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Drag minimization for Navier–Stokes Flow
Author(s) -
Gao Zhiming,
Ma Yichen,
Zhuang Hongwei
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20392
Subject(s) - mathematics , drag , minification , parametrization (atmospheric modeling) , differentiable function , partial derivative , stokes flow , balanced flow , minimax , partial differential equation , state space , flow (mathematics) , mathematical optimization , mathematical analysis , geometry , mechanics , physics , statistics , quantum mechanics , radiative transfer
This paper investigates the drag minimization in a two‐dimensional flow which is governed by a nonhomogeneous Navier–Stokes equations. Two approaches are utilized to derive shape gradient of the cost functional. The first one is to use the shape derivative of the fluid state and its associated adjoint state; the second one is to utilize the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. Finally, a gradient type algorithm is effectively formulated and implemented for the mentioned drag minimization problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009