Issue N^{o} 2, 1988 
GRAPHICS SOFTWARE SYSTEM
S. V. Gagarinov, G. B. Kulikova VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 310.
We propose a graphics system with an implementation of the GKS international standard for a basic system as its kernel. Issues of human interface to a graphics system via a problemoriented superstructure are adressed. Input data structure is proposed for application program interface to the graphics system which makes the latter different from those used in our country. Introducing the GRAFOR package functional capabilities into the systems allows to use existing GRAFORoriented application programs.

AN APPROACH TO CONSTRUCTING HYBRID SCHEMES WITH HIGHER ORDER APPROXIMATION N. Ya. Moiseev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 1116.
A fivepoint pattern is used to construct a new higherorder approximation twostep difference scheme. The scheme is hybrid: large discontinuities are calculated using secondorder approximation schemes with normal and abnormal dispersion before and behind the discontinuity, respectively, while smooth solutions use a thirdorder approximation scheme. Model problem results show that the scheme is actually monotonous and more accurate for smooth and discontinuous solutions compared to the Godunov scheme.

ON OPTIMAL CHOICE OF BASIC FUNCTIONS IN A LINEAR REGRESSION PROBLEM А. M. Khotinsky VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 1721.
Optimal choice of basic functions in a linear regression problem is studied. A singlestep algorithm is proposed along with its efficiency estimate valid for a finite measurement number. Conditions are formulated to provide, when met, a correct choice probability, as close to unity as desired. Applying the singlealgorithm to decay curve analysis is justified.

NONCONSERVATIVE DIFFERENCE SCHEME FOR EQUATIONS IN GAS DYNAMICS BASED ON THE GODUNOV SCHEME A. A. Charakhchian VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 2228.
A difference scheme for equations in gas dynamics is examined. The computation process is accomplished in two stages. The first stage performs the computation in Lagrangian variables, while in the second stage the conversion to an Eulerian mesh, possibly moving, takes place. In the first stage the conservative Godunov scheme is reduced to a form which directly yields an approximation for internal energy change equations. A new scheme is derived from the requirement that the coefficients in a resulting pressure interpolation formula should be nonnegative. This requirement importance is illustrated by nonspherical charge burst calculations. The scheme is used to implement a procedure for computing complicated gas dynamic flows. Several computational results for gas compression in solid cone targets are given. Solving this problem with a conservative scheme resulted in a considerable distorted solution.

APPLYING VARIATIONAL MECHANICS PRINCIPLES TO CONSTRUCTING TIMEDTISCRETE DIFFERENCE MODELS IN GAS DYNAMICS. USING H0L0N0MIC CONNECTIONS TO MAINTAIN DIFFERENCE LAGRANGIAN SCHEME QUALITY Yu. A. Bondarenko, O. A. Vinokurov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 2939.
Vie propose a method to stabilize a difference scheme for 2D gas dynamics calculations in Lagrangian variables based on using "good" mesh definition (for example, rectangular cell convexity condition) as a holomonic unidirectional connection to be accounted while constructing finitedifference schemes with a timediscrete variational technique. The difference schemes obtained conserve momentum and full energy. Numerical experiments using cell convexity condition showed a good method performance. An obvious method interpretation is presented which allows to use it in difference schemes obtained with other methods.

AN EXACT SOLUTION FOR A SYSTEM OF SPECTRAL RADIANT ENERGY TRANSPORT EQUATIONS A. A. Shestakov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 4043.
The paper considers exact continuous runningwavetype solutions of a spectral equation for radiationdriven energy transport in a system consisting of different materials. Runningwavetype exact solutions, discontinuous in temperature, for a joint system of energy and monochromatic radiation transport equations were derived earlier. This paper examines kinetic, P_{1}and diffusion approximations to a spectral radiation transport equation with respect to isotropic scat tering. The exact solutions obtained may be used to improve difference methods.

