A Eulerian-compatible split-cell scheme for piston tracking in high-enthalpy wind tunnels

High-speed wind tunnels rely on high-pressure driver systems, often involving free-moving pistons, to achieve hypersonic velocities at high-enthalpy conditions. Modeling of the whole system, starting from the piston, is needed to predict the thermochemical state of the flow in the test section. Traditional Lagrangian methods, while effective for tracking piston dynamics, are more computationally expensive and more algorithmically involved than Eulerian approaches. To address these limitations, a novel Eulerian-compatible split-cell scheme has been developed, allowing piston tracking within a unified finite-volume framework. The method relies on a local remeshing strategy and is applicable to both implicit and explicit time advancing schemes. The performance of the free-piston model derived in this work is evaluated by integrating it into HYQ1D (Hypersonic Quasi-1-Dimensional) code and simulating parts or the entirety of the UQ-T4 (University of Queensland's T4 tunnel) and DLR-HEG (German Aerospace Center - High Enthalpy Shock Tunnel Göttingen) facilities. The results of the tracking algorithm are verified through two different tests: the Jacobs (1998)'s test case [P. A. Jacob, "Shock tube modelling with l1d," Technical Research report 13/98, The University of Queensland (1998)], and the second is a comparison with the L1d code on the UQ-T4 simulations. Furthermore, the code is also validated against experimental results from a now archived shot condition (n. 51) of the DLR-HEG facility. These findings confirm that this approach provides a robust solution for simulating free-piston shock tunnels under realistic test conditions while maintaining compatibility with existing Eulerian fluid dynamics tools.