Abstract:The simulation of extreme Mach astrophysical flows is traditionally viewed through the lens of deterministic positivity-preserving schemes. However, due to phenomena such as Kelvin--Helmholtz instabilities and shock anomalies, the multi-dimensional Euler equations admit a plethora of non-unique entropy solutions in turbulent regimes. For the first time, we computationally explore the weak-strong uniqueness of a Mach 2000 jet by defining the statistical solution as the pushforward of a probability measure through a vectorial lattice Boltzmann method (VLBM) operator. Utilizing highly optimized CUDA kernels, we compute an ensemble of 1000 Monte Carlo samples across a sequence of unprecedentedly refined spatial grids of up to 3.2 million cells, and subsequently post-process the empirical measures via memory-mapped CPU streaming. We contrast the strong sample-wise $L^1$ error divergence with the convergence of the probability measure in the 1-point Wasserstein distance via empirical Cauchy rates. Our mathematical results demonstrate that while individual flow realizations physically diverge due to chaotic shear-layer instabilities, the macroscopic statistical solution converges to a well-defined limit measure at a rate of 0.5. Conclusively, we provide the first numerical verification of statistical solution stability in the extreme compressible regime.
| Subjects: | Numerical Analysis (math.NA); Mathematical Software (cs.MS); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn) |
| MSC classes: | 76N10, 76M25 |
| Cite as: | arXiv:2605.25282 [math.NA] |
| (or arXiv:2605.25282v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25282 arXiv-issued DOI via DataCite (pending registration) |
From: Stephan Simonis [view email]
[v1]
Sun, 24 May 2026 22:34:25 UTC (7,075 KB)
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