Error propagation dynamics of PIV-based pressure field calculation (3): what is the minimum resolvable pressure in a reconstructed field?

An analytical framework for the propagation of velocity errors into PIV-based pressure calculation is extended. Based on this framework, optimal spatial resolution and corresponding minimum field-wide error level in calculated field are determined. This can be viewed as smallest resolvable pressure. We find that a function flow features (patterns length scales), fundamental properties domain (e.g., geometry type boundary conditions), addition to PIV experiments, choice numerical methods. Making general statement about sensitivity difficult. The depends competing effects from experimental due truncation solver, which affected by formulation solver. means experiments motivated measurements should carefully designed so (or close resolution) used. Flows (and $$5\times 10^4$$ ) with exact solutions used examples validate theoretical predictions resolutions sensitivity. results agree well rigorous predictions. also propose posterior method estimate contribution using Richardson extrapolation adding artificially overwhelming noise. provide an introductory analysis interrogation window overlap context calculation.