Itô tracers: continuous-trajectory Lagrangian particles for Eulerian hydrodynamics

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ID: 326320
2026
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Abstract
Abstract Lagrangian tracer particles have long been used to track the history of individual gas parcels in hydrodynamical codes. Particles advected by the cell-centered velocity carry no representation of underlying numerical diffusion, and thus exhibit systematic bias. The Monte-Carlo (MC) tracer resolves this with discrete probabilistic cell-to-cell, flux-based jumps, at the cost of trajectories that are discontinuous in time. We introduce the Itô tracer, a continuous-time Lagrangian particle with moments matched to the advection, diffusion, and dispersion of the gas. A subgrid-scale variant (SGS-Itô) replaces the numerical diffusion with a Smagorinsky–Lilly turbulent diffusivity, illustrating that the form of the diffusion matters less than its magnitude. We validate these methods with a 1D square-pulse advection test and 3D decaying turbulence at σrms = 15 cs. We compare the different tracer particle methods using several statistical tests. Itô tracers largely reproduce or improve upon MC tracers statistics across column-density maps, joint density histograms, log-density-ratio PDFs, and density power spectra. In the turbulence test, Itô tracers improve the correlation between tracers and gas over the MC tracers by >3 %, and reduce the width of the log-density ratio PDF by nearly 50 %. Relative to classical tracers, these improvements are ≳30 % and 230 %, respectively. Because Itô tracers follow a stochastic differential equation, the method maps onto other continuous-trajectory Lagrangian processes (e.g. dust grains, charged particles, cosmic rays), admits variance-reduction techniques, higher-order integrators, and GPU-friendly implementations – all of which are unavailable to discrete-jump schemes.
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Authors Eric R Moseley, R. Teyssier, Tom Abel
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Journal monthly notices of the royal astronomical society
Year 2026
DOI
10.1093/mnras/stag1536
URL
https://doi.org/10.1093/mnras/stag1536
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