Geodesic
Even- and odd-parity kinetic equations of particle transport. 3:~Finite analytic scheme on tetrahedra
Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 34-62

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We derive a finite analytic (not the finite difference) scheme for the even-odd parity transport equations of neutral particles. This discrete scheme utilizes the analytic solution in an adjacent tetrahedral cells to formulate the algebraic representation of partial differential equations. The scheme allows to simulate 3D neutrons and photons transport in heterogeneous absorbing, scattering, multiplying media (problems of nuclear reactors, radiation shielding, radiative heat transfer, radiation gas dynamics) without restrictions on the optical depth of the cell (the product of the extinction coefficient and the cell chord), and no restrictions in the values of jump in extinction coefficient in the transition of particles from one cell to another. Is allowed to change sign the extinction coefficient. The scheme is well combined with different iterative methods for solving deterministic transport problems in which the angular (direction-of-flight) variable is discretized using the discrete-ordinates (Sn) approximation.
Mots-clés : neutron and photon transport equation
Keywords: finite analytic method, tetrahedral mesh, numerical simulation, nuclear reactors, radiative heat transfer. 
@article{MM_2015_27_2_a2,
     author = {A. V. Shilkov},
     title = {Even- and odd-parity kinetic equations of particle transport. {3:~Finite} analytic scheme on tetrahedra},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {34--62},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_2_a2/}
}
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A. V. Shilkov. Even- and odd-parity kinetic equations of particle transport. 3:~Finite analytic scheme on tetrahedra. Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 34-62. http://geodesic.mathdoc.fr/item/MM_2015_27_2_a2/