Collaborative Research: Stochastic approach for material properties and fluid motions in perforated domains

This project develops robust and efficient computational tools to predict how heat and fluids move through complex materials containing many small holes or pores. Such materials appear in important technologies, including water and air filtration systems, battery cooling devices, heat exchangers, and advanced manufactured materials. Accurately simulating these systems is challenging because their microscopic structures strongly influence large-scale behavior, often making conventional simulations prohibitively expensive. By enabling fast and reliable predictions without resolving every microscopic detail, the project aims to significantly reduce computational cost while maintaining accuracy. The resulting advances could improve the design of energy-efficient technologies, industrial processes, and engineered materials. The project also integrates undergraduate education by engaging students in hands-on research in scientific computing and data science, helping to train the next generation of scientists and engineers in modern computational and data-driven methods. The project focuses on developing a non-intrusive computational framework to approximate macroscopic solutions to multiscale heat transfer and fluid flow problems in perforated domains. Building on the Derivative-Free Loss Method, the approach combines a stochastic formulation based on particle trajectories with flexible function representations to capture large-scale behavior without resolving fine-scale geometry. The research extends this framework to time-dependent problems, where a central challenge lies in understanding the interaction between stochastic sampling, time discretization, and physical dynamics. The work will establish theoretical foundations for this coupling and design efficient sampling strategies that improve stability and accuracy across diverse geometries and boundary conditions. In addition, the project will develop a neural-network-free implementation to reduce computational overhead and improve scalability. Applications include the homogenization of transient heat transfer and large-scale fluid simulations in perforated materials, providing both methodological advances and validation benchmarks. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2607647 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Jihun Han | Institution: SUNY at Albany, ALBANY, NY | Award Amount: $176,763 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2607647 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2607647.html