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<p>A topology optimization framework for incompressible fluid flows based on the penalty finite element method (PFEM) is proposed. The discrete formulation that combines the streamline-upwinding Petrov–Galerkin (SUPG) scheme with the single- and double-penalty FEM is presented in detail, the computational procedures for solving the flow problems are described, and the employed preconditioner and iterative solvers are tested and analyzed. Furthermore, the proposed method is compared with the SUPG-pressure-stabilized Petrov–Galerkin (SUPG-PSPG) FEM in terms of execution time and memory consumption for incompressible fluid flow topology optimization. Numerical results indicate that, for the cases investigated in this study, reductions of 70% and 57% in steady and transient execution times for 2-D problems are achieved through the single-penalty FEM. In the 3-D transient case, an 18% reduction in execution time is yielded by the double-penalty approach. Furthermore, a reduction in memory consumption exceeding 40% is observed.</p>

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On the penalty finite element method for density-based topology optimization of time-dependent incompressible fluid flow problems

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • Xin Zhang,
  • Jingjie He,
  • Xiaopeng Zhang,
  • Jifeng Zhang,
  • Yulong Ji

摘要

A topology optimization framework for incompressible fluid flows based on the penalty finite element method (PFEM) is proposed. The discrete formulation that combines the streamline-upwinding Petrov–Galerkin (SUPG) scheme with the single- and double-penalty FEM is presented in detail, the computational procedures for solving the flow problems are described, and the employed preconditioner and iterative solvers are tested and analyzed. Furthermore, the proposed method is compared with the SUPG-pressure-stabilized Petrov–Galerkin (SUPG-PSPG) FEM in terms of execution time and memory consumption for incompressible fluid flow topology optimization. Numerical results indicate that, for the cases investigated in this study, reductions of 70% and 57% in steady and transient execution times for 2-D problems are achieved through the single-penalty FEM. In the 3-D transient case, an 18% reduction in execution time is yielded by the double-penalty approach. Furthermore, a reduction in memory consumption exceeding 40% is observed.