Structure-Preserving Flow Reconstruction from Particle Tracking Data
A Mimetic Spectral Element Approach with Application to Flow over a Surface-Mounted Cube
I. Benyahia (TU Delft - Aerospace Engineering)
M.I. Gerritsma – Mentor (TU Delft - Aerospace Engineering)
S. Shrestha – Mentor (TU Delft - Mechanical Engineering)
F. Scarano – Graduation committee member (TU Delft - Aerospace Engineering)
L.T. Lima Pereira – Graduation committee member (TU Delft - Aerospace Engineering)
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Abstract
Particle tracking velocimetry produces scattered velocity samples that must be reconstructed into continuous fields before quantities such as vorticity and pressure can be evaluated. Standard post-processing methods do not enforce mass conservation, and the resulting non-physical divergence contaminates derived quantities such as pressure.
This thesis develops a constrained least-squares reconstruction method based on mimetic spectral elements. The velocity is represented in H(div), the discrete divergence-free constraint is imposed exactly as a hard algebraic constraint in a saddle-point system, and the vorticity, streamfunction, and pressure are recovered through weak formulations using the same set of discrete differential operators.
The method is verified using a manufactured solution. The measured convergence rates under both p- and h-refinement match the theoretical predictions for all five reconstructed quantities. The method is then applied to three regions of separated flow over a surface-mounted cube using experimental particle tracking data. The reconstructed velocity is divergence-free to machine precision in all cases, while the streamfunction, vorticity, and pressure fields capture the boundary-layer separation, recirculation, and shear-layer features observed in the reference data.