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Issue N^{o} 2, 2001  A METHOD FOR FINEGRAIN PARALLELIZATION OF 2D AND 3D TRANSPORT PROBLEMS ON NONORTHOGONAL GRIDS
A.V. Alekseev, A.A. Nuzhdin, R.M. Shagaliev VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 310.
A method is proposed for finegrain parallelization of numerical solution of 2D transport equation, intended for using multiprocessor with distributed memory allowing computations on a number of computers up to 100 and more. The method is based on the principle of the geometry decomposition of the original system to subdomains (paradomains). The division into paradomains is performed regularly by rows and columns so that data amount to be equal. In general case such a division results in a process topology in the form of 2D grid (by rows and columns). As this takes place, each processor stores data for a special paradomain but not for the whole problem. Each paradomain for a current direction is solved with internal boundary conditions computed at a current iteration, which allows holding solution accuracy and preventing total iteration amount increase as compared with a sequential technique. The idle time of processors is minimized through their loading with useful additional computational work, that is computation of intermediate coefficients. Later grid values of a particle flow function are expressed through these coefficients. For interprocessor messaging the library for MPI parallel coding interface (Message Passing Interface) is used. The results of numerical studies of parallelization efficiency for the method developed are presented. Some extension of this method to the parallelizing 3D transport problems is given.
 APPLICATION OF keMODEL FOR THE DESCRIPTION OF AN ATMOSPHERIC SURFACE LAYER M.G. Anuchin, V.E. Neuvazhayev, I.E. Parshukov VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 1127.
The problem on determination of nondimensional characteristics of turbulent flow in atmospheric surface layer is considered within kemodel. keequations and their singular points are investigated. A mathematical program for calculating characteristics of turbulent flow in the surface atmospheric layer is developed. From the set of integral curves those are chosen which correspond to the solution of a formulated task and ensure the satisfactory experiments description. Here the basic model constants are chosen according to the conventional criteria. At the same time it is shown that the parameter C_{q} corresponding to convection source term of an eequation should be chosen depending on stability conditions. The best agreement with experimental results is reached if C_{q} = 0 for steady stratification and C_{q} 0 for unstable stratification. By a numerical choice of value C_{q} and factor of turbulent diffusion the quite satisfactory description of experimental observations known as analytical interpolational dependencies is received.
 ATTENUATION FACTOR METHOD Yu. A. Dement'ev, E.A. Karpovtsev, I.A. Narozhnaya, V.A. Novichikhin, E.V. Morozova, E.N. Tikhomirova VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 2836.
A new approach to solving timedependent problems of radiant energy transport is developed with the supposition of quasistationary state of boundary surface and paths of substance radiation, absorption and scattering. Attenuation factor method is a method of a consistent description of a radiant energy straightforward transport and distribution function of released energy. The paper under consideration considers isotropic scattering, absorption and equilibrium proper radiation within grey matter approximation. The attenuation factors are calculated by double integrals based on Peierls equation. The possibility exists of their calculation with assured accuracy. A new scheme is successfully tested by solving the simplest problems of stationary and timedependent transport within a grey matter approximation, possessing an analytical solution or verified numerical results.
 A STUDY OF THE INTERACTION BETWEEN A FLAT SHOCK WAVE AND A HEATED GAS LAYER Yu.M. Kovalev, A.Yu. Cheremokhov VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 3741.
The paper considers the results of numerical simulation of the problem on the shock wave propagation in the nonuniformly heated medium: a flat shock wave interacts with a flat gas layer of reduced density, located at some distance away from a solid surface. A structure of an arising gasdynamic flow is studied and its characteristic parameters are estimated. It is shown, that the existence of a gas interlayer with normal conditions between a solid surface and a heated gas layer substantially complicates the flow pattern  two triple points are formed, the rate of the altitude growth for the upper triple point and the relative rate of a portent "growing" out of the basic shock wave are reduced, vortex formations are formed and evolve.
 SOMETHING MORE OF SCHEME PROPERTIES FOR A SPHERICALSYMMETRIC TRANSPORT EQUATION S.V. Mzhachikh, E.V. Groshev, V.F. Yudintsev VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 4248.
A trialanderror technique is stated for scheme parameters, based on the difference forms equivalence for two moment transport equations. From the technique follows one known efficient algorithm for calculating angular parameters as well as a type of difference quasidiffusion equation coefficients, agreed with the scheme.
 A SHOCKFREE STRONG COMPRESSION OF GAS WITH ACTUAL EQUATIONS OF STATE S.A. Yagupov VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 4958.
An equation of state for actual gas is considered. The paper sets two characteristic Cauchy problems, which sequential solution describes a shockfree gas compression with the above actual equation of state. The existence of a local analytical solution for these problems in the vicinity of a background flow is proved. To do this the above problems are limited to a type for which Bautin S.P. has proved the analog of Kovalevskaya theorem. The analysis of zero factors, which set the solution of the first problem allows to conclude that this actual gas can be compressed shockfree up to the finite density only. An isentrope is calculated for this actual equation of state, which shows that the equation of state being considered not only meets physical requirements, but also passes the property like that one revealed under zero factors analysis.
 IMPLEMENTING AND STUDYING EFFICIENCY OF GASDYNAMIC AND HEATCONDUCTION PROGRAMS PARALLELIZATION IN MIMOZA COMPLEX A.V. Babanov, O.A. Vinokurov, L.F. Potapkina VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 5962.
The paper considers some techniques for parallelizing programs for explicit and implicit schemes. The explicit scheme is used for solving gasdynamic equations, the implicit one  for solving heatconduction equations. The parallelization algorithm is based on the principle of geometric decomposition. The denumerable domain is divided into an arbitrary number of fragments computed on different processors. The messaging library, which comes up to MPI standards, is used for performing communication operations in programs. The parallel programs precision is estimated. The efficiency of programs parallelization on multiprocessor Computational Systems with distributed memory is studied.
 EXACT SOLUTIONS OF AN EQUATION SYSTEM FOR ISOTROPIC RADIATION AND ENERGY TRANSPORT IN THE CYLINDER SYMMETRIC GEOMETRY A.S. Vershinskaya, V.Yu. Gusev, V.V. Zavyalov VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 6371.
Exact solutions of the traveling wave type are constructed for nonlinear integrodifferential equation system of isotropic timedependent transport of radiation and energy in the cylinder symmetric geometry with suitably selected absorption and scattering factors both for a "grey matter" approximation and for a spectral case. In so doing the scattering factor is assumed to be proportional to the absorption factor which is in its turn completely estimated by logarithmic derivative of equilibrium density with respect to the selfsimilar variable x and similarly by Planck function for a spectral case. The analytical solutions obtained can be used for testing numerical methods for radiant heat exchange problems computation.
 THE METHOD SVETn FOR SOLVING A RADIATION ENERGY AND TRANSPORT EQUATION SET V.Yu. Gusev, M.Yu. Kozmanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2001. No 2. P. 7278.
The paper presents a modification of the characteristic method that provides an interpolation within high accuracy for solving an equation set containing radiation transport and energy equations. The value at the characteristic endpoint at the nth step is obtained using a highorder interpolation spline and corrected by balancing. The method allows for parallel computations of the above set of equations.
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