[2607.18312] Vakonomic Fluids

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Mathematical Physics

arXiv:2607.18312 (math-ph)

[Submitted on 17 Jul 2026]

Title:Vakonomic Fluids

Authors:Ritoban Roy-Chowdhury, Mohammad Sina Nabizadeh, Oliver Gross, Anthony Gruber, Albert Chern<br>View a PDF of the paper titled Vakonomic Fluids, by Ritoban Roy-Chowdhury and 4 other authors

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Abstract:We introduce a novel discretization of the incompressible Euler equations based on their interpretation as geodesic equations on the Lie group of volume-preserving diffeomorphisms. It is well known that encoding diffeomorphisms and their infinitesimal generators through a discretized Koopman representation places a nonholonomic constraint on discrete velocities, for which there is no consensus on a variational treatment. We show that taking the vakonomic perspective, as opposed to the usual perspective of Lagrange--d'Alembert, yields discrete fluid trajectories that remain geodesics on a (sub-)Riemannian manifold. In particular, the resulting vakonomic dynamics are Lie--Poisson and their solutions admit a discrete relabeling symmetry, leading to machine-precision satisfaction of Casimir invariants along with a discrete analogue of Kelvin's Circulation Theorem. Using an efficient momentum map representation based on low-rank Clebsch variables, we show that these vakonomic fluids behave stably and consistently even at low grid resolutions, leading to increased robustness and physical realism in the long term.

Comments:<br>Roy-Chowdhury and Nabizadeh contributed equally; Chern and Gruber are co-corresponding/senior authors

Subjects:

Mathematical Physics (math-ph); Graphics (cs.GR); Differential Geometry (math.DG); Dynamical Systems (math.DS); Numerical Analysis (math.NA); Fluid Dynamics (physics.flu-dyn)

Cite as:<br>arXiv:2607.18312 [math-ph]

(or<br>arXiv:2607.18312v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2607.18312

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arXiv-issued DOI via DataCite

Submission history<br>From: Mohammad Sina Nabizadeh [view email]<br>[v1]<br>Fri, 17 Jul 2026 17:53:42 UTC (5,701 KB)

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