TWO-DIMENSIONAL ESTIMATE OF EXPLOSION IN WATER-FILLED VOLUME OF CUT-OFF SPHERE FORM

V. B. Adamsky, A. V. Balabanov, L. V. Nesterenko, I. D. Sofronov
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 3-6.

      A number of papers stated that during charge explosion in fluid a vapour-gas bubble formed at explosion point may attract to bottom.
      The paper considers investigation by numerical calculation of the physics of the phenomenon. The numerical test was performed with a program for solving two-dimensional gas dynamics problems on an irregular grid based on the "Meduza” technique.
      Dynamic parameters of matter movement in the volume are obtained for various times. As the computation showed, a vapour-gas bubble formed at explosion attracts to bottom and turns into torus extending in the spherical volume surface direction.

N. M. Barysheva, A. A. Kosorukova
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 7-12.

      Within the framework of self-consistent field model some multicomponent matter thermodynamic functions are estimated on the basis of varions conditions of thermodynamic equllibium. The assumed formulations of equilibrium conditions are shown to yield the same results, if the thermodynamic functions of all mixture components are obtained with this model. Influence of shell effects for matters of nearly the same atomic numbers and component concentrations, as well as for matters, in which there is an element of predominant atomic number and concetration, is illustrated by comparison with Thomas-Fermi model calculations. Comparison with statistic shell model data is made as well.

G. G. Solovyev, A. V. Suchkov
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 13-15.

      Complex computational arrangement in material resources distribution schedule applications and dependence of personnel number on volume of implemented computations led to the need to automate them. The suggested system consists of programs constructing computer jobs on the basis of data analysis and computing situation. The system allows to obtain statistical information and computational state data in automized mode, to increase amount of computations without enlargement of personnel number, as well as simplifies computing run technique. Job control language is extended with including syntax constructions close to that of PL/1 language. It allows to arrange the distribution schedule application software in a sufficiently simple single approach.

G. A. Goncharov, V. P. Gorelov, G. G. Farafontov, V. Kh. Khoruzhiy
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 16-23.

      Results of comparing various isotropizations of group scattering constants are given. A special attention is paid to studying effects of arising negative transport constants. A simple way to overcome negativity is proposed. Computational results are supplied allowing to formulate most desirable way of isotropization for fast neutron transfer applications.

V. V. Basharov
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 24-28.

      A simple tranfer equation in an arbitrary coordinate system specified by a differential equation for transfer elocity is considered.
      Questions of transformation uniqueness and transfer equation evolution in an arbitrary coordinate system are discussed. Two theorems are proved approving the former question and providing sufficient conditions on equation coefficients for transfer velocity maintaining velocity for the latter one.

O. M. Velichkho
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 29-33.

      OS SVS has beep implemented on multiprocessor system SVS since 1986, allowing users to parallel problem runs. These OS SVS capabilities were used for parallel computing in the routine of nonstat ionary space fields of flows near blunted bodies with finite difference Godunov method. Sufficienty large volume of virtual memory embodied computing blocks and problem data and thereby allowed to refuse their dynamic loading during step count. The task is represented as a control and several computation processes. The computation processes compute gas dynamics flow parameters simultaneously for several workspaces. The control process performs coordinating functions. Interprocessor information communications are handled by means of semaphores and events. Timings showed that for four processor the total CPU time taken by a task per astronomical time unit amounts to 3,8 units.

N. P. Pleteneva, R. M. Shagaliyev
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 34-41.

      For a two-dimensional transfer equation on quadrangular special grids a conservative finite-difference scheme with additional relations is derived in which grid values of the desired function are evaluated simultaneously, at vertexes (nodes), edges and centers of quadrangular grid cells. The difference transfer operator is of triangular structure. Results of numerical study are supplied showing second-order accurate convergence of the grid solution to the accurate one both on rectangular and on sufficiently non-orthogonal space grids. The scheme is extended to transfer equation numerical solution on grids of arbitrary convex polygonals.

Gorelov V.P., Travin V.V.
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 42-48.

      A complete solution of P_2N-1-approximation of neutron transfer equation is obtained for the central region of a sphere containing an isotropic source at the origin of coordinates. The involved unknown coefficients are suggested to evaluate with the Adamskaya-Godunov method. Divergence of r^-2 even components of the desired vector, divergence of r^-1 odd components are found as compared to known solution, the logarithmic singularity is taken into account.

