О построении двумерных локально-модифицированных квазиструктурированных сеток и решении на них краевых задач в областях с криволинейной границей
Аннотация
Разработаны новые подходы к локальной модификации квазиструктурированных сеток, которые позволяют отследить неоднородности краевой задачи в расчетной области и адаптивны к криволинейным границам, а также просты в использовании и не требуют хранения большого объема данных, как это необходимо в неструктурированных сетках. На примере решения модельной задачи показан второй порядок точности при расчетах на предлагаемых сетках. Даны рекомендации по построению сеток на границах сопряжения подобластей (интерфейсе).
Ключевые слова
Полный текст:
PDFЛитература
Sveshnikov V.M., Belyaev D.O. Construction of Quasi-Structured Locally Modified Grids for Solving Problems of High Current Electronics. Vestnik Yuzho-Uralskogo gosudarstvennogo universiteta. Seriya “Vychislitelnaya matematika i informatika” [Bulletin of South Ural State University. Series: Computational Mathematics and Software Engineering. 2012. no. 40(299). pp. 130–140. (in Russian)
Syrovoj V.A. Vvedenie v teoriyu intensivnykh puchkov zaryazhennykh chastits [Introduction to the Theory of Intense Charged Particle Beams]. Moscow, Energoatomizdat, 2004. 552 p.
Liseikin V.D. Grid Generation methods. Berlin, Springer-Verlag, 1999. 363 p.
Shokin Yu.I., Danaev N.T., Hakimzyanov G.S., Shokina N.Yu. Lektsii po raznostnym skhemam na podvizhnykh setkakh. Chast' 2 [Lectures on the Difference Scheme on Moving Grids.Part 2]. Almaty, Kazakh National University, 2008. 184 p.
Sidorov A.F. An Algorithm for Calculating the Optimal Difference Grids. Trudy matematicheskogo instituta im. V.A. Steklova. [Proceedings of the Mathematical Steklov Institute]. 1966. vol. 74. pp. 147–151. (in Russian)
Ushakova O.V. An Algorithm for Constructing Two-dimensional Optimal Adaptive Grids. Matematicheskoe modelirovanie [Mathematical modeling]. 1997. vol. 9, no 2. pp. 88–90. (in Russian)
Anuchina A.I., Artemova N.A., Bronina T.N., Gordeychuk V.A., Ushakova O.V. On the development of the algorithm for constructing grids in the constructions formed by volumes of rotation, including when their deformation. Tezisy dokladov VIII Vserossiiskoi konferentsii, posvyashchennoi pamyati akademika A.F. Sidorova i Vserossiiskoi molodezhnoi shkoly-konferentsii (Abrau–Dyurso, 5–10 sentyabrya 2016 g.). [Abstracts of the VIII All–Russian conference dedicated to the memory of A.F. Sidorov and Russian youth school–conference (Abrau–Durso, 5–10 September 2016)]. Ekaterinburg: Publishing House of the Krasovsky Institute of Mathematics and Mechanics. UB RAS, 2016. pp. 7–9. (in Russian)
Matsokin A.M. Automation triangulation of domains with smooth boundary for solving elliptic equations. Preprint. Novosibirsk: Computing Center of USSR Academy of Sciences, 1975. no. 15. 15 p.
Ilin V.P., Itskovich E.A., Kuklina G.Y., Sander I.A., Sander S.A., Sveshnikov V.M. Calculation of Electrostatic Fields on Locally Modified Grids. Vychislitel'nye metody i tekhnologiya resheniya zadach matematicheskoi fiziki [Computational methods and technology solutions of problems of mathematical physics]. Novosibirsk: Computing Center of SB RAS, 1993. pp. 63–72. (in Russian)
Sveshnikov V.M. The numerical calculation of charged particle beams on locally modified grids. Preprint. Novosibirsk: Computing Center of Russian Academy of Sciences, 1997. Vol. 1109. 28 p.
Sander I.A. The program of Delaunay triangulation construction for the domain with the piecewise smooth boundary. Bulletin of the Novosibirsk Computing Center. Series: Numerical Analysis. Novosibirsk: NCC Publisher, 1998. pp. 71–79.
Ilin V.P., Sveshnikov V.M., Synakh V.S. On Grid Technologies for Two-Dimensional Boundary Value Problems. Sibirskii zhurnal industrial'noi matematiki [Journal of Applied and Industrial Mathematics]. 2000. vol. 3, no. 1. pp. 124–136. (in Russian)
Sveshnikov V.M. Construction of Direct and Iterative Methods of Decomposition. Sibirskii zhurnal industrial'noi matematiki [Journal of Applied and Industrial Mathematics]. 2009. vol. 12, no. 3(39). pp. 99–109. (in Russian)
Ilin V.P. Metody i tekhnologii konechnykh elementov [Methods and Technologies of Finite Elements]. Novosibirsk, ICM&MG SBRAS, 2007. 370 p.
Skvortcov A.V. Overview of Algorithms for Constructiong Delanau Triangulation. Vychislitel'nye metody i programmirovanie [Numerical Methods and Programming]. 2002. vol. 3, no. 1. pp. 18–43. (in Russian)
Belyaev D.O., Kozyrev A.N., Sveshnikov V.M. Program Package ERA-DD for Solving Two-Dimensional Boundary Value problems on Quasi-Structured Grids. Vestnik NGU [Novosibirsk State University Journal of Information Technologies]. 2010. vol. 8, no. 1. pp. 3–11. (in Russian)
Samarskiy A.A. Teoriya raznostnykh skhem [The Theory of Difference Schemes]. Moscow, Nauka, 1977. 656 p.
Marchuk G.I. Metody vychislitel'noy matematiki [Methods of Computational Mathematics]. Moscow, Nauka, 1977. 456 p.
DOI: http://dx.doi.org/10.14529/cmse170201