Abstract
We consider a number of computational features of two-dimensional Lagrangian schemes on triangular grids: loss of approximation near the axis (cylindrical symmetry) and measures to counteract this effect; approximation and operator interpretation at corner points where the type of the boundary conditions changes; loss of stability with free approximation of type II boundary conditions; distortion of the Lagrangian grid associated with first-order accuracy on the boundary of an irregular grid.
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Literature Cited
V. M. Goloviznin, V. K. Korshunov, and A. A. Samarskii, "Two-dimensional difference schemes on triangular Lagrangian grids in magnetohydrodynamics," Zh. Vychisl. Mat. Mat. Fiz., No. 4, 926–942 (1982).
N. V. Ardelyan and I. S. Gushchin, "On one approach to the construction of fully conservative difference schemes," Vestn. Mosk. Gos. Univ., Ser. Vychisl. Mat. Kibern., No. 3, 3–10 (1982).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
N. V. Ardelyan, "On stability of difference schemes for multidimensional equations of acoustics," Vestn. Mosk. Gos. Univ., Ser. Vychisl. Mat. Kibern., No. 2, 65–69 (1979).
N. V. Ardelyan, "On convergence of difference schemes for the equations of acoustics and Maxwell's equations," Zh. Vychisl. Mat. Mat. Fiz., No. 5, 1168–1176 (1983).
N. V. Ardelyan, "On application of Newton's method for implementation of difference schemes in gas dynamics," in: Computational Methods and Programming [in Russian], No. 35, Moscow State Univ. (1981), pp. 136–144.
N. V. Ardelyan, "On grid analogs of the basic differential operators on an irregular triangular grid," in: Difference Methods of Mathematical Physics (Theory of Difference Schemes) [in Russian], Moscow State Univ. (1981), pp. 49–58.
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Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 10–20, 1985.
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Ardelyan, N.V., Kosmachevskii, K.V. & Chernigovskii, S.V. Some computational features of two-dimensional problems of gas dynamics on irregular triangular grids. Comput Math Model 1, 5–11 (1990). https://doi.org/10.1007/BF01128303
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DOI: https://doi.org/10.1007/BF01128303