleva
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 15-20.
We present a system of differential equations including radiation gas dynamics and kinetics equations for plasma particle ionization and excitation. A numerical method.for solving it is given. We report the results obtained by solving problems having analytical solutions.
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| DESIGNING SOFTWARE FOR COMPUTATIONAL EXPERIMENTS. GUIDELINES AND CHALLENGES V. I. Legonkov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 21-28.
The paper discusses difficulties involved in developing a modular/structured approach to programming, creating problem-oriented data definition languages, reasonable combination of higher and lower level languages, designing general service-type program subsystems.
A general structure of computational experiment software is given and some results obtained from its implementation and operation are reported.
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| RADIANT HEAT EXCHANGE OF OPTICALLY THICK SPHERE SHELLS VIA A NEAR-TRANSPARENT HOT PLASMA LAYER V. S. Imshennik
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 29-39.
In order to obtain efficient solutions of 1-D sphere-symmetry problems in radiation gas dynamics, where optically thick and thin material layers exist at the same time, a model is developed for radiant heat exchange in a multilayer system which consists of optically thick spheres with intermediate high- -temperature (hot) plasma layers. The model proposed describes a radiation transfer in optically thick layers using a well-known radiant heat conduction approximation. However, for heat conduction equations we derive integral boundary conditions including the effect of irradiating this layer with bulk radiation of optically thin plasma and degraded radiation of an optically thick neighbor layer (in combination with self-irradiation). For hot plasma, we formulate an effect of local material heating by the surface radiation of surrounding optically thick layers due to its absorption by plasma. The model equations satisfy energy conservation laws and correspond to the Kirchhoff’s law.
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| A METHOD FOR REPRODUCING NEUTRON RADIATION SPECTRUM AND KINETICS FROM OBSERVATIONS AT TWO TRANSIT-TIME STATIONS V. F. Karyakin, A. A. Stasevich
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 40-48.
Using special features of transit-time measurements, we have found a procedure for reproducing the radiation spectrum and kinetics from observations made at two transit-time stations with recording device pulse characteristics omitted. The approximate solution is shown to converge to an exact one in a uniform manner. A class of functions is given where this procedure is theoretically possible. Numerical calculations demonstrate the practical importance of our method and some of its advantages.
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| EXPLICIT/IMPLICIT RID METHOD FOR SOLVING PROBLEMS IN GAS DYNAMICS A. D. Gadzhiev, S. N. Lebedev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 49-53.
The paper describes a new difference scheme for solving 2-D equations of gas dynamics in Lagrangian coordinates. The method relies upon applying the ROMB scheme to solve a diffusion-type equation in order to determine pressure for advanced times. This equation used a stabilizing correction method. To suppress short wave perturbations the velocities are smoothed by using fourth-order differences. The results of test calculations are presented to illustrate the method performance.
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| AN APPROXIMATION OF LAGRANGIAN SURFACES WITH EULER IAN MESH IN SPACE Yu. A. Dementiev, A. I. Kirillov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 54-60.
An approximation of Lagrangian boundaries in space is proposed which relies upon information about intersections of boundary surfaces with coordinate lines defining the Eulerian mesh. Each mesh cell is assumed to be a hexahedron. The description is in terms of Cartesian coordinates. The movement of closed continuous Lagrangian surfaces within a given velocity vector field is described.
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| SOYUZ PROGRAM PACKAGE FUNCTIONAL STRUCTURE V. I. Zuev, V. I. Legonkov, V. N. Ogibin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 61-64.
The SOYUZ program package is designed to solve 2-D time-dependent problems in continuum mechanics.
The package is defined as a set of programs which are written based on modular/structured programming by means of common languages and tools. These programs, when executed, use the same data definition languages, houskeeping and service subsystems, and databases.
An overview of package component interactions in design and application execution phases is presented.
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| ON NUMERICAL SOLUTION OF THE VLASOV EQUATION USING PARTICLE PATHS A. I. Koryakin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 65-68.
A method is proposed for numerically solving the kinetic collisionless Vlasov equation using random particle paths. For simulations of charged particle beam dynamics, a faster solution convergence is shown to be possible as the number of beam particle paths increases.
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| STABILITY OF DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS IN ARBITRARY NORMS. PART I N. Yu. Bakaev
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 69-75.
The paper studies the issues related to difference scheme stability for abstract parabolic equations in Banach space norms. Sufficient stability conditions are obtained for schemes with fixed and variable operators.
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| SOME ASPECTS OF 3-D NUMERICAL PROBLEM SOLUTIONS IN CONTINUUM MECHANICS V. V. Rasskazova, I. D. Sofronov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1987. No 1. P. 76-87.
We consider some issues related to the numerical solution of 3-D heat conduction and gas dynamics problems. Splitting the space with a difference mesh is examined to approximate these equations. A method for retaining convex trihedral angles is presented. We analyze whether it is possible to avoid edge intersections inside the cells.
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