Computing statistical solutions of a Mach 2000 astrophysical jet
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arXiv
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| Format: | Preprint |
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2026
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| author | Simonis, Stephan Wissocq, Gauthier |
| author_facet | Simonis, Stephan Wissocq, Gauthier |
| contents | The simulation of extreme Mach astrophysical flows is traditionally viewed through the lens of deterministic positivity-preserving schemes. However, due to Kelvin--Helmholtz instabilities and shock anomalies, the multi-dimensional Euler equations admit a variety of non-unique entropy solutions in turbulent regimes. Here, we computationally explore the limits of 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 operator. Utilizing optimized CUDA kernels, we compute an ensemble of 1000 Monte Carlo samples across a sequence of highly 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 results demonstrate that while individual flow realizations physically diverge due to chaotic shear-layer instabilities, the statistical solution converges to an admissible limit measure at a rate of 0.5. Consequently, we provide numerical evidence that the statistical solution to the considered problem is non-Dirac and remains stable in the extreme compressible regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25282 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing statistical solutions of a Mach 2000 astrophysical jet Simonis, Stephan Wissocq, Gauthier Numerical Analysis Mathematical Software Computational Physics Fluid Dynamics 76N10, 76M25 The simulation of extreme Mach astrophysical flows is traditionally viewed through the lens of deterministic positivity-preserving schemes. However, due to Kelvin--Helmholtz instabilities and shock anomalies, the multi-dimensional Euler equations admit a variety of non-unique entropy solutions in turbulent regimes. Here, we computationally explore the limits of 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 operator. Utilizing optimized CUDA kernels, we compute an ensemble of 1000 Monte Carlo samples across a sequence of highly 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 results demonstrate that while individual flow realizations physically diverge due to chaotic shear-layer instabilities, the statistical solution converges to an admissible limit measure at a rate of 0.5. Consequently, we provide numerical evidence that the statistical solution to the considered problem is non-Dirac and remains stable in the extreme compressible regime. |
| title | Computing statistical solutions of a Mach 2000 astrophysical jet |
| topic | Numerical Analysis Mathematical Software Computational Physics Fluid Dynamics 76N10, 76M25 |
| url | https://arxiv.org/abs/2605.25282 |