Research / Boundary-aware reconstruction

Boundary-aware reconstruction

Volumetric particle tracking gives scattered tracks that must be put on a grid before gradients can be computed. When a solid body sits in the measurement volume, standard methods treat everything as fluid and are weakest right next to the body, where it matters most.

Three panels: particles around a moving sphere, grid nodes classified as solid, shell or fluid, and the reconstructed flow — LE-DM in three steps: (a) scattered tracks around a moving body, (b) signed-distance classification of grid nodes into solid, boundary shell and fluid, (c) the reconstructed divergence-free field with the shell fixed to the body velocity. From Jose et al., Meas. Sci. Technol. (2026).

I developed LE-DM (Lagrangian-to-Eulerian reconstruction with Dynamic Masking). At every instant, a time-dependent signed-distance function sorts the grid into open fluid, boundary shell and solid interior. The particle data, incompressibility, the prescribed surface velocity and regularization are then solved together on the masked domain.

The method needs only the instantaneous surface geometry and velocity, so stationary walls and translating, rotating, multiple or deforming bodies fit the same formulation. It was tested on an analytical oscillating sphere, synthetic tracks from a CFD rising sphere, a freely rising prolate spheroid that tumbles strongly, and a refractive-index-matched tomographic PTV experiment.

Velocity slices around a tumbling spheroid, CFD on top and LE-DM below — Tumbling prolate spheroid: CFD reference (top) and LE-DM reconstruction (bottom) on three planes through the body. From Jose et al., Meas. Sci. Technol. (2026).

Velocity magnitude around a rising sphere from four reconstruction methods — Experiment on a freely rising sphere: velocity magnitude from four reconstruction methods, node classification, and the reconstructed surface speed against the measured sphere speed. From Jose et al., Meas. Sci. Technol. (2026).