Issue N^{o} 3, 1993 
SATURN TECHNIQUE FOR NUMERICAL SOLUTION OF 3D TIMEDEPENDENT TRANSPORT EQUATION
A.V. Aleкseev, V.V. Evdokimov, R.M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 38.
A computational technique for numerical solution of 3D timedependent transport equation in classical cylinder system of coordinates on nonorthogonal spatial grids is formulated. The finitedifference approximation for the transport equation is developed according to the scheme with additional relations. The scheme formed is conservative, the corresponding difference transport operator is of the packageddelta form. For the case when the righthand side is known the costefficient method for solving the gridequation system based on the running computation idea is formulated. In the general case when the righthand side is unknown the suggested algorithm is used in combination with simple iteration method and simple iteration convergence acceleration methods. The method suggested allows an efficient parallelization in several directions, which is critical for multiprocessor implementation.

CONTACT SYMMETRIES AND CONSERVATION LAWS FOR SOME EQUATIONS IN ISENTROPIC GAS DYNAMICS V.E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 915.
A sufficient point transformation condition is derived for contact symmetries within a special class of secondorder quasilinear equations with three independent variables. A simple criterion is found for variational nature of symmetries for MongeAmper equations and second order quasilinear equations that are EulerLagraage equations for a variational problem. The results obtained allowed to evaluate the contact symmetries and conservation laws for equations that result from the systems describing vortexfree steadystate isentropic 3D and 2D unsteady plane and symmetric flows of polytropic gas. Group classification is made for these equations regarding к parameter that represents the gas adiabatic index for к > 1.

KINETIC THEORY OF ION MOTION THROUGH A SOLID WITH RESPECT TO TIME DEPENDENCE G.N. Pоtetуunко VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 1621.
The problem of heavy charged secondary particle motion is considered within the kinetic theory of ion motion through a solid, based on Boltzmann equation in nonstationary formulation; the particles are generated in a plane semiinfinite target as a result of some primary radiation. The consideration is oriented to energies corresponding to the maximum of material electron deceleration level or to those which are somewhat lower where the electron component dominates the deceleration process.

HYPERBOLIC FORM OF ELASTICPLASTIC FLOW EQUATIONS T.A. Bychenkov VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 2225.
Correctness (hyperbolic nature) of elasticplastic medium model with respect to friability using an associated flow law is studied. The paper gives mathematically correct form of elastic plastic dynamic equations for isotropic medium deformation which allows to take into account shearing stress relaxation kinetics, dilatancy, anisotropic cracking. The explicit difference scheme stability conditions according to von Neumann conditions are obtained.

NUMERICAL SIMULATION OF SHOCK WAVE MOTION THROUGH SHIELDING LATTICES V.Yu. Meltzas, G.F. Portnyagina, V.F. Sоlоviоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 2631.
Godunov method was used to develop a computational technique for gas flows through fixed latticetype shields allowing severed, times altenuation of shock wave intensities. A model of "frozen" gas suspension (the lattice nodes are assumed to be fixed, gas/node heat exchange is neglected), the lattice volume content and perforation degree are Included. 1D computation results are given for shock propagation through the duet medium, across the layer of meshes differing in boundary conditions and 2D computation data on the attenuation of explosive effect on cylinder vessel walls where lattice type shields are placed.

THE WEAKNONLINEAR WAVE FRONTS STRUCTURE IN A DIFFERENCE SOLUTION V.A. Svidinsку VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 3240.
Application of conservative difference method for the problem of propagation of a steady square wave is considered. It Is analytically shown for waves with front speed Independent on the discontinuities intensity that Godunov type monotonized schemes must give local disbalance of conservative variables within the wave front. Satisfaction of total balance in the computation region results in emanation of side waves by the basic front that distorts the Initial wave configuration. Calculation remits for model problems are presented: the gasdynamic contact discontinuity and the wave which simulates a transverse wave in a thread.

USING THE MODEL OF A THIN DEFORMING SHELL FOR GENERATION AND ANALYSIS OF 2D GAS DYNAMICS SCHEMES G.P. Simоnоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 4146.
Some numerical algorithms are studied for thin liquid behavior in terms of spherical motion symmetry conservation on a 2D mesh where it must take place as given bу the problem physics. Sane similar features are indicated for rotational shell schemes generation within the thin shell model and continuum approximation. These were used to generate a scheme for 2D Lagrange gets dynamics with the scheme retaining the spherical motion symmetry even on angular nonuniform mesh (when determining the accelerations) and fully conservative in the case of sphericalsymmetry motion on a 2D uniform mesh. Initially the accelerations are at the centers of all sides and further they are overaged to the nodes.

UNCONDITIONALLY STABLE DIFFERENCE SCHEMES FOR RADIANT ENERGY TRANSPORT IN TWO DIFFUSION AND P_{1} APPROXIMATIONS A.A. Sheatakоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 4753.
The paper formulates and proves the maximum/minimum principle for radiant energy transport on P_{1} approximation using Romb difference scheme. Unconditionally stable difference schemes are studied in parameter space of the twoparameter Romb family. It is shown that unconditionally stable difference schemes in grid norms of С and L_{2} spaces оan be selected from the Romb family.

