Level set topology optimization of fluids in Stokes flow

Abstract

SUMMARYWe propose the level set method of topology optimization as a viable, robust and efficient alternative to density-based approaches in the setting of fluid flow. The proposed algorithm maintains the discrete nature of the optimization problem throughout the optimization process, leading to significant advantages over density-based topology optimization algorithms. Specifically, the no-slip boundary condition is implemented directly-this is accurate, removes the need for interpolation schemes and continuation methods, and gives significant computational savings by only requiring flow to be modeled in fluid regions. Topological sensitivity information is utilized to give a robust algorithm in two dimensions and familiar two-dimensional power dissipation minimization problems are solved successfully. Computational efficiency of the algorithm is also clearly demonstrated on large-scale three-dimensional problems.

Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model

“…The pressure loss of the optimal solution ( Figure 5(a)) is 18.46, whereas the pressure loss of the channel with a narrowed inlet ( Figure 5(b)) is 19.33. Reference [25] reports the similar result that the wider inlet indicates the lower pressure loss when finer mesh is employed. Although it is thought that this issue comes from the mesh resolution in previous study [25,26], the fundamental cause is not clear because of several unclear factors in previous studies such as whether the width of the flow profile w in Equation (16) is modified adaptively with the change of the inlet length during the optimization.…”

“…The third constraint aims to avoid aberrant flow channels with excessive pressure loss, which may make the estimation accuracy of the Kriging model worse. Moreover, in this case, because the boundary of flow channel is curved as in the previous work [25], infinitesimal control points are suitable to represent various topological changes.…”

Mechanics-Based Solution Verification for Porous Media Models

“…Pipe bend problem. As another application of the proposed techniques, we consider an engineering problem commonly found in the fluid mechanics literature, which is called the pipe bend problem (for example, see References [Borrvall and Petersson, 2003;Hansen et al, 2005;Aage et al, 2008;Pingen et al, 2009;Challis and Guest, 2009;Hassine, 2012]). In the pipe bend problem, the computational domain Ω is a square with L = 1.…”

Shape and topology optimization based on the convected level set method

“…Many previous studies have applied structural optimization based on the level set method to a variety of optimization problems, such as a stiffness maximization problem for linear and nonlinear elastic structures (Allaire et al 2004;Luo and Tong 2008), a shell structure design problem (Park and Youn 2008), and a multi-material design problem (Wang and Wang 2004;Luo et al 2009). In addition, level set-based approaches have been applied to other physical problems such as fluid problems (Amstutz and Andrä 2006;Challis and Guest 2009), and electromagnetic problems (Khalil et al 2010;Zhou et al 2010). …”

“…The advantage of this approach is that since it is unnecessary to include holes corresponding to the void domain in the initial design, the dependency of optimal shapes with respect to the initial design settings can be mostly avoided. This approach has been applied to various optimization problems such as a stress minimization problem (Allaire and Jouve 2008), and fluid problems (Amstutz and Andrä 2006;Challis and Guest 2009).…”