KORAT 3-D A MATHEMATICAL METHOD FOR NUMERICAL SOLUTION OF 3-D 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. 3-10.

      A numerical method for 3-D equation of neutron diffusion on regular and irregular spatial grids composed of convex quadrangles is presented.
      The method is implemented in KORAT 3-D program within SATURN complex and intended for calculation of 3-D stationary and time-dependent problems of reactor physics characterized by complex geometry. Some comparative computational results for 2-D and 3-D four group test problems for reactor SNR-300 are given.

G.P. Prokopov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 11-17.

      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.

A.F. Sidorov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 18-22.

      Classes of exact solutions were derived for Euler-Ostrogradsky’s equations, corresponding to non-linear 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 8-th order for which the problem of Cauchy is posed. In a specific symmetric case the system is reduced to one non-linear equation of the 4-th 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.

O.A. Voronova, R.Ya. Gatilova, T.G. Ivchenko, M.S. Samigulin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 23-32.

      RATEG program is intended for numerical simulation of nonstationary thermohydraulic processes in branching nets with two-phase coolant. The description of the models used in the program is presented: net elements (pumps, branchings, local resistences); flow models for vapor-fluid coolant and heat transfer in heat elements and numerical solution methods. Two- velocity, two-temperature 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 semi-implicit one-step difference scheme, in which the time-step is not restricted by resistence conditions. Heat transfer in heat elements is calculated in 1-D heat, conduction approximation. The program capabilities allow to use it for simulation of loss-of-coolant accidents in nuclear power systems.

O.A. Voronova, R.Ya. Gatilova. T.G. Ivchenko, M.S.Samigulin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 33-38.

      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 loss-of-coolant, 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 WWER-440 reactor circuit is performed in simulating of real systems for demonstration of program capabilities.

V.B. Barakhnin, G.S. Khakimzyanov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 39-44.

      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 non-linearly-dispersive shallow water models. Calculation results of test problems on wave run-up on the walls of reservoirs and water tanks are discussed.

V.P. Zakharov, E.P. Shurina
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 45-52.

      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.

S.M. Bakhrakh, N.P. Kovalev, T.A. Toropova
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 53-57.

      The properties and behavior of the penetration process in elastic-plastic 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 = V₀/C₀ and strength yield . Some problems are discussed concerning calculations of elastic-plastic flows in multicomponent, media.

T.A. Toropova, Yu.V. Yanilkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 58-66.

      A calculational method for 2-D flows in multicomponent medium with respect to strength properties of materials, implemented by EGAK complex is considered. Rigid-plastic and elastic-plastic models are used. Computational results are compared with those obtained by other methods.

E.A. Zabrodina, M.D. Churazov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 67-70.

      Compression and heating of a two-dimensional 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 PBFA-II facility experiment (SNL, USA). The heat distribution in DT plasma and the end wall effect were studied in the one-temperature approximation.

A.L. Stadnick, A.A. Shanin, Yu.V. Yanilkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 71-78.

      A finite-difference scheme in Eulerian variables, implemented within TRACK program complex and designed for calculations of 3-D 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.

Yu.V. Yanilkin, V.V. Nikiforov, G.V. Zharova
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 79-84.

      kε-model of turbulent mixing in 2-D compressible flows is described. The model is implemented in Lagrangian-Eulerian 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.

V.N. Rodigin
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 85-87.

      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 2-D 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.

A.A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc. 1994. No 4. P. 88-89.

      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 non-equilibrium radiation transfer problems with Compton’s dissipation, and in some other problems. Three Fokker-Plank equation solutions are considered in the paper which have been obtained for non-equilibrium case with specially selected coefficients.