Rigorous justification of the asymptotic model describing a curved-pipe flow in a time-dependent domain
| Autor: | José M. Rodríguez, Eduard Marušić-Paloka, Igor Pažanin, Gonzalo Castiñeira |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Asymptotic analysis Applied Mathematics 0206 medical engineering Mathematical analysis Computational Mechanics 02 engineering and technology 020601 biomedical engineering 01 natural sciences Pipe flow Domain (software engineering) Physics::Fluid Dynamics 010101 applied mathematics curved pipe time-dependent domain Navier-Stokes equations asymptotic analysis error estimates 0101 mathematics Navier–Stokes equations |
| Zdroj: | ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 99:e201800154 |
| ISSN: | 0044-2267 |
| DOI: | 10.1002/zamm.201800154 |
| Popis: | This paper is devoted to the mathematical justification of an asymptotic model of a viscousflow in a curved tube with moving walls by proving error estimates. To this aim, we first construct the space correctors near the pipe’s inlet and outlet due to the boundary layer phenomenon. In order to guarantee the adequate properties for these correctors we study what we called modified Leray’s problem defined in a semi-infinite strip. We ensure the existence and uniqueness of an exponential decaying solution when the axial variable tends to infinity. Then, by deriving a Poincar´e’s type inequality and other estimates for the boundary value problems taking into account the condition on the pipe’s lateral boundary, we evaluate the difference between the asymptotic approximation and the exact solution of the problem. |
| Databáze: | OpenAIRE |
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