HYPERsonic flows Simulation with innOvative NumerICS – HYPERSONICS

The HYPERSONICS project aims to significantly innovate in the field of numerical methods for simulating aerodynamic flows around vehicles traveling at speeds far exceeding the speed of sound, i.e., hypersonic speeds. The flight regime considered in this project corresponds to altitudes where the flow regime is continuous. This means that the characteristic length of the vehicle is much larger than the mean free path of air molecules. Under this assumption, the flow can be described within the framework of continuum mechanics using the Navier-Stokes equations, which simply express the conservation of mass, momentum, and energy of the fluid.

Hypersonic flows are characterized by extreme physical phenomena, such as detached shock waves through which the flow variables undergo a sharp discontinuity. Moreover, in a very thin region adjacent to the wall, called the boundary layer, strong velocity and temperature gradients are concentrated in the normal direction, inducing a transfer of momentum and energy to the wall. The accurate prediction of viscous friction and heat flux is crucial for controlling trajectory and designing thermal protection systems for hypersonic vehicles. Given the severity of the physical phenomena and their multi-scale nature, there is a real challenge for numerical methods as they must combine robustness and accuracy to capture intense shock waves while accurately resolving the flow in the boundary layer. This trade-off between precision and robustness requires perfect control of the inherent dissipation in numerical discretization methods.

Most production codes developed and used in national laboratories (NASA, DLR, ONERA, JAXA) or by industries (ARIANE GROUP) are based on Finite Volume numerical methods, developed in the early 1980s, where the numerical flux at interfaces is evaluated through approximated Riemann solvers. To our knowledge, none of these numerical methods guarantee both robustness and accuracy without resorting to ad hoc modifications/hybridizations. In this regard, the Roe solver (1981), which is certainly the most widely used method in production codes, requires some adjustments: an entropy correction, which increases numerical dissipation, is added to ensure robustness against strong shocks. However, this correction must be deactivated in the boundary layer to ensure faithful calculation and thus an accurate evaluation of friction and heat flux at the wall.

Based on this observation, the HYPERSONIC project aims to enrich the foundation of available numerical methods by proposing innovative approaches based on recently developed numerical methods by the team members, endowed with very interesting properties in terms of robustness: ability to handle arbitrary meshes, guarantee of mass density and energy positivity, and insensitivity to numerical instabilities that affect classical methods. The necessary increase in precision for an accurate description of the boundary layer will be achieved by developing extensions of these new numerical methods to very high precision orders, relying on the expertise of the team members in this field. The idea is to combine robustness and precision within the same numerical approach, while remaining not sensitive to the quality of the meshes and efficient in terms of computational cost.