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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 9, Pages 1685–1697 (Mi zvmmf116)  
This article is cited in 1 scientific paper (total in 1 paper)

Finding nonoscillatory solutions to difference schemes for the advection equation

S. L. Kivva

Institute of Mathematical Machines and Systems, National Academy of Sciences of Ukraine, pr. Akademika Glushkova 42, Kiev, 03187, Ukraine
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Abstract: The advection equation is solved using a weighted adaptive scheme that combines a monotone scheme with the central-difference approximation of the first spatial derivative. The determination of antidiffusion fluxes is treated as an optimization problem. The solvability of the optimization problem is analyzed, and the differential properties of the cost functional are examined. It is shown that the determination of antidiffusion fluxes is reduced to a linear programming problem in the case of an explicit scheme and to a nonlinear programming problem or a sequence of linear programming problems in the case of an implicit scheme. A simplified monotonization algorithm is proposed. Numerical results are presented.
Key words: advection equations, difference schemes, optimization problem, linear programming problems.
Received: 01.06.2007
Revised: 12.11.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 9, Pages 1646–1657
DOI: https://doi.org/10.1134/S0965542508090133
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: S. L. Kivva, “Finding nonoscillatory solutions to difference schemes for the advection equation”, Zh. Vychisl. Mat. Mat. Fiz., 48:9 (2008), 1685–1697; Comput. Math. Math. Phys., 48:9 (2008), 1646–1657
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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