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. Вып.1. С. 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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