Topology optimization of heat conduction problems using the finite volume method

This note addresses the use of the finite volume method (FVM) for topology optimization of a heat conduction problem. Issues pertaining to the proper choice of cost functions, sensitivity analysis, and example test problems are used to illustrate the effect of applying the FVM as an analysis tool for design optimization. This involves an application of the FVM to problems with nonhomogeneous material distributions, and the arithmetic and harmonic averages have here been used to provide a unique value for the conductivity at element boundaries. It is observed that when using the harmonic average, checkerboards do not form during the topology optimization process.