Document Type

Article

Author ORCID Identifier

Zhao Pan https://orcid.org/0000-0003-1654-3205

Journal/Book Title/Conference

Measurement Science and Technology

Volume

35

Issue

9

Publisher

Institute of Physics Publishing Ltd.

Publication Date

6-21-2024

Journal Article Version

Version of Record

First Page

1

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Last Page

24

Abstract

We analyze a smooth pressure solver based on the ‘modified Poisson equation’: ∇2p + ξ2 ∂2p/∂t2 = f(u(t)), where p is the pressure field, u(t) is the velocity field measured by time-resolved image velocimetry, and ξ2 is a tunable parameter to control the solver’s diffusive behaviour in time. This modified Poisson equation aims at obtaining smooth pressure fields from potentially noisy image velocimetry measurements, and is a part of the current four-dimensional (4D) pressure solver (implemented in, for example, DaVis 10.2) by LaVision. This work focuses on investigating three aspects of the ‘modified Poisson equation’: smoothing effect, error propagation, and drift in time. We first provide rigorous analysis and validate that this solver can sufficiently smooth the computed pressure field by setting a large enough ξ2. However, a large value of ξ2 may cause large errors in the reconstructed pressure fields. Then we introduce an upper bound on the error in the reconstructed pressure fields to quantify the error propagation dynamics. Finally, we discuss the potential drift due to the partitioning in time, which is an optional strategy used in LaVision’s current 4D pressure solver to reduce computational costs. Our analysis and validation not only show that careful choice of the parameters (e.g. ξ2) is needed for smooth and accurate pressure field reconstruction but provide theoretical guidelines for parameter tuning when similar pressure solvers are used for time-resolved image velocimetry data.

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