Optimal Shape Design for the Viscous Incompressible Flow

Details Optimal Shape Design for the Viscous Incompressible Flow Optimal Shape Design for the Viscous Incompressible Flow

2007-01-17

arxiv.org/abs/math/0701470v1

Mathematics

Optimization and Control

20 pages, 22 figures

Scientific paper

This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem of total dissipated energy was established in the fluid domain. We derive the structures of shape gradient of the cost functional by using the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. Finally a gradient type algorithm is effectively used for our problem.

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