Shape optimization of viscous flow domain considering unsteady fluid structure interaction

Abstract

This paper presents numerical solution to shape design problems of viscous flow field for unsteady fluid-structure-interactive (FSI) fields. In the FSI analysis, a strong coupled analysis is used to analyze the governing equation of the flow domain and the structural domain considering nonlinearity of strain. A minimization problem for total dissipation energy is formulated for the shape optimization of viscous flow domain in the FSI fields. Also, a shape design problem is formulated to control the flow velocity distribution in the sub-domains of the flow domain. This latter problem can be treated as an inverse problem for minimizing the square error integration between the actual flow velocity distribution and the target flow velocity distribution in the sub-domains. Shape gradient of these shape design problems are derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the H¹ gradient method proposed as an approach to solving shape optimization problems. Numerical analysis programs for these shape optimization problems are developed by using FreeFEM, and the validity of proposed method is confirmed by results of 2D numerical analyses.