Issue No 1, 2007 |
RHOMB IMPLICIT FINITE-VOLUME METHOD FOR NUMERICAL SOLUTION OF 2D EQUATIONS OF HEAT CONDUCTIVITY ON NON-REGULAR GRIDS WITH TRIANGULAR AND QUDRAN- GULAR CELLS
A. D. Gadzhiev, S. A. Novakovskaya, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 3-13.
The RHOMB implicit finite-volume method for solution of 2D equation of heat conductivity on non-regular grids with triangular and quadrangular cells is considered. The non-regular grid of the RHOMB method is built basing on the integral law of energy conservation in the grid cell and basing on the integration of the flow equation over the same cell. The approximation is built in the frames of one grid cell in the terms of temperatures and normal flow components on the cell edges. In contrast to traditional schemes with spaced template, the RHOMB method has two distinctive features: 1) the coefficient of heat conductivity is used only in the cell centers and its interpolation on the cell edges, where it can be discontinuous, is not needed; 2) application of varying template covering wide neighborhood is not needed for providing satisfactory accuracy on strongly deformed grids. All this makes the scheme of the RHOMB method simple, efficient; at the same time, the provided accuracy is rather good, which is confirmed by the results of test computations presented in the paper.
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| NUMERICAL SOLUTION OF 2D EQUATIONS OF GAS DYNAMICS WITH HEAT CONDUCTIVITY USING DIMENSION-WISE VARIABLE DIFFERENCE TEMPLATE S.L Skrypnik, N. M. Rud’ko, R. A. Korolev, V. V. Lyapin, A. V. Popov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 14-26.
The method of numerical solution of 2D equations of gas dynamics with heat conductivity is discussed; it is based on the using of a dimension-wise variable difference template. This method allows tracking of the interface between materials along all space directions. Set-ups and computation results of test problems of gas dynamics and heat conductivity, performed under the program which realized the specified technique.
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| RESULTS OF NUMERICAL STUDIES OF ANGULAR ADAPTIVE METHOD FOR SOLVING 2D RADIATION TRANSPORT EQUATION R. M. Shagaliev, A. V. Alekseev, A. I. Bochkov, V. V. Evdokimov, E. A. Irinichev, N. P. Pleteneva, S. V. Subbot
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 27-37.
The results of the numerical study of angular adaptive methods for solving 2D radiation transport equations and equations of radiation interaction with environment are considered. The main goal of the adaptive method is overcoming of ray effects. The transport equation is written in the cylindrical system of coordinates on nonorthogonal spatial grids. The method of discrete ordinates with approximation over the DSn-type schemes is put in the basis of the numerical solution of the transport equation. The results of the numerical study confirm the workability of the adaptive method.
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| AUTOMATED LOCAL REBUILDING OF NON-REGULAR QUADRANGULAR GRIDS WHEN CALCULATING PROBLEMS WITH SEVERE DEFORMATIONS A. V. Skovpen’, V. A. Bychenkov, I. I. Kuznetsova
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 38-45.
At 2D simulation of flows with severe shear deformations on non- stationary grids the cells may deteriorate and become intolerable for further calculations. As a possible solution of this problem local automatic gridrebuilding and re-interpolation of physical quantities in the cells and the nodes of the reconstructed sub-domain can be considered. First, the grid is smoothed in the local sub-domains selected for reconstruction. If it does not help improve the grid quality to the required state, a new grid is built in this sub-domain. For this purpose the QMV frontal algorithm of non-regular quadrangular grid building is used. The algorithm works in the automatic mode and does not modify boundary nodes. An example of the calculation where the local automatic grid rebuilding is used is given in the paper. The calculation is performed under the SPRUT code (RFNC-VNIITF). The performed calculation series confirms that using the local grid rebuilding allows automatic support of the integrity and the geometry of the used computational grid. This significantly expands the scope of simulation problems and reduces the time needed for calculation of complex systems with severe deformations.
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| 3D CALCULATION METHOD FOR DIFFUSION PROCESSES ON UNSTRUCTURED GRIDS A. I. Panov, I. V. Sobolev
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 46-54.
The technique of building implicit difference schemes for solving 3D equation of heat conductivity and equation magnetic field diffusion on unstructured computational grids is discussed. The technique is based on differential-projection method. The results of test calculations are presented and compared with analytical solutions.
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| ALGORITHMS OF BUILDING NON-REGULAR POLYHEDRAL GRID FOR THE TIM TECHNIQUE A. A. Voropinov, S. S. Sokolov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 55-66.
The TIM technique is destined for solving 3D problems of continuum mechanics on non-regular polyhedral grids. At that the technique is also efficient on the grids with random structure. Two grid types are used as the initial computational grid of the TIM technique: 1) layered grid obtained from a 2D regular or non-regular grid by its shift along the direction or by its rotation around an axis; 2) the Dirichlet grid which building algorithm is based on the Voronoy diagram.
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| COMPUTATION METHOD FOR 3D INTERFACES IN THE D TECHNIQUE E. E. Chuprakov, Yu. D. Chernyshev, D. M. Linnik
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 67-73.
A parallel computation method for interfaces for solving 3D non- stationary problems of continuum mechanics in Lagrangian variables on regular grids in the frames of the D technique is discussed. The method is destined for computation of contact interactions between mathematical domains with noncoincident computational grids. It allows computation of serious tangential gaps, objects’ collisions, separation of thin shells under the impact of rarefaction waves. The method supports problem computation in both gas-dynamics and elastic-plastic approximation. The essence of the considered method is presented in the paper, general parallelization organization is discussed. A number of model problems is presented.
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| MATHEMATICAL SIMULATION OF AUTO-STEREOSCOPIC DEVICES A. A. Luk’yanitsa
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 74-82.
New types of auto-stereoscopic devices — a monitor and a projection system — are proposed. Mathematical models were built for describing their operation; effective computation algorithms for the images are developed, which allow forming 3D light field on the mentioned devices. Both the monitor and the projection system can be used for 3D data visualization for the purposes of scientific research.
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| SOLUTION METHODS FOR THE PROBLEMS OF DYNAMIC OBJECTS TRACKING M. P. Volchenkov
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 83-88.
Problems of automatic image analysis and tracking dynamic objects in the video-flow are used for different applications. High dimensionality of these problems does not allow processing of all images as a set of points. To scale down the dimensionality we propose passing from the whole image to a set of its characteristic points. The ways of characteristic points selection and using of selected points for dynamic objects tracking by means of solving the interpolation problem and the assignment problem are discussed. The problem of object reconstruction over the coordinates of its characteristic points incorrectly measured is solved.
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| DETERMINATION OF THE AIRCRAFT ROTATION FREQUENCY OVER THE SEQUENCE OF VIDEO IMAGES V. M. Ponyatsky
VANT. Ser.: Mat. Mod. Fiz. Proc. 2007. No 1. P. 89-103.
The issues of determination of the rotation frequency over video images of an on-board radiation source of a rotating aircraft obtained using matrix photodetector are discussed. Continuous and discrete quasi-optimal algorithms with the third-order phase frequency autoadjustment coefficients are developed for 2D signal. The field of permissible values of phase frequency auto-adjustment coefficients is determined, which provides evaluation of the phase and the signal frequency during the whole flying period of the aircraft. The developed algorithms are compared with the Fourier transformation in a running window and with the Kalman filter. The obtained estimation and prediction algorithms for the frequency of the measured signals are simulated in the Matlab environment. The measured signals are presented in compliance with the sequence of the video images.
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