This paper has been withdrawn by Arun Govind Neelan
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Abstract:In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture shocks and other discontinuities in compressible flows. Conversely, utilizing non-conservative forms often introduces significant errors near these discontinuities or results in smeared shocks. This dependency poses a considerable limitation, particularly as many PDEs encountered in complex physical phenomena, such as multi-phase flows, are inherently non-conservative. This inherent non-conservativity restricts the direct applicability of standard numerical solvers designed for conservative forms. This work aims to thoroughly investigate the sensitivity of Physics-Informed Neural Networks (PINNs) to the choice of PDE formulation (conservative vs. non-conservative) when solving problems involving shocks and discontinuities. We have conducted this investigation across a range of benchmark problems, specifically the Burgers equation and both steady and unsteady Euler equations, to provide a comprehensive understanding of PINNs capabilities in this critical area.
| Comments: | Some mistakes in the claims |
| Subjects: | Fluid Dynamics (physics.flu-dyn); Numerical Analysis (math.NA) |
| MSC classes: | 35L65, 35Q70, 65M70, 76N15, 68T07 |
| Cite as: | arXiv:2506.22413 [physics.flu-dyn] |
| (or arXiv:2506.22413v3 [physics.flu-dyn] for this version) | |
| https://doi.org/10.48550/arXiv.2506.22413 arXiv-issued DOI via DataCite |
From: Arun Govind Neelan [view email]
[v1]
Fri, 27 Jun 2025 17:39:36 UTC (578 KB)
[v2]
Thu, 2 Apr 2026 12:08:05 UTC (1 KB) (withdrawn)
[v3]
Fri, 22 May 2026 14:35:45 UTC (1 KB) (withdrawn)
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