Obstacle detection in fluid flow using asymptotic analysis technique

Abstract

Abstract We consider the geometric inverse problem of determining an immersed obstacle in a two-dimensional non-stationary Stokes fluid flow. We use the topological gradient method to solve this problem. The unknown obstacle is located and reconstructed using the leading term of the Khon–Vogelius shape function variation. We propose a simple and fast detection algorithm. The efficiency and accuracy of the proposed approach are illustrated by some numerical examples.

Keywords

• Geometric inverse problem
• Kohn–Vogelius formulation
• Topological sensitivity analysis
• Non-stationary Stokes system