Itô tracers: continuous-trajectory Lagrangian particles for Eulerian hydrodynamics

Le résumé fourni par la source

ABSTRACT Lagrangian tracer particles have long been used to track the history of individual gas parcels in hydrodynamical codes. Particles advected by the cell-centred 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 $\sigma _{\rm rms} = 15\, c_{\rm s}$. 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 (probability density functions), and density power spectra. In the turbulence test, Itô tracers improve the correlation between tracers and gas over the MC tracers by >3 per cent, and reduce the width of the log-density ratio PDF by nearly 50 per cent. Relative to classical tracers, these improvements are $\gtrsim$30 per cent and 230 per cent, respectively. Because Itô tracers follow a stochastic differential equation, the method maps onto other continuous-trajectory Lagrangian processes (e.g. dust grains, charged particles, and cosmic rays), admits variance-reduction techniques, higher order integrators, and Graphics-Processing-Unit-friendly implementations – all of which are unavailable to discrete-jump schemes.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.