Issue N^{o} 4, 1994 
KORAT 3D A MATHEMATICAL METHOD FOR NUMERICAL SOLUTION OF 3D GROUP PROBLEMS ON NEUTRON DIFFUSION ON REGULAR AND IRREGULAR SPATIAL GRIDS
L.P. Fedotova, R.M. Shagaliyev VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 310.
A numerical method for 3D equation of neutron diffusion on regular and irregular spatial grids composed of convex quadrangles is presented. The method is implemented in KORAT 3D program within SATURN complex and intended for calculation of 3D stationary and timedependent problems of reactor physics characterized by complex geometry. Some comparative computational results for 2D and 3D four group test problems for reactor SNR300 are given.

THE LOCAL ALGORITHMS FOR SMOOTH CURVE REPRODUCTION AND FUNCTION INTERPOLATION G.P. Prokopov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 1117.
The algorithms for reproduction of a flat curve, specified by reference point sequence, allowing to obtain parameter representation of smoothness classes Cl and C2 are developed. Only information about values of neighbouring element derivatives in integration points is used when obtaining the representation for a curve element connecting two reference points. After their specification the element calculation becomes independent.

EXAMPLES OF EXACT CONSTRUCTION OF GEOMETRICALLY OPTIMAL TWODIMENSIONAL GRIDS A.F. Sidorov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 1822.
Classes of exact solutions were derived for EulerOstrogradsky’s equations, corresponding to nonlinear combined functional, with the help of which regular curvilinear grids, close to uniform and ortogonal ones are constructed. In general case, the above mentioned classes are described by the system of ordinary differential equations of the 8th order for which the problem of Cauchy is posed. In a specific symmetric case the system is reduced to one nonlinear equation of the 4th order, which has been integrated to the end in quadratures. The influence of the weight in terms of the functional responsible for orthoganality on quality of grids has been investigated. The results of numerical calculations are given. The constructed solutions may, for example, serve as tests for investigation of different numerical methods for grid generation.

RATEG: A PROGRAM FOR NUMERICAL SIMULATION OF NONSTATIONARY THERMOHYDRAULICS OF NETS WITH TWOPHASE COOLANT. CALCULATIONAL MODEL AND NUMERICAL SOLUTION METHOD O.A. Voronova, R.Ya. Gatilova, T.G. Ivchenko, M.S. Samigulin VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 2332.
RATEG program is intended for numerical simulation of nonstationary thermohydraulic processes in branching nets with twophase coolant. The description of the models used in the program is presented: net elements (pumps, branchings, local resistences); flow models for vaporfluid coolant and heat transfer in heat elements and numerical solution methods. Two velocity, twotemperature model (2V2T) of coolant flow allows to take into account velocity and temperature nonequilibrium of flow structure, the mode of heat exchange with channel walls and so on. The difference equation system for coolant flow is approximated by linear semiimplicit onestep difference scheme, in which the timestep is not restricted by resistence conditions. Heat transfer in heat elements is calculated in 1D heat, conduction approximation. The program capabilities allow to use it for simulation of lossofcoolant accidents in nuclear power systems.

RATEG: A PROGRAM FOR NUMERICAL SIMULATION OF NON STATIONARY THERMOHYDRAULICS OF NETS WITH TWOPHASE COOLANT. TEST CALCULATIONS O.A. Voronova, R.Ya. Gatilova. T.G. Ivchenko, M.S.Samigulin VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 3338.
The test results are presented for RATEG program intended for numerical simulation of nonstationary flows in branching thernriohydraulic nets, particularly in circulation circuits of nuclear power systems. The simulation is performed for phenomena characteristic of lossofcoolant, accidents: outflow of boiling fluid at depressurization, chocking and turning over of a flow in the vertical channel; flows with heat exchange crisis in the heated channel. The comparison of calculational and experimental data proves acceptability of program accuracy for some applications in describing of such flows. The calculation of stationary mode of WWER440 reactor circuit is performed in simulating of real systems for demonstration of program capabilities.

APPLICATION OF DYNAMIC ADAPTIVE GRIDS TO NUMERICAL CALCULATION OF SHALLOW WATER THEORY PROBLEMS V.B. Barakhnin, G.S. Khakimzyanov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 3944.
The advantage of moving adaptive grids constructed by equidistrilnition method over stationary grids is shown for numerical solution of shallow water equations. Difference schemes on adaptive grids are presented for calculation of fluid flows with surface waves within nonlinear and nonlinearlydispersive shallow water models. Calculation results of test problems on wave runup on the walls of reservoirs and water tanks are discussed.

