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Crosslisted article(s) found for physics.comp-ph. https://arxiv.org/list/physics.comp-ph/new
[1/1]:
- A High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for the Boltzmann Equati...
Atakan Aygun, Onur Ata, Tim Warburton, Ali Karakus
https://arxiv.org/abs/2607.00199 https://mastoxiv.page/@arXiv_physicsfludyn_bot/116849258941218034
- A Multi-Resolution Finite-Volume Inspired Deep Learning Framework for Spatiotemporal Dynamics Pre...
Xin-Yang Liu, Xiantao Fan, Jian-Xun Wang
https://arxiv.org/abs/2607.00460 https://mastoxiv.page/@arXiv_csCE_bot/116849212144848429
- When is vaccine prioritization worth optimizing?
Mi Feng, Zhaohua Lin, Changsong Zhou, Liang Tian
https://arxiv.org/abs/2607.00484 https://mastoxiv.page/@arXiv_physicsbioph_bot/116849279781216938
- A Nonstandard Finite Difference Scheme for a Nonlinear Parabolic Equation with p-Laplacian-Type D...
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
https://arxiv.org/abs/2607.00489 https://mastoxiv.page/@arXiv_mathNA_bot/116849363932310131
- The BiP-PRISM algorithm for fast and scalable core-loss STEM-EELS simulations
Philipp Pelz
https://arxiv.org/abs/2607.00756 https://mastoxiv.page/@arXiv_condmatmtrlsci_bot/116849366488683473
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Crosslisted article(s) found for physics.comp-ph. https://arxiv.org/list/physics.comp-ph/new
[1/1]:
- A High-Order Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for the Boltzmann Equati...
Atakan Aygun, Onur Ata, Tim Warburton, Ali Karakus

If you want to feel bad about everything you've accomplished in life, compare yourself to Euler

Self-focusing of helicity drives finite-time singularities in inviscid flows
Mokhtar Adda-Bedia, Sergio Rica
https://arxiv.org/abs/2605.17569 https://arxiv.org/pdf/2605.17569 https://arxiv.org/html/2605.17569
arXiv:2605.17569v1 Announce Type: new
Abstract: This paper deals with the longstanding quest of the possible existence of finite-time singularities in the equations governing the dynamics of inviscid fluids, namely, Euler equations. Here, two contributions are brought for the case of perfect fluids with finite initial energy. First, a self-similar velocity field inspired by Leray Ansatz is proposed which allows for a separation of variables that transforms the original partial differential Euler equations to a nonlinear system of ordinary differential equations. This system can be solved semi-analytically and allows a continuum set of solutions parametrised by a self-similar exponent, $\nu$. Second, we use the conservation laws of Euler equations to select the possible finite-time singular solutions and the related self-similar exponents. We find that the helicity is the driving mechanism of the blow-up through a self-focusing mechanism. The flow near the singularity separates into two phases. A first phase is within a tubular region that shrinks as a power-law $(t_c-t)^\nu$, with $t_c$ the blow-up time, where the helicity is focused. This region is separated by a sharp interface from an outer region where the vorticity, and thus helicity, is identically zero. We found that the finite-time singularity may be either point-like or line-like depending on the dynamics of the tubular region along its axis of symmetry. Incidentally for a point-like singularity we recover the Leray scaling $\nu=1/2$ paving the way to a generalisation of this approach for the Navier-Stokes equations. Finally, we conjecture that if the helicity vanishes initially, no finite-time singularity would be possible, since in this case the singularity occurs at infinite time from the initial condition.
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Mapping the Turn: An Eulerian Binormal-Axis Diagnostic for Recirculating 3D Flows
John Marshall Cooper, Wen Wu
https://arxiv.org/abs/2605.18439 https://arxiv.org/pdf/2605.18439 https://arxiv.org/html/2605.18439
arXiv:2605.18439v1 Announce Type: new
Abstract: Three-dimensional (3D) recirculating flows are often interpreted qualitatively from selected streamline visualizations. In separated flows, such recirculating motion is central to the drag modulation, but the local orientation of recirculation remains difficult to quantify in a field-based form. This work introduces an Eulerian binormal-axis diagnostic that locally evaluates the orientation of streamline turning at each point in the velocity field, yielding a spatially resolved field of the recirculating direction. Motivated by the Frenet-Serret binormal direction of a curved streamline, the diagnostic uses the velocity vector and its convective acceleration to extract the local streamline-turning axis without requiring explicit streamline integration. The resulting direction is encoded with barycentric RGB weights to visualize streamwise, spanwise, and wall-normal turning axis contributions. The diagnostic is first applied to Hill's spherical vortex, which provides a controlled analytic example of 3D recirculating motion for interpreting the binormal-axis direction and the associated barycentric RGB encoding. It is then applied to the mean field of a pressure-gradient-induced 3D separation bubble. The resulting visualizations show that the diagnostic reveals orientation changes that are not apparent from streamline visualization. The proposed diagnostic therefore converts qualitative streamline impressions into a spatially resolved measure of local streamline-turning orientation, providing a quantitative complement to conventional 3D flow visualization.
