A Simple Boundary Condition Regularization Strategy for Image-Velocimetry Based Pressure Field Reconstruction

We propose a very simple and low computational cost boundary condition regularization strategy to suppress error propagation in pressure field reconstruction from corrupted image velocimetry data (e.g., Particle Image Velocimetry or Lagrangian Particle Tracking). The key idea is to replace the canonical Neumann boundary conditions with derived Dirichlet ones obtained by integrating the tangential part of the pressure gradient along the boundaries. Rigorous analysis and numerical experiments justify the effectiveness of this technique and provide an estimate for when practicing this regularization is beneficial. Despite only showcasing a straightforward, yet long-overlooked, idea in the current work, this technique inspires a new family of boundary regularization strategies. The high flexibility of these strategies can be easily extended and adopted as an "add-on" to many other data assimilation, regularization, and machine-learning techniques for flow reconstruction.