Computational methods for designing geometry-engineered thermoelectric devices

Thermoelectric devices (TEDs) have attracted great attention due to their capability to directly convert heat into electricity or vice versa, enabling applications in waste heat recovery and active cooling. The energy conversion efficiency of TEDs is dictated by both intrinsic material properties and device-level structural features that govern heat and charge transport. Recently, the geometric design of thermoelectric (TE) legs has emerged as a transformative strategy to regulate thermal and electrical transport and ultimately improve efficiency. These geometric designs are increasingly developed through computational modeling and numerical simulations. This article provides a comprehensive overview of computational modelling methods for designing geometry-optimized TEDs, emphasizing how advanced geometric designs and modelling techniques are used to enhance energy conversion efficiency and thermal management. We cover fundamental principles, theoretical modelling, and various computational methods, including gradient-based and non-gradient-based techniques as well as machine learning approaches. Key factors influencing device performance are identified, and representative case studies illustrate the impact of innovative leg geometries on power density and reliability. Finally, we summarize current challenges and propose future research directions to advance the geometric optimization of TEDs through intelligent, robust, and efficient computational frameworks.