An explicit level set approach for generalized shape optimization of fluids with the lattice Boltzmann method

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 (C) 2009 John Wiley & Sons, Ltd.