Scalable Control-Volume-Based Length-Scale Constraints for Thermofluid Topology Optimization
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The ability to control geometric length scales is central to topology optimization for thermofluid problems, where local feature sizes directly influence flow regime, pressure losses, and heat-transfer performance. Multiple strategies have been proposed in the literature to enforce minimum feature sizes, including geometric projection-based constraints and curvature-based indicators applied to filtered density fields. While effective in specific settings, these approaches either rely on discrete geometric constructions or are intrinsically limited to minimum length-scale control, and their extension to robust maximum feature size enforcement in thermofluid topology optimization remains challenging. Control-volume-based measures provide a natural geometric interpretation of local feature size and have been widely used for characterization purposes. However, their direct use in density-based topology optimization is often hindered by discrete estimation errors, non-smooth activation, and are usually hard to implement efficiently in parallel distributed architecture. To address these limitations, this work presents a control-volume-inspired length-scale constraint base on a tuned Helmholtz-filtered density field. Local material accumulation is evaluated through a smoothly filtered physical density field, avoiding explicit discrete volume estimation while retaining a geometric interpretation and easy of evaluation for parallel distributed solver architecture. The proposed formulation enables the enforcement of both minimum and maximum local feature size constraints using the same underlying framework. Constraint activation is governed by volumetric thresholds calibrated on canonical geometries, ensuring consistent behavior across mesh resolutions and providing well-defined geometric meaning. Numerical tests in thermofluid topology optimization demonstrate stable convergence under gradient-based optimization and effective regulation of both thin and overly bulky features. The method offers a robust and adjoint-compatible alternative to existing length-scale control techniques for thermofluid topology optimization.
