Geodesic
Monotonization of high accuracy bicompact scheme for stationary multidimensional transport equation
Matematičeskoe modelirovanie, Tome 27 (2015) no. 8, pp. 32-46

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A variant of hybrid scheme for solving non-homogeneous stationary transport equation is constructed. A bicompact scheme of the fourth order approximation over all space variables and the first order approximation scheme from a set of short characteristic methods with interpolation over illuminated faces are chosen as a base. It is shown that the chosen first order approximation scheme is a scheme with minimal dissipation. Monotone scheme is constructed by continuous and homogeneous procedure in all mesh cells by keeping the fourth approximation order in domains where solution is smooth and maintaining high practical accuracy in a domain of discontinuity. Logical simplicity and homogeneity of suggested algorithm make this method well fitted for supercomputer calculations.
Mots-clés : transport equation
Keywords: bicompact schemes, short characteristic method, monotonic schemes, minimal dissipation, hybrid schemes. 
@article{MM_2015_27_8_a2,
     author = {E. N. Aristova and B. V. Rogov and A. V. Chikitkin},
     title = {Monotonization of high accuracy bicompact scheme for stationary multidimensional transport equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {32--46},
     publisher = {mathdoc},
     volume = {27},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_8_a2/}
}
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E. N. Aristova; B. V. Rogov; A. V. Chikitkin. Monotonization of high accuracy bicompact scheme for stationary multidimensional transport equation. Matematičeskoe modelirovanie, Tome 27 (2015) no. 8, pp. 32-46. http://geodesic.mathdoc.fr/item/MM_2015_27_8_a2/