Topology optimization for subsonic compressible flows based on the material field series expansion model

The Material Field Series Expansion (MFSE) method has gained attention in structural topology optimization problems owing to its advantages, including well-defined structure boundaries and dimensionality reduction. In this work, we propose a fluid topology optimization method based on MFSE to address a entropy variation minimization problem governed by the equations of compressible flow. The proposed method defines a bounded material field with spatial correlation to characterize flow channel topology and expands it into a linear combination of eigenvectors and coefficients through a series expansion approach, employing the modal truncation strategy to truncate low-order modes to reduce the dimension of the optimization design space. This method inherently prevents checkerboard patterns and mesh dependency while effectively decoupling design variables from computational grids. The effectiveness of the proposed method is evaluated through several 2D and 3D optimization cases. Numerical experiments demonstrate that MFSE achieves comparable objective function values and topological configurations to conventional density-based methods under identical volume constraints. Concurrently, this approach accomplishes an order of magnitude reduction in design variables, decreasing from O(${10}^4$) to O(${10}^3$), which directly improves computational efficiency. Parameter studies on truncation error and correlation length further demonstrate their controllability over both the number of optimization variables and the intricacy of resulting topological features. Crucially, these studies provide practical guidance for balancing optimization computational cost against solution accuracy.