An improved implicit re-initialization method for the level set function applied to shape and topology optimization of fluid

This paper presents an accurate implicit re-initialization approach in the framework of a level set method. The improved method includes two schemes for keeping the zero level set unperturbed. The first scheme is to derive and use a new formula for the smoothing parameter in the conventional re-initialization equation based on the principle of the interface not moving. The second scheme is to reduce the local time step to avoid the interface moving across grid points when the sign of the level set function near the interface is changed. The example presented suggests that the new algorithm has a better approximation to the signed distance function and obtains a more accurate interface than the algorithm presented by Sussman et al. (1994). For shape and topology optimization of fluid, the effectiveness of the developed method in this paper was demonstrated by the internal and external flow examples.