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[Text] / V. Shaydurov, A. Vyatkin // AIP Conference Proceedings. - 2015. - Vol. 1648: International Conference on Numerical Analysis and Applied Mathematics (SEP 22-28, 2014, Rhodes, GREECE). - Ст. UNSP 85004, DOI 10.1063/1.4913096. - Cited References:11 . - ISSN 0094-243XРУБ Mathematics, Applied + Physics, Applied

Аннотация: We consider a semi-Lagrangian algorithm and formulate the basic equality for a local temporal-spatial domain. This equality involves integrals over domains at neighboring temporal levels. To get the numerical scheme, we approximate each component of the equality within second-order accuracy. To compute an integral at the previous time level, we make the change of variables. After that the quadrature formulas are implemented with nodes and weights defined with the help of the Cauchy problem for a system of ordinary differential equations.

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Держатели документа:
Siberian Fed Univ, Krasnoyarsk 660041, Svobodny Prospe, Russia
Inst Computat Modeling SB RAS, Akademgorodok 660036, Russia

Доп.точки доступа:
Vyatkin, Alexander; Вяткин, Александр Владимирович; Шайдуров, Владимир Викторович

[Text] / A. Vyatkin ; ed. M. D. Todorov // APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES : AMER INST PHYSICS, 2015. - Vol. 1684: 7th International Conference on Application of Mathematics in Technical (JUN 28-JUL 03, 2015, Albena, BULGARIA). - Ст. UNSP 090012. - (AIP Conference Proceedings), DOI 10.1063/1.4934337. - Cited References:12 . - РУБ Mathematics, Applied + Physics, Applied

Аннотация: We construct an algorithm of the family of semi-Lagrangian methods for the three-dimensional advection problem. The algorithm is based on the integral balance equation for the cubic neighbourhood of a grid node. This equation involves integrals over two neighbouring time levels. To compute an integral at the previous time level, we make the domain transformation. This allows us to simplify appreciably the algorithm and to reduce the computation time in numerical examples. The algorithm is of first-order accuracy. Numerical experiments confirm the suitability of the proposed scheme.

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Держатели документа:
SB RAS, Inst Computat Modelling, Krasnoyarsk 660036, Russia.

Доп.точки доступа:
Vyatkin, A.; Todorov, M.D. \ed.\