On a class of flux schemes for convection-diffusion equations
https://doi.org/10.23947/2587-8999-2017-2-169-179
Abstract
The article is devoted to the investigation of difference schemes for equations of convectiondiffusion type. Such equations are widely used in the description of non-linear processes. In this
paper we consider a spatially one-dimensional variant, although the main features of the equation are retained here: nonmonotonicity and quasilinearity.
The purposes of the work were the development and calculation of flux schemes with a double exponential transformation. This paper presents the results of constructing and generalizing conservative weakly monotonic schemes of second-order accuracy on space on uniform and quasiuniform grids. A generalization of the proposed schemes to the case of the use of cellular meshes
was performed.
Keywords
convection-diffusion equation,
difference schemes,
integral transforms,
algorithm of nonmonotonic sweep,
iteration
Supporting agencies: The research is done with the financial support from Russian Foundation for Basic Research, Projects No. 15-01-04620-a, 16-07- 00206-a.
About the Authors
Yuriy Nikolaevich Karamzin
Keldysh Institute of Applied Mathematics of RAS
(Miusskaya square, 4, Moscow, Russia)
Russian Federation
Russian Federation
Karamzin Yuriy Nikolaevich, Doctor of Science in Physics and Maths, Professor, Keldysh Institute of Applied Mathematics of RAS (Miusskaya square, 4, Moscow, Russia)
Tatyana Alekseevna Kudryashova
Keldysh Institute of Applied Mathematics of RAS
(Miusskaya square, 4, Moscow, Russia)
Russian Federation
Russian Federation
Kudryashova Tatyana Alekseevna, Candidate of Science in Physics and Maths, Senior Research Keldysh Institute of Applied Mathematics of RAS (Miusskaya square, 4, Moscow, Russia)
Sergey Vladimirovich Polyakov
Keldysh Institute of Applied Mathematics of RAS
(Miusskaya square, 4, Moscow, Russia)
Russian Federation
Russian Federation
Polyakov Sergey Vladimirovich, Doctor of Science in Physics and Maths, Senior Researcher,
Keldysh Institute of Applied Mathematics of RAS (Miusskaya square, 4, Moscow, Russia)
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Review
For citations:
Karamzin Yu.N., Kudryashova T.A., Polyakov S.V. On a class of flux schemes for convection-diffusion equations. Computational Mathematics and Information Technologies. 2017;1(2). https://doi.org/10.23947/2587-8999-2017-2-169-179
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