Topology optimization of incompressible Navier–Stokes problem by level set based adaptive mesh method
This paper presents a level set based adaptive mesh method for solving the topology optimization of incompressible Navier–Stokes problem. The objective is to minimize the dissipated power in the fluid, subject to the Navier–Stokes problem as state equations with a fluid volume constraint. The materi...
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| Published in | Computers & mathematics with applications (1987) Vol. 72; no. 4; pp. 1131 - 1141 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.08.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0898-1221 1873-7668 |
| DOI | 10.1016/j.camwa.2016.06.034 |
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| Abstract | This paper presents a level set based adaptive mesh method for solving the topology optimization of incompressible Navier–Stokes problem. The objective is to minimize the dissipated power in the fluid, subject to the Navier–Stokes problem as state equations with a fluid volume constraint. The material distribution information that implicitly represented via level set function is considered as the design variable, which provides an easy way to construct the refinement indicator. Shape and topology sensitivity analysis suggest the steepest descent direction. By the proposed method, the computational expense is mainly focused near the interfaces, which lead to a significant reduction of the computational cost. Although illustrated by the Navier–Stokes problem, we would like to emphasize that our method is not restricted to this particular situation, it can be applied to a wide range of shape or topology optimization problems arising from the fluid dynamics. |
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| AbstractList | This paper presents a level set based adaptive mesh method for solving the topology optimization of incompressible Navier–Stokes problem. The objective is to minimize the dissipated power in the fluid, subject to the Navier–Stokes problem as state equations with a fluid volume constraint. The material distribution information that implicitly represented via level set function is considered as the design variable, which provides an easy way to construct the refinement indicator. Shape and topology sensitivity analysis suggest the steepest descent direction. By the proposed method, the computational expense is mainly focused near the interfaces, which lead to a significant reduction of the computational cost. Although illustrated by the Navier–Stokes problem, we would like to emphasize that our method is not restricted to this particular situation, it can be applied to a wide range of shape or topology optimization problems arising from the fluid dynamics. |
| Author | Duan, Xianbao Qin, Xinqiang Li, Feifei |
| Author_xml | – sequence: 1 givenname: Xianbao surname: Duan fullname: Duan, Xianbao email: xianbaoduan@hotmail.com – sequence: 2 givenname: Feifei surname: Li fullname: Li, Feifei – sequence: 3 givenname: Xinqiang surname: Qin fullname: Qin, Xinqiang |
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| Cites_doi | 10.1006/jcph.1999.6345 10.1002/fld.426 10.1137/S106482759732455X 10.1006/jcph.1994.1187 10.1002/nme.4463 10.1002/nme.1468 10.1051/cocv:2005012 10.1017/S002211207300145X 10.1016/j.jmaa.2009.02.045 10.1016/0021-9991(88)90002-2 10.1006/jcph.1998.6106 10.1007/s00158-007-0105-7 10.1016/0045-7825(88)90086-2 10.1016/j.jcp.2008.08.022 10.1006/jcph.1996.0130 10.1002/fld.715 10.1002/nme.1560 10.1002/nme.2616 10.1002/nme.1620371408 10.1016/j.physleta.2007.09.070 10.1006/jcph.1995.1098 10.1007/BF01650949 |
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| Keywords | Topology optimization Material distribution Adaptive mesh refinement Level set method Navier–Stokes problem |
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| SubjectTerms | Adaptive mesh refinement Computational fluid dynamics Fluid flow Fluids Incompressible flow Level set method Material distribution Mathematical models Navier-Stokes equations Navier–Stokes problem Sensitivity analysis Topology optimization |
| Title | Topology optimization of incompressible Navier–Stokes problem by level set based adaptive mesh method |
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