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An explicit level set approach for generalized shape optimization of fluids with the lattice Boltzmann method
Author(s) -
Kreissl Sebastian,
Pingen Georg,
Maute Kurt
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2193
Subject(s) - lattice boltzmann methods , topology optimization , level set method , shape optimization , nonlinear system , level set (data structures) , mathematics , mathematical optimization , flow (mathematics) , boundary value problem , fluid dynamics , interpolation (computer graphics) , boundary (topology) , representation (politics) , computer science , topology (electrical circuits) , mathematical analysis , geometry , finite element method , combinatorics , politics , political science , law , animation , physics , computer graphics (images) , quantum mechanics , segmentation , artificial intelligence , mechanics , image segmentation , thermodynamics
This study is concerned with a generalized shape optimization approach for finding the geometry of fluidic devices and obstacles immersed in flows. Our approach is based on a level set representation of the fluid–solid interface and a hydrodynamic lattice Boltzmann method to predict the flow field. We present an explicit level set method that does not involve the solution of the Hamilton–Jacobi equation and allows using standard nonlinear programming methods. In contrast to previous works, the boundary conditions along the fluid–structure interface are enforced by second‐order accurate interpolation schemes, overcoming shortcomings of flow penalization methods and Brinkman formulations frequently used in topology optimization. To ensure smooth boundaries and mesh‐independent results, we introduce a simple, computationally inexpensive filtering method to regularize the level set field. Furthermore, we define box constraints for the design variables that guarantee a continuous evolution of the boundaries. The features of the proposed method are studied by two numeric examples of two‐dimensional steady‐state flow problems. Copyright © 2009 John Wiley & Sons, Ltd.