We show a supersonic turbulence simulation in a periodic box fueled by perpetual kinetic energy injection on the largest three modes. Such setups are subject of active research in astrophysics and are believed to play an important role in the dynamics of galactic clouds and star formation, e.g., [1,2,3]. An initially uniform density distribution (left plot in the video) is gradually driven to a turbulent state till an average velocity of Mach 3.5 is reached (about t=0.19). Locally, speeds can spike above Mach 35 (bottom right plot in the video). The simulation was computed on FLUXO (https://github.com/project-fluxo/fluxo) with a robust invariant domain preserving Discontinuous Galerkin scheme (DG) [4] solving the compressible, quasi-isothermal ($\gamma =1.001$) Euler equations on a uniform grid with $128^3$ degrees-of-freedom.

Smooth blending with a monotone finite volume scheme stabilizes the high-order DG at strongly shocked regions (filaments of high density concentration) displayed by the blending parameter plot (top right in the video). Blue encodes regions of 100% high order DG while red dots indicate focused blending with FV. Hypersonic turbulence regimes are very challenging for any numerical scheme considering the stark gradients in density, bubbles of near-vacuum and the extremely high speeds involved in such simulations.

[1] https://academic.oup.com/mnras/article/436/2/1245/1126116
[2] https://adsabs.harvard.edu/full/1981MNRAS.194..809L]
[3] https://academic.oup.com/mnras/article/480/3/3916/5060766
[4] Rueda-Ramírez, A. M., Pazner, W., & Gassner, G. J. (2022). Subcell limiting strategies for discontinuous Galerkin spectral element methods. arXiv preprint arXiv:2202.00576.