Computing statistical solutions of a Mach 2000 astrophysical jet
Abstract
The multi-dimensional compressible Euler equations admit non-unique entropy solutions in turbulent regimes, and extreme-Mach astrophysical flows are a natural setting in which this breakdown of deterministic well-posedness becomes computationally visible. We compute statistical solutions of a Mach~2000 astrophysical jet, defined as the pushforward of an initial probability measure through a vectorial lattice Boltzmann method, by Monte Carlo sampling with M=1000 realizations on grids of up to $12.8$ million cells. Under mesh refinement the individual realizations diverge pathwise, while the statistical solution converges: Wasserstein distances of the one- and two-point marginals, the ensemble mean, and the ensemble standard deviation all exhibit stable positive convergence rates. A spatially resolved analysis along the jet axis traces this dichotomy to the structure of the one-point laws, which are numerically Dirac in the undisturbed core, skewed in the sheared turbulent regions, and intermittent two-state mixtures at the random leading front. We conclude that the computed statistical solution is non-Dirac and remains stable in the extreme compressible regime, in which no strong solution is expected to exist.
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BibTeX
@misc{simonis2026computing,
title = {{Computing statistical solutions of a Mach 2000 astrophysical jet}},
author = {Stephan Simonis and Gauthier Wissocq},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.25282},
eprint = {2605.25282},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25282},
}
RIS
TY - UNPB
TI - Computing statistical solutions of a Mach 2000 astrophysical jet
AU - Stephan Simonis
AU - Gauthier Wissocq
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2605.25282
UR - https://arxiv.org/abs/2605.25282
AB - The multi-dimensional compressible Euler equations admit non-unique entropy solutions in turbulent regimes, and extreme-Mach astrophysical flows are a natural setting in which this breakdown of deterministic well-posedness becomes computationally visible. We compute statistical solutions of a Mach~2000 astrophysical jet, defined as the pushforward of an initial probability measure through a vectorial lattice Boltzmann method, by Monte Carlo sampling with M=1000 realizations on grids of up to $12.8$ million cells. Under mesh refinement the individual realizations diverge pathwise, while the statistical solution converges: Wasserstein distances of the one- and two-point marginals, the ensemble mean, and the ensemble standard deviation all exhibit stable positive convergence rates. A spatially resolved analysis along the jet axis traces this dichotomy to the structure of the one-point laws, which are numerically Dirac in the undisturbed core, skewed in the sheared turbulent regions, and intermittent two-state mixtures at the random leading front. We conclude that the computed statistical solution is non-Dirac and remains stable in the extreme compressible regime, in which no strong solution is expected to exist.
ER -