ON ONE NUMERICAL INTEGRATION ALGORITHM OF NAVIER STOKES EQUATION SYSTEM V.P. Zakharov, E.P. Shurina VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 4552.
Channels of various technical device cooling systems are characterized by the presence of curvilinear areas differently oriented relative to the external mass force (gravitational, centrifugal). The need of studying hydraulic, and heat transfer parameters of these areas encourages algorithm and program development for solving equation systems which describe hydrodynamic processes and are represented in an arbitrary orthogonal curvilinear coordinate system. This work is performed in order to make a comparative analysis of convergence iteration rate process based on various linearization systems, to investigate acceptability of solutions obtained using degenerate approximation scheme, and to develop a program basis for continua flow simulation in curvilinear channels in fields of external mass force action.

A NUMERICAL STUDY OF THE PROCESS OF NONDERFORMABLE CYLINDRICAL BODIES PENETRATION INTO ELASTICPLASTIC MEDIUM S.M. Bakhrakh, N.P. Kovalev, T.A. Toropova VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 5357.
The properties and behavior of the penetration process in elasticplastic medium of the absolute rigid cylindrical bodies are studied by numerical simulation. Resistance force, stress distribution along cylinder end, cavity position and so on are studied depending on basic dimensionless parameters  Mach number M = V_{0}/C_{0} and strength yield . Some problems are discussed concerning calculations of elasticplastic flows in multicomponent, media.

A CALCULATIONAL METHOD FOR 2D FLOWS IN MULTICOMPONENT MEDIUM WITH ACCOUNT OF STRENGTH MATERIAL PROPERTIES T.A. Toropova, Yu.V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 5866.
A calculational method for 2D flows in multicomponent medium with respect to strength properties of materials, implemented by EGAK complex is considered. Rigidplastic and elasticplastic models are used. Computational results are compared with those obtained by other methods.

CYLINDR1C TARGET WITH MAGNETIC HEAT INSULATION FOR AN EXPERIMENT WITH ENERGY CONTRIBUTION E = 87,4 kJ/cm E.A. Zabrodina, M.D. Churazov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 6770.
Compression and heating of a twodimensional cylindrically symmetric target are considered with the magnetic insulation that is supposed. Target parameters and the form of energy contribution was chosen in conformity with the conditions of the PBFAII facility experiment (SNL, USA). The heat distribution in DT plasma and the end wall effect were studied in the onetemperature approximation.

TRACK: EULERIAN METHOD FOR 3D GASDYNAMIC FLOWS CALCULATIONS IN MULTICOMPONENT MEDIUM A.L. Stadnick, A.A. Shanin, Yu.V. Yanilkin VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 7178.
A finitedifference scheme in Eulerian variables, implemented within TRACK program complex and designed for calculations of 3D gasdynamic flows in multicomponent medium is given. The calculated problem classes are characterized by presence of large deformations up to flow conversion to turbulized mode. A concentration method is used to confine and prevent the computational diffusion of contact boundaries. The computational results for some problems are given.

TWOEQUATION MODEL AND CALCULATIONAL METHOD FOR TURBULENT MIXING IN 2D COMPRESSIBLE FLOWS Yu.V. Yanilkin, V.V. Nikiforov, G.V. Zharova VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 7984.
kεmodel of turbulent mixing in 2D compressible flows is described. The model is implemented in LagrangianEulerian gasdynamic method used to calculate flows with large strains. The above method can be used also to simulate turbulent mixing due to combined effect of gravitational and tangential instabilities. Computational results are compared with experimental and other methodical data.

ANALYTICAL SOLUTION OF THE PROBLEM OF DETONATION FRONT MOTION IN AXISYMMETRICAL INERT CORE EXPLOSIVE SYSTEMS V.N. Rodigin VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 8587.
The problem is solved in acoustic’ approximation based on constant explosive detonation rate condition for the systems with the convex outer surface and the inner surface in the shape of rotation ellipsoid. The solution may be used to control 2D gasdynamics problem computations as well as to generate an orthogonal computation grid, for which numerical computation of detonation front at each time step is not needed.

PRECISE SOLUTIONS OF FOKKERPLANK EQUATION A.A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 8889.
The paper is devoted to the problem of Fokker—Plank equation analytical solutions. This equation appears under consideration of quick electron thermalization in plasma, in nonequilibrium radiation transfer problems with Compton’s dissipation, and in some other problems. Three FokkerPlank equation solutions are considered in the paper which have been obtained for nonequilibrium case with specially selected coefficients.

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