Solution of the heat equation on unstructured curvilinear grids

V. M. Goloviznin^a, V. N. Koterov^b, V. M. Krivtsov<sup>b

a</sup> Institute of Safety in Nuclear Power Engineering, Russian Academy of Sciences, ul. B. Tul’skaya 52, Moscow, 113191 Russia
^b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991 Russia

Abstract: A computational approach to the solution of the heat equation is proposed. In the case of three-dimensional oblique (nonorthogonal) unstructured grids, this approach results in a compact grid stencil and unconditionally stable computational algorithm. A feature of the proposed approach is the use of flux functions as dependent separate variables. Mainly hexagonal grids are considered in which every cell can be continuously mapped onto a unit cube. Computational examples are presented.

Key words: numerical methods, heat equation, flux variables, nonorthogonal grids, unstructured grids.

UDC: 519.633

Received: 25.03.2011
Revised: 23.05.2011

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:11, 1953–1961

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