Issue N^{o} 2, 1992 
GODUNOV METHOD MODIFICATION FOR EULERIAN TIMEINDEPENDENT EQUATIONS
I.S. Menshоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 313.
The paper considers a classical selfsimilar problem for the interaction of two homogeneous supersonic gas flows which is generalized to the case where the flows are nonhamogeneous that is gasdynamic parameter distributions are arbitrary and, in general, nonfixed. An explicit analytic solution is locally derived for this nonselfsimilar problem in the small vicinity of the flow interaction profile which is then used to increase the Godunov scheme accuracy for gasdynamic timeindependent equations.

TEST SET DESCRIPTION FOR METHODS AND PROGRAMS DESIGNED FOR 2D HEAT CONDUCTION CALCULATIONS Yu.A. Bondarenko, B.L.Vогоnin, V.V. Gоrev, V.I. De1оv, E.N. Zubоv, Yu.M. Matveev, A.I. Mоrenко, S.S. Sоко1оv, V.E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 1420.
A description of four test problems is proposed intended for testing methods and programs for numerical 2D heat conduction calculations.

EXACT SOLUTIONS FOR QUASILINEAR DIFFUSION EQUATIONS WITH HEAT WAVES MOVING AT AN ANGLE TO MATERIAL BOUNDARIES Yu.A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 2123.
For a multilayer medium consisting of various materials with their boundaries being straight lines, a method is described to derive exact solutions for the quasllinear diffusion equation: where the constants c_{i}, v_{i} and æ_{i}, differ for each material i while being interrelated. Wellknown 1D solutions are used such as the solution for a heat wave moving with a constant velocity through zero background. Temperature and flow equivalence requirements for the boundary between different materials imply some constraints on parameters c_{i}, v_{i} and æ_{i} resulting from the angle between the heat wave front and material boundary and also from the heat wave velocity. A specific problem is cited to be used as a test one.

ONE CLASS OF SPLITTED DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS N.Yu. Bакaуev VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 2428.
Inequalities are obtained a priori which represent instability for one class of splitted difference schemes in Banach spaces. The theory developed is used to study stability in space norms L_{ph} I ≤ p ≤ ∞ of splitted difference schemes for a 2D heat conduction equation.

A MODEL FOR OPTICAL FIBER STRETCH V.V. Belоv, V.G. Niкоlaev VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 2931.
A numerical method is developed for solving equations which describe fiber stretch processes for a quasionedlmensional case. Newton iteration method is used to resolve the nonlinearity of equations. Our method relies upon ADI algorithm for linear systems with shaped matrices.

CALCULATIONS OF ELECTRIC BREAKDOWN PARAMETERS FOR IRRADIATED CYLINDRICAL DIELECTRIC STRUCTURES V.V. Goncharov, S.I. Коva1уоv, Yu.V. Kоsse, S.Yu. Malкоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 3236.
This paper examinee electrodynamic and radioactive effect of penetrating radiation on a dielectric cylinder structure represented as an infinite cylinder with a filling material. Electric breakdowns are shown to occur in the structure shell due to the above effects. A method is presented which allows to estimate potential and current distributions along the inner shell surface, a numerical solution is derived using finite element method. Numerical results for a specific structure are used to determine possible location of a breakdown due to radiation which was represented by a flux of neutral hydrogen atoms. A condition is defined for breakdown occurrence in a cylindrical dielectric shell.

TEMPERATURE FIELD STUDIES IN A COMPOSITE MATERIAL DECAYING DUE TO THE EFFECT OF 30 MEV PROTON BEAM V.P. Vagin, V.V. Zhakhоvsку, М.P. Ivanоv, V.V. Saviсhev VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 3741.
Experimental and theoretical studies were performed to investigate temperature fields in samples of phenolphormaldehyderesin based glass plastic Irradiated by a continuous 30 Mev proton beam at a rate of 10^{14} particles/cmsec. A model is constructed which allows to describe the temperature evolution in glass plastic samples with thermal material destruction, highly nonlinear ther mophysical coefficients and energy output variations. Experiments agree well with calculations which permit to conclude that the radiation component of the phenolphormaldehyde decomposition is negligible under above conditions.

ELECTROMAGNETIC WAVE EXCITATIONS DUE TO PHOTOEMISSION RESULTING FROM PULSE XRAY ЕРРЕСТ L.P. Priadкo VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 4245.
Electromagnetic radiation and surface current excitation laws are Investigated for a powerful incident xray pulse impacting the target surface in the vacuum. The motion of knockedon photoelectrons is determined both by the electrostatic field and the emitted wave field. The radiation field is shown to dominate for grazing Incidence of xrays. Such situation is interesting from a general physics point of view as it provides an example of system with the motion being determined by the radiation brake force. A simple analytical model is presented for this case.

A MODEL OF TНЕ GOVERNING EQUATION FOR POROUS MEDIUM V.N. Maгкelоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 4650.
A computer model is proposed for a phenomenological thermodynamic equation describing a porous medium allowing thermal stress relaxation when an expansion Into voids occurs. For Incomplete compaction region, pressures are described based on a volume plasticity model with a variable volume compaction modulus for a porous medium. For a complete compaction region and relaxation, we use the wellknown equation of state for solids which includes material vaporisation. Stress deviator components are computed using shear plasticity model with TreskSenVenan yield strength. The model of a porous medium gives a threewave configuration for a shook in a low pressure region. Experiments and predictions are compared for shook compression of the PS1 foam. Relaxation dynamics of thermal stresses is calculated for KT11.

COERSION ESTIMATES FOR ONE CLASS OF DIFFERENCE SCHEMES N.Yu. Baкaуev VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 5153.
Coersion inequalities are established for RungeKutta difference scheme stability for parabolic equations.

NUMERICAL COMPARISON OP KELLOG, SPLITTING AND FORWARD PROCEDURES FOR CALCULATING K_{ef} WITH CONSECUTIVE APPROXIMATIONS V.P. Gоrelоv, A.N. Grebenniкоv, G.O. Parafontov VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 5457.
Numerical comparison is performed for three calculational procedures using consecutive approximations of K_{ef} The studies allowed to conclude that the forward procedure is efficient and costeffective. This is recommended to use in 2D and 30 calculations of critical parameters.

SPLITTING SCHEMES FOR AN IRREGULAR SYSTEM OF MAXWELL EQUATIONS V.M. Melniкоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1992. No 2. P. 5862.
Costefficient splitting schemes are proposed for a Maxwell system with a retard time τ (τ is the time elapsed from electromagnetic wave arrival to a given point) which does not refer to the Cauchy Kovalevskaya class. A typical problem is used to study the scheme properties which were tested by numerical calculations. Real scheme characteristics (computation accuracy and time) are compared with other parameters used in practice.

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