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Drag minimization for the obstacle in compressible flow using shape derivatives and finite volumes. (English) Zbl 1407.49067

Summary: In the paper the shape optimization problem for the static, compressible Navier-Stokes equations is analyzed. The drag minimizing of an obstacle immersed in the gas stream is considered. The continuous gradient of the drag is obtained by application of the sensitivity formulas derived in the works of one of the co-authors. The numerical approximation scheme uses mixed finite volume-finite element formulation. The novelty of our numerical method is a particular choice of the regularizing term for the non-homogeneous Stokes boundary value problem, which may be tuned to obtain the best accuracy. The convergence of the discrete solutions for the model under considerations is proved. The nonlinearity of the model is treated by means of the fixed-point procedure. The numerical example of an optimal shape is given.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
35Q30 Navier-Stokes equations
74S10 Finite volume methods applied to problems in solid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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