I. A. Adamskaya
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 49-55.

      Applicability of the special solution orthogonal sweeping method (the Godunov method) is justified for the solution of spherical harmonics differential equations for the one-dimensional stationary kinetic equation in multigroup approximation. Boundary conditions of the probiem are proved to allow to derive a full set of linear independent vectors needed to implement the method considered also in the case of multigroup approximation of the kinetic equation.

A. A. Gadzhiev, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 56-65.

      Iteration speeding-up methods are considered for combined solution of energy and radiation transfer equations in multigroup P₁-approximation witn the "ROMB" method. Speeding-up of iteration convergency is achieved by means of introduction of additional stage at which temperature is computed with a certain simplified model of transfer equation. The speeding-up methods are based on either Jacobi-type iterations or spectrum-averaging method. Extension of Jacobi-type iterations to two-point-type differnce schemes is suggested, and a new algorithm of iteration convergency speeding-up is derived for the averaging method. The methods considered may be extended to other transfer equation approximations and to more complex geometries.

A. D. Gadzhiev, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 66-70.

      Solution of radiation transfer equation in multigroup P₁-approximation combined with the energy equation is considered. The difference technique is based on the two-point scheme "ROMB", possessing a number of advantages, such as single difference cell approximation, single computation of absorbtion coefficient in cell per iteration, simplicity of formulating boundary conditions, extentionabi1ity to many dimensions. The difference scheme includes parameters, the appropriate choice of which allows to combine second-order accuracy and monotonicity in optically dense media.Solution of radiation transfer equation in multigroup P;-approximation combined with the energy equation is considered. The difference technique is based on the two-point scheme "ROMB", possessing a number of advantages, such as single difference cell approximation, single computation of absorbtion coefficient in cell per iteration, simplicity of formulating boundary conditions, extentionabi1ity to many dimensions. The difference scheme includes parameters, the appropriate choice of which allows to combine second-order accuracy and monotonicity in optically dense media.

N. Ya. Moiseyev
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 71-74.

      It is suggested to use intermediate values found at cell edges from the solution of the Riemann problem in the difference scheme derived in arbitrary curvilinear coordinates on the basis of the Godunov method when approximating volume Integrals. This approach to approximating integrals allows to match times at the choice of intermediate values of gas dynamics quantities in the left and right parts of difference equations.
      Computations of model problems showed higher accuracy of the results and maintaining movement symmetry at approximating geometry with circumferences or straight lines using difference meshes close to uniform.

O. B. Gushchin, M. M. Savitsky, Yu. V. Feodoritov
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 75-77.

      A software system has been developed for local uniform star-type multicomputing systems on the basis of the PDP-11-type computers. The host computer is controlled by the NTS operating system. NTS communications are used allowing the speed gain and the lower communication overheads in the system.

O. I. Butnev, A. L. Komarova, A. M. Mikiychuk, V. A. Novichikhin
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 78-83.

      The FORPOST automatized system run on ES computer and designed for development, employment, and modifications of FORTRAN-IV and FORTRAN-Dubna programs is described. Problems of organization of the system and its structure are considered. Tool set of the system frame is described.

M. M. Basko, V. S. Imshennik, D. G. Koshkaryev, M. D. Churazov, K. B. Sherstnev
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 84-97.

      The current state of work on the Herational heavy-ion fusion and the principal physical aspects of this field of controlled thermonuclear fusion are described. Optimization problems are considered on the example of spherically-symmetrie target with tritium-deuterium fuel. Possibility of deriving deuterium targets of iterational haavy-ion fusion is investigated. A design of cylindrical deuterium target with magnetic thermal isolation and deuterium-fuel combustion detonation mode is suggested.

G. P. Prokopov
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 98-108.

      In view of a great number of papers on constructing algorithms for deriving difference grids there is a need of formulating unified criteria for checking grid quality and deriving test problems for approbation and comparison of various techniques. The paper deals with discussion of these questions and contains some concrete proposals as for their practical realization.

B. L. Voronin
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 109-111.

      On the basis of the well-known statement that the Volterra operator with limited nucleus is a compressing transformation, the compressibility condition is formulated for the general-type integral operator with asymmetric nucleus.

A. S. Sukhikh
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. No 3. P. 111-112.

      On the basis of the well-known statement that the Volterra operator with limited nucleus is a compressing transformation, the compressibility condition is formulated for the general-type integral operator with asymmetric nucleus.