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Issue N^{o} 4, 2008  PRACTICAL CONDITIONS TO PROVIDE STABILITY OF HEAT WAVE SIMULATIONS IN IMPLICIT DIFFERENCE SCHEMES
Yu. A. Bondarenko, A. A. Gorbunov VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 312.
Implicit difference schemes with an explicit timedependent heat conductivity factor, as well as twostage implicit difference schemes with single refinement of the explicit heat conductivity factor are considered as applied to the quasilinear diffusion equation. Conditions to provide stability of such difference schemes have been obtained. For implicit difference schemes with an implicit heat conductivity factor, conditions to provide convergence of simple iterations with respect to the heat conductivity factor have been obtained that have minor differences as against the stability conditions for the twostage difference schemes with the refined explicit heat conductivity factor. Results of 2D heat wave simulations on irregular grids show that apart from being commensurately accurate, the use of the explicit (with single refinement) heat conductivity factor with automatic time step selection is more efficient than simple iterations with respect to the nonlinearity of implicit heat conductivity factor. At the same time, simulations without time step constraint may lead to considerable uncertainties.
 DS_{n}LIKE SCHEME FOR SOLVING THE TRANSPORT EQUATION ON RECTANGULAR SPATIAL GRIDS A. I. Bochkov, V. A. Shumilin VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 1318.
A DS_{n}like scheme has been developed for 2D transport equation simulations on rectangular spatial grids. In this scheme, grid values of the desired function are defined at cell edges and in cell centers as major values, and values at cell verges (grid nodes) are used as auxiliary ones. The paper presents data of numerical analysis that show that the grid solution has practically the second order of conversion to the exact solution on essentially nonorthogonal spatial grids.
 GODUNOVBASED MARKERS FOR STRONG DISCONTINUITIES N. Ya. Moiseyev, T. V. Topchiy, N. L. Frolova VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 1930.
The paper discusses an approach to ID gas dynamics simulations using the Godunov method with singled out strong and weak discontinuities that move across the difference grid. The discontinuities are described by the markers that correspond to contact line, shock and detonationlike discontinuities. An abstract class, “cMarker”, has been developed on the basis of C+H+ objectoriented programming with derived classes that describe specific discontinuities for applied simulations. The paper provides a comparison of test simulations with markers and without them versus exact solutions.
 AN ANALYTICAL TEST FOR GAS DYNAMICS SIMULATIONS WITH NONLINEAR HEAT CONDUCTION В. P. Tikhomirov VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 3136.
A problem of discontinuous running waves propagating in cold matter at a constant velocity is considered for ID gas dynamics equations in Lagrange variables. As an equation of state we use the EOS of ideal gas without energy and pressure of equilibrium radiation and with it. The heat conduction coefficient is chosen in a special way: in the form of a product of an arbitrary power function of temperature and some welldefined density and temperaturedependent function. As a result, selfsimilar equations of the running wave problem become much simpler and easier to integrate. The resulting exact solution has a simple analytical representation. For still gas, it agrees with the wellknown solution to the heat wave problem. The exact solution thus obtained can be used as a benchmark for codes and numerical solvers of gas dynamics equations with nonlinear heat conduction. The analytical solution is compared with a solution obtained by the difference technique.
 Scientificview  A PARALLEL POSTPROCESSOR FOR PHYSICS NUMERICAL SIMULATION DATA A. L. Potekhin, V. I. Tarasov, S. A. Firsov, I. V. Loginov, V. A. Nikitin, M. G. Kuznetsov, N. V. Popova, A. K. Demanova, Yu. V. Kozachek VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 3745.
The paper describes a parallel postprocessor, ScientificView, developed at the RFNCVNIIEF Computational Department. The system serves for filtering, display and tabular processing of results of physics simulations on regular difference grids. Plots of performance versus number of processors for some algorithms are presented.
 TO THE MATTER OF EVOLUTION OF AXIALLY SYMMETRIC PERTURBATIONS ON THE TOP OF A RISING AIR BUBBLE S. Yu. Sedov VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 4653.
Possible interpretations of the evolution of axially symmetric perturbations on the surface of a large rising air bubble are presented.
 MARKOVIAN MODELS AS APPLIED TO THE PROBLEM OF SLEEP ONSET RECOGNITION AND FATIGUE D. V. Parkhomenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 5459.
As a result of advances in video engineering, all stateoftheart sleep recognition systems rest upon driver video image processing. Such systems do not disturb the driver and are highly noise resistant. Most of such systems use the width of human eye opening and the rate of winking as the basic criteria. The paper considers a new approach to the problem of driver sleep onset recognition. This approach makes it possible to track the rate of winking and predict that the driver is likely to fall asleep. This approach uses probabilistic automatons and is widely used in speech processing. This approach is focused on the analysis of human winking and instructing the automaton in behaving (winking) like a human based on widerange sampling. A software model implementing this approach has been developed and tested against real data. The paper discusses some simplest features of the model and results of its validation.
 ANALYSIS OF UNCERTAINTIES IN EPIGNOSTIC GROUNDWATER RADIONUCLIDE TRANSPORT SIMULATIONS I. V. Tokarev, M. G. Khramchenkov, A. N. Chekalin, N. D. Yakimov VANT. Ser.: Mat. Mod. Fiz. Proc. 2008. No 4. P. 6068.
The paper analyzes simulation approaches and models for hydraulic and isotopic groundwater dating. As an isotopic technique we used the heliumtritium method. Simulated formulas were obtained that enable assessing deviation of these parameters from each other. The resulting relationships are important for a number of applied hydrogeochemistry problems, including those dealing with variations of environmental isotopic composition introduced by radioactive contamination.
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