Effects of small boundary perturbation on flow of viscous fluid
We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude ɛ≪1 is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of ε is derived....
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| Published in | Zeitschrift für angewandte Mathematik und Mechanik Vol. 96; no. 9; pp. 1103 - 1118 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Weinheim
Blackwell Publishing Ltd
01.09.2016
Wiley Subscription Services, Inc |
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| Abstract | We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude ɛ≪1 is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of ε is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem.
The author studies the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude ɛ≪1 is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of ε is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem. |
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| AbstractList | We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude
is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of ε is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem. We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude 1 is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of [epsi] is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem. We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude ɛ≪1 is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of ε is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem. The author studies the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude ɛ≪1 is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of ε is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem. We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude [Formulaomitted] is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of epsilon is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem. The author studies the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude [Formulaomitted] is applied on part of the boundary of the fluid domain. The complete asymptotic expansion of the solution of the Stokes system, in powers of epsilon is derived. First two terms are explicitly computed. A simple example shows that the perturbation is nonlocal, i.e. not concentrated near the boundary. The convergence of the expansion is proved. The results are applied on a simple optimal shape design problem. |
| Author | Marušić-Paloka, Eduard |
| Author_xml | – sequence: 1 givenname: Eduard surname: Marušić-Paloka fullname: Marušić-Paloka, Eduard email: emarusic@math.hr, emarusic@math.hr organization: Department of Mathematics, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia |
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| Cites_doi | 10.1080/00036811.2014.930823 10.1006/jdeq.2000.3814 10.1007/s00033-011-0167-7 10.1080/17476933.2013.831846 10.1006/jdeq.1996.0122 10.1006/jcph.1998.6088 10.1016/S0022-0396(02)00105-5 10.1007/s10958-013-1204-1 |
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| References_xml | – volume: 63 start-page: 475 issue: 3 year: 2012 end-page: 502 article-title: On multiscale homogenization problems in boundary layer theory publication-title: ZAMP – volume: 59 start-page: 1269 issue: 9 year: 2014 end-page: 1282 article-title: Asymptotic formula for the solution of the Stokes problem with small perturbation of the domain in two and three dimensions publication-title: Complex Var. Elliptic Eq. – volume: 94 start-page: 1305 issue: 7 year: 2015 end-page: 1333 article-title: High‐order approximations for an incompressible viscous flow on a rough boundary publication-title: Appl. Anal. – year: 2005 – volume: 188 start-page: 591 issue: 2 year: 2003 end-page: 624 article-title: Dirichlet problems on varying domains publication-title: J. Differ. Eq. – volume: 147 start-page: 187 year: 1998 end-page: 218 article-title: Effective boundary conditions for laminar flows over periodic rough boundaries publication-title: J. Comput. Phys. – volume: 129 start-page: 358 issue: 2 year: 1996 end-page: 402 article-title: Domain perturbation for linear and nonlinear parabolic equations publication-title: J. Differ. Eq. – volume: 170 start-page: 96 issue: 1 year: 2001 end-page: 122 article-title: On the roughness‐induced effective boundary conditions for an incompressible viscous flow publication-title: J. Diff. Eq. – year: 2001 – volume: 323 start-page: 313 year: 1996 end-page: 331 article-title: Influence de la rugosit en hydrodynamique laminaire publication-title: C.R. Acad. Sci. Paris Sr. I – volume: 189 start-page: 525 issue: 3 year: 2013 end-page: 535 article-title: On a thin layer of non‐Newtonian fluid on rough surface percolating through perforated obstacle publication-title: J. of Math. Sci. – ident: e_1_2_10_12_1 doi: 10.1080/00036811.2014.930823 – ident: e_1_2_10_3_1 doi: 10.1006/jdeq.2000.3814 – ident: e_1_2_10_6_1 doi: 10.1007/s00033-011-0167-7 – ident: e_1_2_10_11_1 doi: 10.1080/17476933.2013.831846 – volume-title: London Mathematical Society Lecture Notes Series, 318 year: 2005 ident: e_1_2_10_2_1 contributor: fullname: Henry D. – ident: e_1_2_10_7_1 doi: 10.1006/jdeq.1996.0122 – ident: e_1_2_10_4_1 doi: 10.1006/jcph.1998.6088 – ident: e_1_2_10_8_1 doi: 10.1016/S0022-0396(02)00105-5 – ident: e_1_2_10_9_1 – volume-title: Applied Shape Optimization for Fluids year: 2001 ident: e_1_2_10_13_1 contributor: fullname: Mohammadi O. – ident: e_1_2_10_10_1 doi: 10.1007/s10958-013-1204-1 – volume: 323 start-page: 313 year: 1996 ident: e_1_2_10_5_1 article-title: Influence de la rugosit en hydrodynamique laminaire publication-title: C.R. Acad. Sci. Paris Sr. I contributor: fullname: Amirat Y. |
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| Snippet | We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude ɛ≪1 is applied on... We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude is applied on... We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude 1 is applied on... We study the effects of small boundary perturbation on the flow of viscous fluid using asymptotic analysis. A small perturbation of magnitude [Formulaomitted]... |
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| SubjectTerms | 35B25 35B40 75D07 76D55 asymptotic analysis Asymptotic expansions Boundaries boundary perturbation Computational fluid dynamics Convergence error estimate Fluid flow Optimization Perturbation methods Stokes system Viscous fluids |
| Title | Effects of small boundary perturbation on flow of viscous fluid |
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