2006/12/06 by Zhiming Gao, Gao, Zhiming, Yichen Ma +3
Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Topology Optimization in Engineering #math.AP #math.OC #msc:35B37 #msc:35Q30 #msc:49K40
paper · pdf · doi:10.48550/arxiv.math/0612154
22 pages, 5 figures
arxiv created 2006/12/06 · arxiv updated 2009/12/01
This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for time-dependent cost functionals by using the state derivative with respect to the shape of the fluid domain and its associated adjoint state. Finally we apply a gradient type algorithm to our problem and numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible in low Reynolds number flow.