Flow measurement: an inverse problem formulation. (English) Zbl 1522.35589
Summary: This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we formulate an inverse source problem that can recover the flow field from the observation data on boundary receivers. To our knowledge, this is the first mathematical model of flow measurement using partial differential equations. This model is proved well-posed, and the corresponding algorithm is derived to compute the velocity field efficiently. Extensive numerical simulations are performed to demonstrate the accuracy and robustness of our model. The comparison results demonstrate that our model is ten times more accurate than ADCP. Our formulation is capable of simulating a variety of practical measurement scenarios.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
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