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High-Order ADER-DG Hydrodynamics with ExaHyPE: Implementation, Validation, and Astrophysical Benchmarking
Andr\'es Mauricio Su\'arez Mantilla, Leonardo Casta\~neda Colorado
https://arxiv.org/abs/2605.17132 https://arxiv.org/pdf/2605.17132 https://arxiv.org/html/2605.17132
arXiv:2605.17132v1 Announce Type: new
Abstract: We describe a high-order ADER-DG solver for the compressible Euler equations within the ExaHyPE framework. The implementation combines a high-order ADER-DG polynomial representation, a local space-time DG predictor, adaptive mesh refinement, and an a posteriori subcell finite-volume limiter. We test the code on a deliberately mixed set of one- and two-dimensional problems: a strong-shock Sod-type problem, the Shu-Osher shock-entropy interaction, the Woodward-Colella blast wave, a contact-driven vortex sheet, and a shock-interface interaction. The one-dimensional cases recover the expected Euler wave patterns and show clear order-dependent gains in smooth and oscillatory regions. The two-dimensional cases probe a different part of the method, namely contact preservation, shear-driven roll-up, baroclinic vorticity deposition, and Richtmyer-Meshkov-type growth. In these tests the high-order update gives the expected resolution away from discontinuities, whereas the subcell limiter keeps the calculation stable near shocks and steep interfaces. The resulting code provides a reproducible ExaHyPE implementation for idealised inviscid, non-relativistic flows in which shocks, contacts, and multidimensional interfaces are the dominant features.
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A Measure-Theoretic Approach to Spontaneous Stochasticity
Wandrille Ruffenach, Eric Simonnet, Nicolas Valade
https://arxiv.org/abs/2607.16328 https://arxiv.org/pdf/2607.16328 https://arxiv.org/html/2607.16328
arXiv:2607.16328v1 Announce Type: new
Abstract: Spontaneous stochasticity (SpSt), originating in Richardson's picture of turbulent dispersion and Lorenz's Eulerian view of finite-time loss of predictability, was later formulated under this name by Gaw\k{e}dzki and collaborators and developed in shell models by Mailybaev and collaborators. Whether it occurs in fully developed turbulence remains a major open question.
Beyond a few specific classes of systems, however, SpSt has lacked a general mathematical definition. We introduce a measure-theoretic formalism in which it is understood as a measure-selection principle. Given an inviscid problem, a well-posed regularization, and an ambient measure, we study the pushforward of that measure by the regularized flow. Strong SpSt occurs when these pushforward measures converge to a non-Dirac probability law, replacing classical deterministic selection by statistical selection.
For finite-dimensional systems, we establish several structural results. Our central attainability theorem shows that, whenever the inviscid problem is nonunique, any probability measure supported on the set of inviscid states can be selected as the limiting law of a suitable regularization. We also identify singular sets in the inviscid dynamics, detected through Dini-type directional growth, as necessary obstructions underlying nonuniqueness. We analyze the relation between SpSt and sensitivity to initial data, clarifying the scope and limitations of turbulence-inspired finite-time separation criteria. Finally, we develop a renormalization-(semi)group viewpoint in which limiting statistics arise as statistical attractors. Explicit examples illustrate how ambient measures, inviscid singularities, regularization scales, and initial-data sensitivity interact in the emergence of SpSt.
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Hard Guarantees at a Measured Price: Entropy-Stable Learned Finite Volumes for Compressible Flow
Denis Gueyffier (ONERA -- Institut Polytechnique de Paris)
https://arxiv.org/abs/2607.20171 https://arxiv.org/pdf/2607.20171 https://arxiv.org/html/2607.20171
arXiv:2607.20171v1 Announce Type: new
Abstract: Learned solvers for compressible flow are usually compared to classical methods at equal mesh resolution rather than at equal computational cost, and they typically offer no guarantee that their solutions remain physically admissible. We present a learned finite volume scheme for the two-dimensional Euler equations on unstructured meshes, admissible by construction and with an entropy-stable interior flux. We evaluate it under protocols fixed before any computation: frozen thresholds, falsification clauses, negative controls, a factor decomposition of the learned components, and an iso-cost comparison against the refined classical baseline. The decomposition produced the central result: the guarantee machinery alone, with both learned heads switched off (the unlearned skeleton), is the strongest scheme at equal mesh on every periodic case. At equal wall-clock cost the picture inverts into a map. Learning pays robustly only on the wall case whose boundary-condition type it never saw (10.8%). Its periodic gains flip sign with the evaluation draw ( 10% on one held-out case, -12% on the hardest). The skeleton is the only method whose iso-cost gain never changes sign, at a measured overhead of 1.74x per step. The guaranteed variant completes 36 of 36 rollouts, Mach extrapolation and unseen wall included, with zero negativity events. We fix the guaranteed scheme's one remaining out-of-distribution weakness, Mach extrapolation, at inference time: with scale-invariant network inputs, a specific-entropy floor, and no retraining, the corrected arm overtakes the unconstrained arm on one Mach case, cuts its deficit on the other by a third, passes the skeleton on the unseen wall, and keeps the guarantee. A spatial gate closes the loop: activating the heads only near the walls beats both the skeleton and the corrected arm, and transfers unchanged to a second wall geometry.
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