Efficient multi-stage aerodynamic topology optimization using an operator-based analytical differentiation

Abstract A high-performance density-based topology optimization tool is presented for laminar flows with focus on 2D and 3D aerodynamic problems via OpenFOAM software. Density-based methods are generally robust in terms of initial design, making them suitable designing purposes. However, these require relatively fine resolutions external flow to accurately capture the solid-fluid interfaces Cartesian meshes, which makes computationally very expensive, particularly problems. To address such high computational costs, two techniques developed here. Firstly, an operator-based analytical differentiation (OAD) proposed, efficiently computes exact partial derivatives solver (simpleFOAM). OAD also facilitates a convenient development process by minimizing hand-coding utilizing chain-rule technique, contrast full hand-differentiation, complex prone implementation errors. Secondly, multi-stage design proposed further reduce costs. In this instead using fixed refined mesh, processes initiated coarse converged solutions projected locally mesh (as guess) secondary stage, can be repeated obtain sufficient accuracy. set were studied, promisingly confirmed utility present approach, adopted as starting point developing large-scale engineering applications. addition, indicated that less than $$3\%$$ 3 % total CPU-time devoted OAD, multi-staging up $$45\%$$ 45 has reduced overall