A stabilized parametric level‐set <scp>XFEM</scp> topology optimization method for thermal‐fluid problem
Yi Lin, Yi Lin, An Li, An Li
Abstract
Abstract This article presents a stabilized level‐set topology optimization method for the design of a thermal‐fluid system. The steady‐state laminar Navier–Stokes equation and the convection–diffusion equation are used to model the thermal‐fluid problem. The compactly supported radial basis functions are employed to describe the fluid–solid interfaces. The extended finite element method is used to interpolate the material domain and the non‐slip interface conditions are weakly enforced by the Nitsche's method. To overcome the numerical instabilities during the optimization process, a distance‐regularized method based on adopting a modified energy potential functional is proposed and the signed distance property around the structural boundaries is obtained. In the numerical experiments, two‐dimensional numerical models considering minimizing the average or maximum temperature are used to reveal the validity and merits of the proposed method.