On the joint estimation of flow fields and particle properties from Lagrangian data

A new data-assimilation framework can jointly reconstruct flow fields and unknown particle properties from Lagrangian particle tracking data, according to a numerical study posted to arXiv. The method couples an Eulerian flow representation with Lagrangian particle models to infer carrier-fluid states and particle characteristics simultaneously. The framework, developed by Samuel Grauer and colleagues, addresses a core limitation of Lagrangian particle tracking (LPT): experimental tracks are spatially sparse and often noisy, and inertial particles can slip relative to the carrier fluid, complicating flow-field reconstruction [1][2]. By embedding the governing equations of disperse multiphase flow into the assimilation procedure, the approach treats particle properties such as position, size, and density as unknowns to be estimated alongside the velocity, pressure, and density fields of the fluid [2]. The researchers tested the method across three distinct flow regimes. In a turbulent boundary layer seeded with tracer particles whose Stokes number approaches zero, the framework jointly estimated the flow field and true particle positions, effectively performing a physics-informed particle-tracking correction on noisy tracks [2]. In homogeneous isotropic turbulence with inertial particles at Stokes numbers between roughly one and five, the system recovered flow states and particle diameters simultaneously, demonstrating what the authors describe as implicit particle characterization [2]. In the third and most demanding case—a compressible, shock-dominated flow—the team reported the first joint reconstructions of velocity, pressure, density, and inertial-particle diameter and density in a supersonic regime. The results highlight both the potential and certain limits of joint estimation when shocks are present [2]. A systematic sensitivity study accompanying the work shows that seeding density, measurement noise level, and Stokes number are the primary factors governing reconstruction accuracy [2]. Numerical modeling of this kind draws on techniques developed across many fields. In geology, for instance, finite-difference methods are routinely used to approximate solutions to partial differential equations that describe fluid flow in the subsurface or the thermal evolution of rock masses [3]. The broader challenge of tracking discrete particles under mutual interactions has a long history in physics: the classical n-body problem, which asks how a group of gravitationally interacting bodies will move, is analytically solvable only for two bodies and becomes chaotic for three or more, requiring numerical integration [4]. The LPT assimilation framework extends this lineage by coupling a continuum Eulerian grid with discrete Lagrangian particle models, allowing the equations of motion to constrain the inference of both phases [2]. The work appears as a preprint on arXiv and has been revised through May 2026. It has not yet been reported in a peer-reviewed journal [1].