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Optimum design in fluid mechanical distributed-parameter systems. (English) Zbl 0571.49022

A new numerical method for the computation of the sensitivity of the design performance functional with respect to flow boundary variations is used to study the optimum design problems in fluid mechanics. This method is based on a modification of schemes in functional derivative sensitivity analysis and includes a specification of the optimal control algorithms in distributed-parameter systems. The control variable is the location of the boundary. Based on sensitivity considerations, iterative methods are derived for the determination of the optimum boundary location that minimizes a design performance functional defined by flow variables and their derivatives. Necessary conditions for minimum drag profile in time-dependent Navier-Stokes flows are derived and numerical algorithms based on the gradient method are formulated.

MSC:

90C52 Methods of reduced gradient type
49K40 Sensitivity, stability, well-posedness
76D05 Navier-Stokes equations for incompressible viscous fluids
93B35 Sensitivity (robustness)
93C10 Nonlinear systems in control theory
35Q30 Navier-Stokes equations
49K20 Optimality conditions for problems involving partial differential equations
65K10 Numerical optimization and variational techniques
93B40 Computational methods in systems theory (MSC2010)
93C20 Control/observation systems governed by partial differential equations
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