Drag minimization for the obstacle in compressible flow using shape derivatives and finite volumes
| Autor: | Anna Kaźmierczak, Jan Sokołowski, Antoni Zochowski |
|---|---|
| Přispěvatelé: | University of Lódź, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems Research Institute [Warsaw] (IBS PAN), Polska Akademia Nauk = Polish Academy of Sciences (PAN) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Control and Optimization Finite volume method Applied Mathematics Numerical analysis 010102 general mathematics Mathematical analysis 02 engineering and technology 01 natural sciences Compressible flow Finite element method 020901 industrial engineering & automation Drag Compressibility Shape optimization Boundary value problem 0101 mathematics [MATH]Mathematics [math] ComputingMilieux_MISCELLANEOUS ComputingMethodologies_COMPUTERGRAPHICS Mathematics |
| Zdroj: | Mathematical Control & Related Fields Mathematical Control & Related Fields, 2018, 8 (1), pp.89-115. ⟨10.3934/mcrf.2018004⟩ |
| ISSN: | 2156-8499 |
| DOI: | 10.3934/mcrf.2018004⟩ |
| Popis: | 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 non-linearity of the model is treated by means of the fixed point procedure. The numerical example of an optimal shape is given. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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