Dynamic masking for boundary-aware velocity reconstruction in volumetric particle tracking with moving solids

Abstract

Volumetric particle tracking velocimetry (PTV) produces scattered Lagrangian tracks that must be reconstructed on an Eulerian grid before velocity gradients, pressure, or hydrodynamic loads can be evaluated. This step is usually performed on a domain treated as entirely fluid. When a solid body lies within the measurement volume, its surface kinematics are not imposed and the reconstruction is weakest in the steep-gradient region next to the body. We introduce LE-DM (Lagrangian-to-Eulerian reconstruction with Dynamic Masking), a constrained reconstruction framework for moving solid boundaries. A time-dependent signed-distance function classifies grid nodes as open fluid, boundary shell, or solid interior. The particle data, incompressibility constraint, prescribed surface velocity, and regularization terms are then assembled on the masked domain within a single solve. The method requires only a signed-distance field and a surface velocity, allowing stationary walls, translating, rotating, multiple, and deforming bodies to be represented in the same formulation. LE-DM is assessed using an analytical oscillating sphere, synthetic tracks from a CFD rising-sphere simulation, and a refractive-index-matched tomographic-PTV experiment on a freely rising sphere. The surface kinematics are enforced to solver tolerance, while the bulk reconstruction remains unchanged where no body is present. In the analytical case, the first-cell error is reduced from 14\% to 3\% of the body speed. In the experiment, LE-DM recovers the independently measured surface velocity, whereas an all-fluid reconstruction does not. The result is a divergence-free, boundary-consistent velocity field for pressure and force estimation.