Optimal shape design for fluid flow using topological perturbation technique

Abstract

This paper is concerned with an optimal shape design problem in fluid mechanics. The fluid flow is governed by the Stokes equations. The theoretical analysis and the numerical simulation are discussed in two and three-dimensional cases. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. An asymptotic expansion is derived for a large class of cost functions using small topological perturbation technique. A fast and accurate numerical algorithm is proposed. The efficiency of the method is illustrated by some numerical examples.

Optimization of Injectors Location in a Water Reservoirs Aeration Problem

“…We note that the topological sensitivity function depends on 0 and 0 solutions, respectively, to the direct and adjoint problems computed in the domain Ω (not in the perturbed one Ω \ , ) which is an interesting feature of the used approach. The mixed finite element method " 1 + bubble/ 1 " [16] is used for the space approximation of the problems (15) and (20). The obtained linear system is solved using Uzawa method [13].…”

“…where 0 and 0 are, respectively, solutions to the generalized Stokes problem (15) and its associated adjoint problem (20).…”

Topology Optimization of Time Dependent Viscous Incompressible Flows

“…Abstract and Applied Analysis 3 where is the velocity field solution to the Navier-Stokes system (9) in the perturbed domain Ω , = Ω \ O , :…”

“…They treated the material phase as porous medium where fluid flow is governed by Darcy's law. In [9], we have proposed a new topological optimization approach, for the Stokes system, based on the topological sensitivity analysis [10][11][12][13][14][15][16][17]. The optimal domain is constructed through the insertion of some obstacles in the initial one.…”

Shape optimization of turbine blade cooling system using topological sensitivity analysis method

“…This technique has been successfully used in different applications: identification of gas bubbles created during the mould filling process [12], optimization of injectors locations in water reservoirs [13], geometric control problem for fluid flow [14], etc.…”