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Entropy-conservative high-order method for real gas flows

Simulation of complex multi-species reacting flows (such as those occurring in combustion processes or during spacecraft re-entry) requires modelling of the internal degrees of freedom of the constituent chemical species. At the same time, it is desirable to have numerical methods that are entropy-conservative/entropy-stable, which necessitates the development of entropy-conservative flux functions. Bringing these two requirements (the ability to model internal degrees of freedom and entropy conservation) is not trivial, as the internal energies can have very complicated dependencies on the gas state.

We propose a numerical method that works for arbitrary internal energy functions, based on linear interpolation of discretized and tabulated values of the internal degrees of freedom-related quantities (energy, specific heat, entropy). The method has been implemented in the Trixi.jl numerical framework for DG-based simulations of hyperbolic problems, and compared to results obtained via the DLR TAU code, showing excellent agreement between the two approaches.

This figure shows the pressure field for a supersonic flow around a cylinder, computed using the DLR TAU code (left) and the newly developed entropy-conservative method implemented in Trixi.jl (right).

This figure shows the temperature profiles along the stagnation line computed using the DLR TAU code and the new method.

arXiv preprint / Code repository

Contact: Dr. Georgii Oblapenko