Exponential difference schemes for solving boundary-value problems for convection-diffusion type equations
- Authors: Polyakov S.V.1,2, Karamzin Y.N.1, Kudryashova T.A.1, Tsybulin I.V.3
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Affiliations:
- Keldysh Institute of Applied Mathematics
- Moscow Institute of Engineering Physics
- Moscow Institute of Physics and Technology
- Issue: Vol 9, No 1 (2017)
- Pages: 71-82
- Section: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/201510
- DOI: https://doi.org/10.1134/S2070048217010124
- ID: 201510
Cite item
Abstract
The paper considers the numerical solution of boundary-value problems for multidimensional convection-diffusion type equations (CDEs). Such equations are useful for various physical processes in solids, liquids and gases. A new approach to the spatial approximation for such equations is proposed. This approach is based on an integral transformation of second-order one-dimensional differential operators. A linear version of CDE was chosen for simplicity of the analysis. In this setting, exponential difference schemes were constructed, algorithms for their implementation were developed, a brief analysis of the stability and convergence was made. This approach was numerically tested for a two-dimensional problem of motion of metallic particles in water flow subject to a constant magnetic field.
About the authors
S. V. Polyakov
Keldysh Institute of Applied Mathematics; Moscow Institute of Engineering Physics
Author for correspondence.
Email: polyakov@imamod.ru
Russian Federation, Moscow, 125047; Moscow, 115409
Yu. N. Karamzin
Keldysh Institute of Applied Mathematics
Email: polyakov@imamod.ru
Russian Federation, Moscow, 125047
T. A. Kudryashova
Keldysh Institute of Applied Mathematics
Email: polyakov@imamod.ru
Russian Federation, Moscow, 125047
I. V. Tsybulin
Moscow Institute of Physics and Technology
Email: polyakov@imamod.ru
Russian Federation, Dolgoprudnyi, Moscow oblast, 141700