COMPUTATIONAL PHOTONS METHOD. 1. APPROXIMATE EQUATIONS, COMPUTATIONAL SCHEME E.G. Vasina, Yu.A. Dementiev, I.D. Sоfrоnov VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 5458.
The method is intended for 3D nonstationary radiant energy transport calculations including isentropic scattering, absorption and equilibrium radiation. Strict restrictions are introduced for the fixed timestep size and typical photon path lengths within the fixed all of a spatial grid. These allow to oatoh physical process and mesh distributions. The well known physical relations (Bouguer and Kirckhoff laws. Shauder principle, Lambert´s cosine law for surface radiation) are used to derive approximate equations. The approximation accuracy is studied for the corresponding integrodlfferential equations. The scheme and approximate solution properties are discussed.

XRAY RANGE TUNGSTEN TARGET BREMSSTRAHLUNG. THE FULL YIELD E.N. Donskoy VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 5963.
A method is discribed for calculating the bremsstrahlung. Data for the full backword and forward yield for bremsstrahlung and characteristic radiation are given as well as for electrons emitted from the tungsten target of optimal thickness. The incident electron energy range varies from 100 to 600 keV.

SOME DIFFERENCE ALGORITHMS FOR NUMERICAL SIMULATIOH OF IMPURITY TRANSFER THROUGH ATMOSPHERE V.A. Andrоnоv, A.N. Razin VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 6469.
The paper is devoted to the description of some difference algorithms for numerical simulation of environment problems. The model includes HavierStokes equations for background wind components. The impurity transfer is modeled with diffusion and convection equation. Discrete approximation generation and numerical method selection are discussed. Some computational results are given.

GRACE: A PROGRAM PACKAGE FOR SIMULATION OF THREEDIMENSIONAL GASDYNAMIC PROBLEMS ON PARALLEL COMPUTERS A.S. Shvedоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 7076.
Multizone procedure for solution of spatial inltlalboundary problems for the equations of gas dynamics in domains with moving boundaries is described. A method for creation of programs for parallel computers based on those for sequential computers is suggested. Realization of this method for the gasdynamic procedure is shown.

EGAK CODES. ALGORITHM FOR MATERIAL PRESSURE ALIGNMENT IN MIXED CELLS G.V. Zhаrоva, Yu.V. Yanilкin VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 7781.
The paper describes the algorithm for material pressure alignment in mixed cells. The algorithm was developed within EGAK complex for 2D gas dynamic flow calculations in Eulerian variables. Methodical results are presented.

BASIC ACCESS PROCEDURE PACKAGE FOR TELEPROCESSING ON ES COMPUTER V.S. Kholushkin VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 8289.
A basic access procedure package for teleprocessing on ES computer is described. The basic access procedure package is considered to be a software tool for multiterminal and multifunctional interactive systems on ES computers.

ON CODE DEVELOPMENT PRACTICES FOR AXISYMMETRIC GASDYNAMIC FLOW CALCULATIONS ON SIMD ARCHITECTURES EXAMPLIFIED BY PS2100 V.A. Andrоnоv, M.V. Artamonov, S.M. Bakhrakh, S.V. Veliсhко, S.P. Egоrshin, A.A. Kuznechikhia, A.N. Razin, V.F. Spiridonov, Yu.G. Fedоrоva VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 9096.
The paper presents the implementation practices for axisymmetric gasdynamic flows in heterogeneous medium; the calculations run on STMD PS2100 computer. The LEGAK method was previously implemented on BESM6 and ES1G66. When porting the method to a SIMD multiprocessor only those modifications were made that are needed for a more efficient algorithm parallelization. The main algorithms are given and the organizational code structure is presented for SIMD architectures.

THE ROLE OF DISSIPATIVE PROCESSES FOR CYLINDER SHELLS IMPLOSION V.A. Ogorodnikov, A.A. Sadovoy, V.N. Sofronov, T.S. Tyunkin VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 97101.
Experimental and theoretical data are presented for burst driven implosion of cylindrical shells in the deformation rate range varying from 10^{3} to 10^{6} s^{1}.

THERMONUCLEAR GAIN OF CYLINDER DTTARGET FOR HEAVYION FUSION WITH MAGNETIC THERMAL INSULATION E.A. Zabrodina, M.D. Churasоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 102104.
Implosion and detonation combustion of cylinder heavyion fusion DTtarget are considered. The thermonuclear gain, G = 16, is calculated with energy input scale E_{0} ≈ 100 MJ and thermal insulation (H_{0,z} ≈ 10^{5} oersted). Certain estimates are also obtained from 1D gasdynamic calculations and hydraulic approximation.

THERMONUCLEAR DETONATION IN MULTILAYER MAGNETOHYDRODYNAMIC TARGETS FOR HEAVYION FUSION M.V. Sokolovsky, M.D. Churazоv VANT. Ser.: Mat. Mod. Fiz. Proc. 1993. No 3. P. 105110.
A hydraulic approximation technique is used to consider the detonation burning of a D_{0,9}^{3}He_{0,1} cord with ρ R = 0,05 g/cm^{2} in a multilayer magnetohydrodynamic target. Magnetic heat insulation, magnetic confinement and inertial shell properties are used to ensure the burning. The heavyion driver is assumed to be able to create necessary Initial conditions for a desired burning mode. The energy contribution scale is E_{0}~10+100 MJ. This work is an, introduction to more strict and more detailed studies of magnetohydrodynamic heavy ion fusion target capabilities for thermonuclear burning.

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