A stabilized parametric level‐set XFEM topology optimization method for thermal‐fluid problem

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.

Topology optimization of heat exchangers: A review

“…The LSF is set to be zero at the interface, and the nodal values of LSF can be solved based on a governing equation or interpolated on the computational domain by a space function called "basis functions". The LSM has also been applied in the TO of HXs [96], [104], [114]- [123]. Feppon et al [117] even used the LSM to deal with the 2D and 3D HXs involving two fluids.…”

“…As a very valuable attempt, Coffin and Maute [120] combined the XFEM and the LSM in the TO for the 2D and 3D, steady-state and transient single-flow heat transfer problems dominated by natural convection. Recently, Lin et al [123] performed a topology optimization using the LSM-XFEM coupling to optimize the channel topology for a 2D heat sink under steady-state conditions. Thanks to the features of XFEM and LSM, the interface is well captured during the iterative optimization process, while the computational burden increases at the same time.…”

Design of Viscoelastic Damped Plate Structures with a Multi-Material Topology Optimization Method

“…Among structural topology optimization (STO) methods, the level set method (LSM) could be a superior for description of boundaries [3,4]. Farther, parametric methods are proposed to alleviate the difficulty of solving level-set equations [5][6][7]. The discrete adjoint method is used to deal with sensitive boundaries to gain sensitivity with greater precision [8].…”

The Cut-Cell Method for the Conjugate Heat Transfer Topology Optimization of Turbulent Flows Using the “Think Discrete–Do Continuous” Adjoint

“…Regarding the former, the XFEM approach was introduced in [28] to perform TopO based on the level-set approach for 2D laminar flow problems. Recently, it has been utilized to increase the accuracy of TopO solvers in laminar [29] and turbulent flows [20], including heat transfer. In FVM methods for TopO, [30] utilized a ghost-cell immersed boundary method to apply wall boundary conditions for turbulent flow problems, without having to modify the background mesh.…”