Density-Based Topology Optimization for Turbulent Flows with Wall Functions: A Penalty Method for Enforcing Multiple Boundary Conditions

  • Bayat, Amirhossein (University of southern Denmark)
  • Li, Hao (University of southern Denmark)
  • Alexandersen, Joe (University of southern Denmark)

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Density-based topology optimization (TO) for high–Reynolds-number turbulent flows faces three key challenges: (i) accurate near-wall prediction, (ii) prohibitive computational cost if the viscous sublayer must be resolved, and (iii) the absence of an explicit solid–fluid interface in density-based formulations [1]. In this work, we investigate a penalty-based methodology that addresses these challenges within a unified framework. Byincorporating wall functions, accurate boundary-layer profiles are obtained on relatively coarse meshes, improving fidelity while substantially reducing computational cost. Compared with an otherwise identi cal formulation without wall functions, the proposed approach yields markedly better near-wall predic tions and closely matches verification simulations performed on explicit-wall (body-fitted) re-meshes, outperforming conventional density-based turbulent TO treatments. Furthermore, by exploiting gradients of the filtered design field, the wall location and its normal direction are identified implicitly, enabling the wall-function relations to be imposed robustly and in a differentiable manner suitable for gradient-based optimization. Beyond turbulent wall modeling, the same implicit-interface and penalty concept provides a convenient route to implement other boundary conditions within density-based TO, including free-slip boundary condition [2].