Speaker
Description
Background
Hypersonic flows are characterized by strong thermochemical nonequilibrium and complex physical phenomena, making both experimental investigations and numerical simulations particularly challenging. Trustworthy and scalable computational tools are therefore essential for the study of atmospheric entry, hypersonic flight, and other high-enthalpy aerothermodynamic applications. SPARK [1] is a software package dedicated to high-enthalpy aerothermodynamics, providing computational tools for CFD and line-by-line radiation simulations.
Methodology
This work presents HelioSPARK (HelioS), a new high-enthalpy CFD solver written in C++ and developed within the AMReX framework [2]. The solver is designed for block-structured adaptive mesh refinement (AMR) and large-scale high-performance computing. HelioS solves the compressible multi-species Navier–Stokes equations, including conservation of mass, momentum, total energy, chemical species, and internal energy modes. Advective fluxes are computed explicitly using the Colella–Glaz approximate Riemann solver [3], while diffusive fluxes (viscous stresses, species diffusion, and heat conduction) can be treated either explicitly or semi-implicitly. Stiff source terms, including finite-rate chemistry and internal energy exchange, are integrated locally in each computational cell using the CVODE implicit solver from the SUNDIALS library [4]. Time integration is performed using either Strang splitting or Spectral Deferred Correction (SDC) methods.
The solver employs the thermodynamic and kinetic database available within SPARK [1]. Thermodynamic properties are evaluated using NASA-9 polynomial fits, supporting one to four temperature formulations (1T–4T). HelioS includes multi-species finite-rate chemistry, transport properties computed either from Gupta–Yos curve fits or Wright and Levin tabulated data. Rotational, vibrational, and electronic energy modes can be represented using either characteristic temperatures or discrete energy levels.
Results
The solver, more specifically with 2 to 4 temperatures models, is currently undergoing verification and validation through a series of canonical and hypersonic benchmark cases. Verification includes oblique shock-wave problems for numerical solver verification and embedded-boundary verification cases. The validation process includes hypersonic conical bi-ramp simulations compared against experimental data and hypersonic sphere atmospheric-entry simulations benchmarked against SPARK CFD. Early results, for a single temperature model, demonstrate stable and robust numerical behavior across the verification cases, while the validation process is providing encouraging agreement with experimental measurements and reference numerical solutions. These test cases are intended to assess the accuracy and robustness of the numerical implementation for high-enthalpy thermochemical nonequilibrium flows.
Conclusion
HelioS provides a modular and scalable CFD framework for high-enthalpy hypersonic aerothermodynamics, combining adaptive mesh refinement with thermochemical nonequilibrium models. The ongoing verification and validation campaign aims to establish the solver as a reliable platform for future research and engineering applications involving atmospheric entry and other hypersonic flow problems.
The modular software architecture also provides a foundation for future extensions toward state-to-state kinetics and coupled radiation transport.
Acknowledgements
This work was supported by the FCT – Fundação para a Ciência e a Tecnologia, I.P., under projects
UID/50010/2025 (https://doi.org/10.54499/UID/50010/2025),
UID/PRR/50010/2025 (https://doi.org/10.54499/UID/PRR/50010/2025),
UID/PRR2/50010/2025 (https://doi.org/10.54499/UID/PRR2/50010/2025),
and LA/P/0061/2020 (https://doi.org/10.54499/LA/P/0061/2020).
References
[1] Lopez, B., and Lino Da Silva, M., "SPARK: A Software Package for Aerodynamics, Radiation and Kinetics," AIAA AVIATION Forum, AIAA Paper 2016-4025, 2016. https://doi.org/10.2514/6.2016-4025
[2] Zhang, W., et al., "AMReX: a framework for block-structured adaptive mesh refinement," Journal of Open Source Software, Vol. 4, No. 37, 2019, p. 1370. https://doi.org/10.21105/joss.01370
[3] Colella, P., and Glaz, H. M., "Efficient Solution Algorithms for the Riemann Problem for Real Gases," Journal of Computational Physics, Vol. 59, No. 2, 1985, pp. 264–289. https://doi.org/10.1016/0021-9991(85)90146-9
[4] Hindmarsh, A. C., Brown, P. N., Grant, K. E., Lee, S. L., Serban, R., Shumaker, D. E., and Woodward, C. S., "SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers," ACM Transactions on Mathematical Software, Vol. 31, No. 3, 2005, pp. 363–396. https://doi.org/10.1145/1089014.1089020
Summary
HELIOS is a high-enthalpy CFD solver for hypersonic thermochemical nonequilibrium flows. Built on the AMReX framework, it combines adaptive mesh refinement, multi-species finite-rate chemistry, and multi-temperature formulations. Ongoing verification and validation support its development as a scalable research platform for atmospheric-entry and hypersonic aerothermodynamic applications.