Geodesic
Bicompact schemes of solving an stationary transport equation by quasi–diffusion method
Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 51-63.

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High order approximation schemes (up to fourth order) for numerical calculation of neutron transport equation coupled with a quasi–diffusion system of equations (so called a low order system of transport equations), which is used for acceleration of iterations on scattering term, are constructed. These schemes are developed on the basis of the uniform principles of compact approximation (in the frame of single cell of a space mesh). That makes it possible to take into account contact discontinuities correctly. The fourth order approximation on minimal two point stencil is achieved by widening unknowns list. As additional unknowns are considered either the integral averaged values over the cell or a semi integer values. These values are connected by the Simpson integration formula. An equation for determination of additional unknowns in a cell is constructed by implementation of Euler–Maclaurin formula. The calculation of a set of test problem has been carried out. The very good practical accuracy of suggested schemes has been revealed. These schemes might be extended naturally on 2D and 3D geometries. The high accuracy, monotonicity, high efficiency, compact stencil of the schemes make theme very attractive for engineering calculations such as numerical simulation of nuclear reactors and others.
Keywords: linear transport equation, bicompact difference schemes
Mots-clés : quasi–diffusion equations. 
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E. N. Aristova; M. I. Stoynov. Bicompact schemes of solving an stationary transport equation by quasi–diffusion method. Matematičeskoe modelirovanie, Tome 28 (2016) no. 3, pp. 51-63. http://geodesic.mathdoc.fr/item/MM_2016_28_3_a3/

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