Drag Minimization for Navier-Stokes Flow

作者：Gao Zhiming^*; Ma Yichen; Zhuang Hongwei

来源：Numerical Methods for Partial Differential Equations, 2009, 25(5): 1149-1166.

DOI：10.1002/num.20392

• gradient algorithm
• minimax principle
• Navier-Stokes equations
• shape derivative
• shape optimization

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.

• 出版日期2009-9
• 单位北京应用物理与计算数学研究所; 西安交通大学; 中国人民武装警察部队工程大学