Topology optimization using the lattice Boltzmann method incorporating level set boundary expressions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:274

Article

Yaji, Kentaro¹  Yamada, Takayuki¹  Yoshino, Masato²  Matsumoto, Toshiro³  Izui, Kazuhiro¹  Nishiwaki, Shinji¹ 

[1] Kyoto Univ, Grad Sch Engn, Dept Mech Engn & Sci, Kyoto 6158540, Japan

[2] Shinshu Univ, Fac Engn, Dept Mech Syst Engn, Nagano 3808553, Japan

[3] Nagoya Univ, Grad Sch Engn, Dept Mech Engn & Sci, Nagoya, Aichi 4648603, Japan

关键词: Topology optimization;    Level set method;    Phase field method;    Lattice Boltzmann method;    Boltzmann equation;    Adjoint variable method;   

DOI  :  10.1016/j.jcp.2014.06.004

来源: Elsevier

【 摘 要 】

This paper presents a topology optimization method for fluid dynamics problems, based on the level set method and using the lattice Boltzmann method (LBM). In this optimization method, the optimization problems are formulated based on the original Boltzmann equation, and the design sensitivities are precisely obtained without the time-consuming numerical operations encountered when dealing with a large-scale asymmetric matrix, in contrast to previous research in which the LBM uses the lattice Boltzmann equation (LBE) for the formulations of optimization problems and the derivation of their adjoint equations. That is, we newly derive sensitivity formulations from the original Boltzmann equation, not the LBE that can be said to be an approximated equation, and these formulations yield strictly correct sensitivities that are error free. Based on the above formulations, we construct a level set-based topology optimization method incorporating a fictitious interface energy for the design of a fluid channel that minimizes flow friction. Furthermore, two- and three-dimensional numerical examples are provided to confirm the validity and utility of the presented method. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free