Multi-objective Shape Optimization of Unsteady Heat-convection Fields

This paper presents a numerical solution to multi-objective shape optimization problem of unsteady heat-convection fields.
The multi-objective shape optimization problem using normalized objective functional is formulated for the temperature distribution prescribed problem and the total dissipated energy minimization problem in unsteady heat-convection fields. Shape gradient of the multi-objective shape optimization problem is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the traction method proposed as an approach to solving shape optimization problems. Numerical analyses program for the shape optimization is developed based on FreeFem++, and the validity of proposed method is confirmed by results of 2D numerical analyses.