A "TRIANGULAR" VERSION OF THE METHOD FOR SOLVING A 2D SYSTEM OF RADIATION TRANSPORT EQUATIONS M. Yu. Kozmanov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 4448.
The paper formulates and proves the maximum principle for an implicit version of the DSnmethod applied to a 1D system of heat radiation equations. An iterative method for solving difference equations is proposed. For a 2D case, a "triangular" version of the DS_{n} method is presented (DSTmethod). As opposed to a "diamond" version, a conditional maximum principle is met for the DSTmethod. Parameterdependent schemes are developed using the maximum principle.

MODAMS TECHNIQUE FOR SOLVING AXISYMMETRIC STREAM PROBLEMS USING FINITE VOLUME METHOD S. N. Martyushov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 4956.
A technique called MODAMS is proposed which is based on a finite element method modification and is designed to solve stationary and nonstationary axisymmetric stream problems. The modification removes the uncertainty source from the original method which occurs in the vicinity of the symmetry axis. The modification purpose is to replace the integral representation of pressure terms with differential ones in pulse equations. Presented are the calculations of stationary and nonstationary flows near blunt bodies. The results are compared to those obtained by others.

SOLVING PISTON MOTION PROBLEM IN A HETEROGENEOUS MIXTURE OF TWO ISOTHERMAL GASES WITH RESPECT TO "JOINED MASS" EFFECTS O. V. Buryakov, V. K. Mustafin VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 5764.
Assuming component pressures to be locally equivalent we derive an exact solution for a piston motion problem in a mixture of two isothermal gases taking into account the "joined mass" effects. The solution for a piston pulled into a heterogeneous mixture is a combination of large discontinuities moving with different velocities and each having jumps in velocity and partial densities for both components. A rarefaction wave propagates through the medium when the piston is pulled out from a heterogeneous material. It is found that three types of solution structure are possible depending on the piston velocity and force interaction rates.

BEAM REFRACTION IN A FULLY IONIZED AXI SYMMETRIC PLASMA F. M. Abzaev VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 6571.
Analiticai and numerical methods were used to obtain formulae for the refraction angle of a beam propagating through a plasma with power and exponential density profile decrease. In small refraction angle region its dependence on electron density is represented by an exponential functional with an exponent close to unity and its value is inversely proportional to the squared incident radiation frequency.

NUMERICAL SIMULATION OF WAVE FRONT CONVERSION FOR ANDELSCHTAMMBRILLOUIN SCATTERING IN FOCUSED BEAMS Yu. F. Kiryanov, G. G. Kochemasov, N. V. Maslov, I. V. Shestakova VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 7277.
We describe the conversion of coordinate and function systems where HermitianGaussian mode envelope in laser radiation does not change in the propagation direction. Numerical integration uses a finitedifference scheme with improved dispersion properties. The accuracy of Stokes wave calculations is analyzed for a given pumping wave. For divergence slightly exceeding the limit 1 ≤ θ_{L} / θ_{D} ≤ 10 in focused beams wave front conversion accuracy is theoretically calculated in the presence of forced MandelschtammBri1louin scattering.

IVA PROGRAM FOR NUMERICAL SOLUTION OF INTEGRAL RADIATION TRANSPORT EQUATION IN A ROTATION CAVITY G. I. Skidan VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 7879.
This note summurizes the IVA program. Mathematical concepts, general structure and program capabilities are given. The program is designed to numerically solve an integral equation associated with timedependent radiation transfer through a low density material for a negligibly weak interaction with the radiation. Region boundaries delay, shadowing and movement are accounted. The program is written in PL/1 for the ES computers.

SAURS: A WIDE RANGE EQUATION OF STATE USING SPLINE APPROXIMATION N. M. Baryslieva, V. A. Zherebtsov, G. V. Sinko VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki. 1988. No 2. P. 8086.
We propose a method for transmitting heterogeneous data on environment properties to application programs using 2D smoothing splines. The suitability of this method to developing interpolation equations of state is discussed with respect to effect in a wide temperature and density range. Calculation results for aluminium are presented.

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