Zhiming Gao2, Yichen Ma3
CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 135-164, 2010, DOI:10.3970/cmes.2010.066.135
Abstract Shape optimization technique has an increasing role in fluid dynamics problems governed by distributed parameter systems. In this paper, we present the problem of shape optimization of two dimensional viscous flow governed by the time dependent Navier-Stokes equations. The minimization problem of the viscous dissipated energy was established in the fluid domain. We derive the structure of continuous shape gradient of the cost functional by using the differentiability of a saddle point formulation with a function space parametrization technique. Finally a gradient type algorithm with mesh adaptation and mesh movement strategies is successfully and efficiently applied. More >
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