Numerical simulations of boundary layer problems
- Autores: Belov A.1,2, Kalitkin N.2
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Afiliações:
- Department of Physics
- Keldysh Institute of Applied Mathematics
- Edição: Volume 8, Nº 4 (2016)
- Páginas: 341-347
- Seção: Article
- URL: https://journals.rcsi.science/2070-0482/article/view/200944
- DOI: https://doi.org/10.1134/S2070048216040037
- ID: 200944
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Resumo
Boundary layers often appear at the interface of two media. A typical example is the singularly perturbed Helmholz equation. It is shown that the modern finite difference methods solve such problems with a high efficiency under an appropriate choice of the grid. A convergence verification procedure is proposed that does not require majorant estimation. A superfast algorithm yielding an a posteriori asymptotically precise error estimate is described and a quasi-uniform rectangular grid resolving in detail all the segments of the solution is proposed. The algorithm guarantees good precision even on the moderate grids having N ~ 200 points in each direction. This algorithm is implemented in MATLAB.
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Sobre autores
A. Belov
Department of Physics; Keldysh Institute of Applied Mathematics
Autor responsável pela correspondência
Email: belov_25.04.1991@mail.ru
Rússia, Moscow; Moscow
N. Kalitkin
Keldysh Institute of Applied Mathematics
Email: belov_25.04.1991@mail.ru
Rússia, Moscow