Effects of small boundary perturbation on flow of viscous fluid

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 96; no. 9; pp. 1103 - 1118
• Main Author: Marušić-Paloka, Eduard
• Format: Journal Article
• Language: English
• Published: Weinheim Blackwell Publishing Ltd 01.09.2016; Wiley Subscription Services, Inc
• Subjects: 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
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201500195

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.