Level Set-Based Topology Optimization in an Incompressible Viscous Fluid Applying Immersed Boundary Method on Wall Treatment
Atsushi KOGUCHI, Seiji KUBO, Kentaro Yaji, Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki · Sekkei Kougaku, Shisutemu Bumon Kouenkai kouen rombunshuu/Sekkei Kogaku, Shisutemu Bumon Koenkai koen ronbunshu · 2016
This paper describes a new method of topology optimization in fluid mechanics. The basic idea of this method is that level set function is defined to represent a boundary of solid and fluid region for construction of optimal structure. In addition, immersed boundary method is also applied to define Dirichlet and/or Neumann boundary condition on the zero level set function. Applying immersed boundary method, the fluid state field such as velocity and pressure can be estimated just in fluid region so that optimal structure can be obtained more precisely. The optimization problem is formulated to minimize total pressure loss under a volume constraint. During the optimization process, the sensitivity of optimization is also solved effectively because it is based on continuous adjoint method. The level set function updating scheme uses a reaction-diffution equation. Example is shown to confirm this new optimization method.