Topology optimization of simplified convective heat transfer problems using the finite volume method

Topology optimization of simplified convective heat transfer has been widely studied, but most existing studies are based on the finite element method (FEM); methods based on the finite volume method (FVM) have been less studied. In this paper, a topology optimization method based on FVM was proposed for a simplified convective heat transfer problem. We developed a novel adjoint sensitivity analysis method applicable to FVM, which included adjoint equations, corresponding boundary conditions, and sensitivity analysis equations. Additionally, a program for the proposed topology optimization method was developed in open field operation and manipulation (OpenFOAM) and portable, extensibletoolkit for scientific computation (PETSc). Thus, large-scale topology optimizations could be performed in parallel. Furthermore, numerical examples of the classical two-dimensional (2D) and 3D optimization problems were considered. The results verified the effectiveness and feasibility of the proposed method. The results of large-scale 3D examples show an interesting phenomenon that for the optimized designs with few features, the large-scale topology optimization is still valuable for obtaining more effective structural shapes.