Geodesic
Characteristics scheme for the transport equation solving on a tetrahedron grid with barycentrical interpolation
Matematičeskoe modelirovanie, Tome 30 (2018) no. 9, pp. 33-50

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In this paper, the interpolation-characteristic method of order of approximation is not less than a second to solve the transport equation on an unstructured grid of tetrahedra is constructed. The problem of finding numerical solutions by this method, hereinafter method of short characteristics, is divided into two subtasks. First, there is a resolution of the individual simplicial cell. It is necessary to specify a set of discrete values, the setting of which on the litted faces is mathematically sufficient to find all remaining grid values in the cell. Depending on the location of the cell and the direction of propagation of the radiation there are three different types of illumination. The interpolation in barycentrically coordinates of the cell with 14 free coefficients is proposed. The interpolation takes into account the values of radiation intensity at the nodes, and the average integrated intensity values for edges and faces without adding new points of stensil. This interpolation ensures at least the second order of approximation with some additional members of the third order. The method ensures a conservative redistribution of the outcoming fluxes over cell's faces. The second subtask associated with the choice of order and resolution of the cells and can be solved using graph theory. Numerical calculations confirm the order of convergence is approximately the second.
Mots-clés : transport equation
Keywords: method of short characteristics, interpolation-characteristic method, second order of approximation, barycentric coordinates. 
@article{MM_2018_30_9_a2,
     author = {E. N. Aristova and G. O. Astafurov},
     title = {Characteristics scheme for the transport equation solving on a tetrahedron grid with barycentrical interpolation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--50},
     publisher = {mathdoc},
     volume = {30},
     number = {9},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_9_a2/}
}
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E. N. Aristova; G. O. Astafurov. Characteristics scheme for the transport equation solving on a tetrahedron grid with barycentrical interpolation. Matematičeskoe modelirovanie, Tome 30 (2018) no. 9, pp. 33-50. http://geodesic.mathdoc.fr/item/MM_2018_30_9_a2/