Shape optimization method applied to room design based on an incompressible fluid model (Topology optimization theory and applications toward wide fields of natural sciences)

Abstract

This paper presents numerical results obtained, using a numerical method for a flow field shape optimization, for the design of a room from which people can evacuate smoothly. The domain of interest is a two-dimensional Poiseuille flow with sudden contraction in which a disk is located initially. In fact, the compressible fluid model has been used to describe the dynamics of people for the study of evacuation. However, we set a model involving the incompressible Navier-Stokes equation for the first trial. And the shape optimization to minimize the dissipation energy on the disk is demonstrated under the volume constraint. For reshaping numerically, the traction method is used. Numerical results reveal that the shape in the wake of the disk becomes an acute angle to decrease the dissipation energy monotonically, thereby satisfying the volume constraint. Such a shape has never been inferred from results of earlier studies of the evacuation problem in jamology.