Federal Project Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded $176,763 under the Mathematical and Physical Sciences program (CFDA 47.049) to The Research Foundation For The State University Of New York at the University at Albany, effective July 1, 2026, through June 30, 2029. This collaborative research project develops computational tools and theoretical frameworks for predicting heat transfer and fluid flow through perforated materials—complex materials with microscopic pores found in filtration systems, battery cooling devices, heat exchangers, and advanced manufactured products. The deliverables include a non-intrusive computational framework combining stochastic formulations based on particle trajectories with flexible function representations to approximate large-scale behavior without resolving fine-scale geometry, thereby reducing computational costs while maintaining accuracy.

The project extends this framework to time-dependent multiscale problems, with key deliverables encompassing theoretical foundations for understanding interactions between stochastic sampling, time discretization, and physical dynamics, as well as efficient sampling strategies optimized for stability and accuracy across diverse geometries and boundary conditions. The research directly supports the program's objective to strengthen the nation's scientific enterprise while providing broader impact through undergraduate education in scientific computing and data science, training the next generation of scientists and engineers in modern computational and data-driven methodologies applicable to energy-efficient technology design and industrial process improvement.