ALGEBRAIC METHOD FOR VISIBILITY ANGLES DETERMINATION

N.A. Dmitriev

, P.A. Perepelkin

VANT. Ser.: Mat. Mod. Fiz. Proc. 2000. No 4. P. 8-11.

A description is given of one of the algorithms for visibility areas determination in the computations of radiation propagation with integral equations method.

Yu.A. Bondarenko, Yu.V. Yanilkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2000. No 4. P. 12-25.

The techniques of closing differential equations of Lagrangian gas dynamics for multi-component medium in mixed cells are studied when a method of concentrations or similar methods are used for gas-dynamic calculations. Along with a much used assumption of component compressibility equality an assumption of component pressure equality is considered in detail. In addition to these two closing techniques a new technique is proposed, derived from the assumption of component pressure increments equality. As to accuracy the latter technique turned out to be not worse than the technique, based on assumption of total pressures equality, but it is more economical and much better than one, based on the assumption of component compressibility equality. Special attention is paid to explicit difference schemes with precalculated pressure, but main results can be transferred to other difference schemes.

Yu.A. Bondarenko, A.R. Shagalieva, Yu.V. Yanilkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2000. No 4. P. 26-34.

A new model of heat conduction for multi-component medium is proposed. This model does not suggest components temperature equality in mixed cells. The model is founded on accounting intragrid heat exchange between components in mixed cells which is performed in the same manner as that in the normal heat conduction. An essentially higher accuracy of the method proposed as compared with the method using an assumption of components temperature equality is shown.

L.F. Gudarenko, V.G. Kudelkin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2000. No 4. P. 35-44.

There are some well-known effective semiempirical and theoretical models, which allow constructing sufficiently precise equations of state (EOS). But no model has been constructed to date to create global EOS for computing thermodynamic functions (TDF) of substances within a wide range of density and temperature modification. A proposed means for constructing global EOS consists in "sewing" local EOS together using one of the mixture models. The possibilities of this means are exemplified by constructing the wide-range EOS for iron. The EOS chosen for sewing are the following: a semiempirical EOS which allows computing the area well studied in experiments using shock waves and EOS approximating the computations by a theoretical model of Thomas-Fermi and describing the area of super high pressures and specific energies. A detail description is given of the model, using for sewing local EOS and for computing TDF in a transient area. Diagrams are presented to illustrate the behavior of thermodynamic functions, computed both with wide-range EOS and with local EOS being sewn.
    The authors state their belief that the technique proposed for constructing wide-range EOS has the following advantage: it does not require any modifications of the EOS sewn. Local EOS are only supplemented with the algorithm and program for computing TDF in a transient domain. The example under consideration only uses 14 adjusting parameters, which comply with the requirement for minimum thermodynamic inconsistency and minimum TDF curvature in a transient domain.

A.V. Kvitchansky, S.N. Lebedev, V.N. Pisarev, O.V. Stryakhnina
VANT. Ser.: Mat. Mod. Fiz. Proc. 2000. No 4. P. 45-52.

One of the possible approaches to the problem of data preprocessing for the 2D continuum mechanic problem calculations is presented in this paper. SKAT program allows constructing and editing geometrical objects, generating grids according to different methods and describing grid's data.
    The authors aimed to make data presentation process simple, visual and the most fault tolerant. The code has a modern interface typical of windows applications. The visual representation of geometrical data is available with any grain size. The loading operation does not require a strict sequence of operations. Earlier input data can be looked through and edited in graphic and dialog mode. The correctness of user's actions is being tested persistently and if it is necessary the hints and comments are given in the process. Close control over editing operations allows preventing errors completely.

V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc. 2000. No 4. P. 53-57.

An integro-differential recursion operator has been determined for a one-dimensional linear uniform equation, describing the process of uniform liquid filtration in seamy-porous medium (filtration equations). It is shown how a basis can be constructed in the P space of the equation polynomial solutions using this operator. A matrix method for constructing exact solutions is proposed. With this method explicit formulae for polynomials, forming one of the possible P space bases have been gained.
    An integro-differential recursion operator can be used for constructing new exact solutions of a filtration equation, different from polynomial ones, and analytical solutions estimated - for testing numerical techniques and programs intended for computing filtration processes. The matrix method proposed in the paper can be used for constructing exact solutions of a wide range of evolution-type equations with constant coefficients, as well as for some many-dimensional equations, in particular, for two- and three-dimensional equations of diffusion and filtration.

M.E. Lebedeva, S.P. Santalov, S.V. Subbot
VANT. Ser.: Mat. Mod. Fiz. Proc. 2000. No 4. P. 58-60.

An algorithm is described for parallelization in computational domains for 2D transport problems. The efficiency of this algorithm is studied using computations performed on multi-processors with distributed memory.
    The algorithm is derived from the principle of geometrical decomposition of the original domain in subdomains and performance of separate computations by subdomains; mathematical (computational) domains are chosen for the latter. Computational domains exchange boundary conditions. Iterations by boundary conditions are combined with iterations by right-hand side of the transport equation.
    MPI protocol is chosen for exchanging messages between processors. The use of standard functions of synchronous and asynchronous transmissions allows transferring easily programs on different platforms of translators and operating systems, supporting MPI.