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ON THE STABILITY OF A STABILIZING CORRECTION SCHEME WITH CENTRAL DIFFERENCES FOR SPATIAL VARIABLES IN THE 3D TRANSPORT EQUATION
- Authors: Zhukov V.P1
-
Affiliations:
- Federal Research Center for Information and Computational Technologies
- Issue: Vol 64, No 5 (2024)
- Pages: 835-841
- Section: Mathematical physics
- URL: https://ruspoj.com/0044-4669/article/view/665085
- DOI: https://doi.org/10.31857/S0044466924050118
- EDN: https://elibrary.ru/YCZKUW
- ID: 665085
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Abstract
It is generally accepted that the stabilizing correction scheme with central differences for spatial variables in the 3D transport equation is conditionally stable. The work shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and the magnitude of their increments rapidly approach zero as the Courant parameter tends to zero, allowing successful use of this scheme. Therefore, it is more accurate to refer to this scheme as practically conditionally stable.
About the authors
V. P Zhukov
Federal Research Center for Information and Computational Technologies
Email: zukov@ict.nsc.ru
Novosibirsk, Russia
References
- Ковеня В. М., Тарнавский Г. А., Яненко Н. Н., Неявная разностная схема для численного решения пространственных уравнений газовой динамики //Ж. вычисл. матем. иматем. физ. 1980. Т. 20. № 6. С. 1465—1482.
- Ковеня В. М., Яненко Н. Н. Метод расщепления в задачах газовой динамики. Новосибирск: Наука, 1981.
- Яненко Н. Н. Метод дробных шагов решения многомерных задач математической физики. Новосибирск: Наука, Сибирское отделение, 1967.
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